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CN114923623B - Dynamic compensation method of silicon resonance pressure sensor - Google Patents

Dynamic compensation method of silicon resonance pressure sensor Download PDF

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CN114923623B
CN114923623B CN202210851389.5A CN202210851389A CN114923623B CN 114923623 B CN114923623 B CN 114923623B CN 202210851389 A CN202210851389 A CN 202210851389A CN 114923623 B CN114923623 B CN 114923623B
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pressure
temperature
frequency
calibration point
static
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CN114923623A (en
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杨劼立
胡宗达
王思翔
李奇思
苏晓晓
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Chengdu CAIC Electronics Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L19/00—Details of, or accessories for, apparatus for measuring steady or quasi-steady pressure of a fluent medium insofar as such details or accessories are not special to particular types of pressure gauges
    • G01L19/04—Means for compensating for effects of changes of temperature, i.e. other than electric compensation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01L27/005—Apparatus for calibrating pressure sensors

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Abstract

本发明公开了一种硅谐振压力传感器的动态补偿方法，本发明通过静态标定找到压力频率和温度频率与静态压力数据之间的静态标定参数，再通过动态标定，得到动态温度频率和动态压力频率；再通过样本标签与动态温度频率对时间序列预测模型进行训练，找到样本标签与动态温度频率间的对应参数关系，从而计算出校准温度频率，通过校准温度频率和静态标定参数去计算压力，作为硅谐振压力传感器的动态补偿后的压力，以解决硅谐振压力传感器压力值不准确的问题。

Figure 202210851389

The invention discloses a dynamic compensation method for a silicon resonant pressure sensor. The invention finds the static calibration parameters between the pressure frequency and temperature frequency and static pressure data through static calibration, and then obtains the dynamic temperature frequency and dynamic pressure frequency through dynamic calibration. ; Then train the time series prediction model through the sample label and the dynamic temperature frequency, find the corresponding parameter relationship between the sample label and the dynamic temperature frequency, thereby calculate the calibration temperature frequency, calculate the pressure by calibrating the temperature frequency and static calibration parameters, as The pressure after dynamic compensation of the silicon resonant pressure sensor is used to solve the problem of inaccurate pressure value of the silicon resonant pressure sensor.

Figure 202210851389

Description

一种硅谐振压力传感器的动态补偿方法A Dynamic Compensation Method for Silicon Resonant Pressure Sensor

技术领域technical field

本发明涉及压力传感器的压力补偿方法，具体涉及一种硅谐振压力传感器的动态补偿方法。The invention relates to a pressure compensation method of a pressure sensor, in particular to a dynamic compensation method of a silicon resonant pressure sensor.

背景技术Background technique

高精度硅谐振压力传感器是飞行器大气数据系统核心压力传感器，它将外界感知的压力信号转化为数字信号，经过大气数据计算机的解算，传递给飞行器的飞控系统，作为重要的控制信号，因此硅谐振压力传感器的性能指标直接影响着飞行器的安全。硅谐振压力传感器的压力频率不仅取决于被测环境的工作压力，还受到周围环境温度的影响，其需要将感受到的外界压力和温度转化为两路电信号，通过后端驱动检测和拟合公式计算得到准确的压力值。目前大多数硅谐振压力传感器通过在管壳内外接温度二极管，在不同温度下采集二极管的输出信号来表征硅谐振MEMS芯片的工作温度。但是，由于温度二极管与硅谐振MEMS芯片存在空间差异，导致温度二极管无法实时反映硅谐振MEMS芯片的工作温度，从而使得硅谐振压力传感器存在温度跟随性问题，进一步导致拟合得到的压力值不精确。The high-precision silicon resonant pressure sensor is the core pressure sensor of the aircraft air data system. It converts the pressure signal perceived by the outside world into a digital signal. The performance index of the silicon resonant pressure sensor directly affects the safety of the aircraft. The pressure frequency of the silicon resonant pressure sensor not only depends on the working pressure of the measured environment, but also is affected by the ambient temperature. It needs to convert the sensed external pressure and temperature into two electrical signals, which are detected and fitted by the back-end drive The formula calculates the accurate pressure value. At present, most silicon resonant pressure sensors characterize the working temperature of silicon resonant MEMS chips by connecting temperature diodes inside and outside the tube shell, and collecting the output signals of the diodes at different temperatures. However, due to the spatial difference between the temperature diode and the silicon resonant MEMS chip, the temperature diode cannot reflect the working temperature of the silicon resonant MEMS chip in real time, which makes the silicon resonant pressure sensor have temperature following problems, which further leads to inaccurate pressure values obtained by fitting. .

发明内容Contents of the invention

针对现有技术中的上述不足，本发明提供的一种硅谐振压力传感器的动态补偿方法解决了现有硅谐振压力传感器在管壳内外接温度二极管，但温度二极管与硅谐振MEMS芯片存在空间差异，无法实时反映硅谐振MEMS芯片的工作温度，导致硅谐振压力传感器压力值不准确的问题。In view of the above-mentioned deficiencies in the prior art, a dynamic compensation method for a silicon resonant pressure sensor provided by the present invention solves the problem that the existing silicon resonant pressure sensor is connected with a temperature diode inside and outside the tube shell, but there is a spatial difference between the temperature diode and the silicon resonant MEMS chip , the working temperature of the silicon resonant MEMS chip cannot be reflected in real time, resulting in the inaccurate pressure value of the silicon resonant pressure sensor.

为了达到上述发明目的，本发明采用的技术方案为：一种硅谐振压力传感器的动态补偿方法，包括以下步骤：In order to achieve the purpose of the above invention, the technical solution adopted in the present invention is: a dynamic compensation method for a silicon resonant pressure sensor, comprising the following steps:

S1、对硅谐振压力传感器进行静态标定，得到静态标定参数、平均温度频率和标准化后的压力频率；S1. Perform static calibration on the silicon resonant pressure sensor to obtain static calibration parameters, average temperature frequency and standardized pressure frequency;

S2、对硅谐振压力传感器进行动态标定，得到动态温度频率和动态压力频率；S2. Perform dynamic calibration on the silicon resonant pressure sensor to obtain dynamic temperature frequency and dynamic pressure frequency;

S3、根据静态标定的平均温度频率、标准化后的压力频率和动态标定的动态压力频率，构建样本标签；S3. Construct a sample label according to the statically calibrated average temperature frequency, the standardized pressure frequency, and the dynamically calibrated dynamic pressure frequency;

S4、采用样本标签和动态标定的动态温度频率对时间序列预测模型进行训练，得到训练完成的时间序列预测模型；S4. Using the sample label and the dynamically calibrated dynamic temperature frequency to train the time series prediction model to obtain the trained time series prediction model;

S5、采用训练完成的时间序列预测模型计算校准温度频率；S5. Calculating the calibration temperature frequency using the trained time series prediction model;

S6、根据校准温度频率、静态标定参数和标准化后的压力频率，计算硅谐振压力传感器的动态补偿后的压力。S6. Calculate the dynamically compensated pressure of the silicon resonant pressure sensor according to the calibrated temperature frequency, the static calibration parameter and the standardized pressure frequency.

进一步地，所述步骤S1包括以下分步骤：Further, the step S1 includes the following sub-steps:

S11、在硅谐振压力传感器的全温范围内，选取多个温度标定点；S11. Select multiple temperature calibration points within the full temperature range of the silicon resonant pressure sensor;

S12、在硅谐振压力传感器的全压范围内，选取多个压力标定点；S12. Select multiple pressure calibration points within the full pressure range of the silicon resonant pressure sensor;

S13、在压力标定点和温度标定点下采集硅谐振压力传感器的静态四路温度频率、静态压力频率和静态压力数据；S13. Collect static four-way temperature frequency, static pressure frequency and static pressure data of the silicon resonant pressure sensor at the pressure calibration point and temperature calibration point;

S14、对静态四路温度频率取均值，得到平均温度频率；S14. Taking the average value of the static four temperature frequencies to obtain the average temperature frequency;

S15、对平均温度频率和静态压力频率进行标准化处理，得到标准化后的温度频率和压力频率；S15. Standardize the average temperature frequency and static pressure frequency to obtain standardized temperature frequency and pressure frequency;

S16、根据标准化后的温度频率、标准化后的压力频率和静态压力数据，构建第一压力温度模型；S16. Construct a first pressure-temperature model according to the normalized temperature frequency, the normalized pressure frequency, and the static pressure data;

S17、采用最小二乘法对第一压力温度模型进行求解，得到静态标定参数。S17. Solving the first pressure-temperature model by using the least squares method to obtain static calibration parameters.

进一步地，所述步骤S14中平均温度频率的计算公式为：Further, the calculation formula of the average temperature frequency in the step S14 is:

Figure 10601DEST_PATH_IMAGE001
Figure 10601DEST_PATH_IMAGE001

其中，

Figure 253364DEST_PATH_IMAGE002
为第
Figure 649710DEST_PATH_IMAGE003
个温度标定点下第
Figure 336038DEST_PATH_IMAGE004
个压力标定点的平均温度频率，
Figure 450624DEST_PATH_IMAGE005
为第
Figure 231498DEST_PATH_IMAGE006
个温度标定点下第
Figure 747930DEST_PATH_IMAGE008
个压力标定点的静态第一路温度频率，
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为第
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个温度标定点下第
Figure 729290DEST_PATH_IMAGE011
个压力标定点的静态第二路温度频率，
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为第
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个温度标定点下第
Figure 951958DEST_PATH_IMAGE014
个压力标定点的静态第三路温度频率，
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为第
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个温度标定点下第
Figure 951641DEST_PATH_IMAGE016
个压力标定点的静态第四路温度频率。in,
Figure 253364DEST_PATH_IMAGE002
for the first
Figure 649710DEST_PATH_IMAGE003
temperature calibration point
Figure 336038DEST_PATH_IMAGE004
The average temperature frequency of a pressure calibration point,
Figure 450624DEST_PATH_IMAGE005
for the first
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temperature calibration point
Figure 747930DEST_PATH_IMAGE008
The static first channel temperature frequency of a pressure calibration point,
Figure 339580DEST_PATH_IMAGE009
for the first
Figure 144725DEST_PATH_IMAGE010
temperature calibration point
Figure 729290DEST_PATH_IMAGE011
The static second channel temperature frequency of a pressure calibration point,
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for the first
Figure 112047DEST_PATH_IMAGE013
temperature calibration point
Figure 951958DEST_PATH_IMAGE014
The static temperature frequency of the third pressure calibration point,
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for the first
Figure 565659DEST_PATH_IMAGE013
temperature calibration point
Figure 951641DEST_PATH_IMAGE016
The static fourth channel temperature frequency of a pressure calibration point.

进一步地，所述步骤S15中标准化后的温度频率的计算公式为：Further, the calculation formula of the normalized temperature frequency in the step S15 is:

Figure 528116DEST_PATH_IMAGE017
Figure 528116DEST_PATH_IMAGE017

其中，

Figure 202286DEST_PATH_IMAGE018
为第
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个温度标定点下第
Figure 901438DEST_PATH_IMAGE004
个压力标定点所对应的标准化后的温度频率，
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为第
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个温度标定点下第
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个压力标定点的平均温度频率，
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为
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个平均温度频率
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的均值，
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为
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个平均温度频率
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的标准差，
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为温度标定点或压力标定点的数量；in,
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for the first
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temperature calibration point
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The normalized temperature frequency corresponding to a pressure calibration point,
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for the first
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temperature calibration point
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The average temperature frequency of a pressure calibration point,
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for
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average temperature frequency
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the mean value of
Figure 998335DEST_PATH_IMAGE023
for
Figure 959338DEST_PATH_IMAGE021
average temperature frequency
Figure 466542DEST_PATH_IMAGE024
standard deviation of
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is the number of temperature calibration points or pressure calibration points;

所述步骤S15中标准化后的压力频率的计算公式为：The calculation formula of the normalized pressure frequency in the step S15 is:

Figure 463765DEST_PATH_IMAGE026
Figure 463765DEST_PATH_IMAGE026

其中，

Figure 330090DEST_PATH_IMAGE027
为第
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个温度标定点下第
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个压力标定点所对应的标准化后的压力频率，
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为第
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个温度标定点下第
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个压力标定点的静态压力频率，
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为
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个静态压力频率
Figure 210660DEST_PATH_IMAGE031
的均值，
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为
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个静态压力频率
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的标准差。in,
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for the first
Figure 793433DEST_PATH_IMAGE003
temperature calibration point
Figure 403405DEST_PATH_IMAGE004
The normalized pressure frequency corresponding to a pressure calibration point,
Figure 432541DEST_PATH_IMAGE028
for the first
Figure 489009DEST_PATH_IMAGE003
temperature calibration point
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The static pressure frequency of a pressure calibration point,
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for
Figure 533691DEST_PATH_IMAGE030
static pressure frequency
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the mean value of
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for
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static pressure frequency
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standard deviation of .

进一步地，所述步骤S16中第一压力温度模型为：Further, the first pressure-temperature model in the step S16 is:

Figure 530597DEST_PATH_IMAGE035
Figure 530597DEST_PATH_IMAGE035

其中，

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为第
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个温度标定点下第
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个压力标定点的静态压力数据，
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为第
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个温度标定点下第
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个压力标定点所对应的标准化后的压力频率，
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为第
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个温度标定点下第
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个压力标定点所对应的标准化后的温度频率，
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和
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均为计数小标，
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为第
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个静态标定参数。in,
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for the first
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temperature calibration point
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Static pressure data of pressure calibration points,
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for the first
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temperature calibration point
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The normalized pressure frequency corresponding to a pressure calibration point,
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for the first
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temperature calibration point
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The normalized temperature frequency corresponding to a pressure calibration point,
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and
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Both are counting subscripts,
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for the first
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a static calibration parameter.

进一步地，所述步骤S2具体为：在随机变化的温度条件下，采集多个压力标定点下连续多次的硅谐振压力传感器的动态温度频率和动态压力频率。Further, the step S2 specifically includes: under a randomly changing temperature condition, collecting the dynamic temperature frequency and dynamic pressure frequency of the silicon resonant pressure sensor for multiple consecutive times at multiple pressure calibration points.

进一步地，所述步骤S3包括以下分步骤：Further, the step S3 includes the following sub-steps:

S31、根据静态标定过程中的标准化后的压力频率和平均温度频率，构建第二温度压力模型；S31. Construct a second temperature and pressure model according to the standardized pressure frequency and average temperature frequency in the static calibration process;

S32、采用最小二乘法对第二温度压力模型进行求解，得到温度压力系数；S32. Using the least square method to solve the second temperature and pressure model to obtain the temperature and pressure coefficient;

S33、根据温度压力系数和动态标定的动态压力频率，得到样本标签。S33. Obtain a sample label according to the temperature-pressure coefficient and the dynamically calibrated dynamic pressure frequency.

进一步地，所述步骤S32中第二温度压力模型为：Further, the second temperature and pressure model in the step S32 is:

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Figure 346030DEST_PATH_IMAGE043

其中，

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为第
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个温度标定点下第
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个压力标定点的平均温度频率，
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为第
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个温度标定点下第
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个压力标定点所对应的标准化后的压力频率，
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、
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和
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为温度压力系数；in,
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for the first
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temperature calibration point
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The average temperature frequency of a pressure calibration point,
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for the first
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temperature calibration point
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The normalized pressure frequency corresponding to a pressure calibration point,
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,
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and
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is the temperature pressure coefficient;

所述步骤S33中样本标签公式为：The sample label formula in the step S33 is:

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Figure 357159DEST_PATH_IMAGE049

其中，

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为第
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个压力标定点下第
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次采集所对应的样本标签，
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、
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和
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为温度压力系数，
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为第
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个压力标定点下第
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次采集的硅谐振压力传感器的动态压力频率。in,
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for the first
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pressure calibration point
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The sample label corresponding to the second collection,
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,
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and
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is the temperature pressure coefficient,
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for the first
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pressure calibration point
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The dynamic pressure frequency of the silicon resonant pressure sensor acquired for the second time.

进一步地，所述步骤S4包括以下分步骤：Further, the step S4 includes the following sub-steps:

S41、构建时间序列预测模型，得到样本标签

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的预测值
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：S41. Construct a time series prediction model and obtain sample labels
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predicted value of
Figure 594303DEST_PATH_IMAGE057
:

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Figure 777023DEST_PATH_IMAGE058
Figure 556760DEST_PATH_IMAGE059

其中，

Figure 483128DEST_PATH_IMAGE057
为样本标签
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的预测值，
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为时间序列预测模型找到参数间对应关系的函数，其函数括号内的参数为第
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个压力标定点下多次采集的动态温度频率，
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为第
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路第
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个压力标定点下第
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次采集的动态温度频率，
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为第
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路第
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个压力标定点下第
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次采集的动态温度频率，
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为第
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路第
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个压力标定点下第
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次采集的动态温度频率，
Figure 697629DEST_PATH_IMAGE071
；in,
Figure 483128DEST_PATH_IMAGE057
Label the sample
Figure 313812DEST_PATH_IMAGE056
predicted value of
Figure 198591DEST_PATH_IMAGE060
It is a function to find the corresponding relationship between parameters for the time series forecasting model, and the parameters in the function brackets are the first
Figure 996783DEST_PATH_IMAGE061
The dynamic temperature frequency collected multiple times under a pressure calibration point,
Figure 461262DEST_PATH_IMAGE062
for the first
Figure 864562DEST_PATH_IMAGE063
roadside
Figure 405396DEST_PATH_IMAGE065
pressure calibration point
Figure 425304DEST_PATH_IMAGE066
The dynamic temperature frequency of the second acquisition,
Figure 224633DEST_PATH_IMAGE067
for the first
Figure 279177DEST_PATH_IMAGE063
roadside
Figure 722403DEST_PATH_IMAGE065
pressure calibration point
Figure 495187DEST_PATH_IMAGE068
The dynamic temperature frequency of the second acquisition,
Figure 770310DEST_PATH_IMAGE069
for the first
Figure 679361DEST_PATH_IMAGE063
roadside
Figure 811265DEST_PATH_IMAGE065
pressure calibration point
Figure 822077DEST_PATH_IMAGE070
The dynamic temperature frequency of the second acquisition,
Figure 697629DEST_PATH_IMAGE071
;

S42、构建代价函数，度量预测值

Figure 726765DEST_PATH_IMAGE072
与样本标签
Figure 763991DEST_PATH_IMAGE073
差值，其中，代价函数为：S42. Construct a cost function and measure the predicted value
Figure 726765DEST_PATH_IMAGE072
with sample tags
Figure 763991DEST_PATH_IMAGE073
difference, where the cost function is:

Figure 714630DEST_PATH_IMAGE074
Figure 714630DEST_PATH_IMAGE074

其中，

Figure 879026DEST_PATH_IMAGE075
为代价函数，
Figure 28248DEST_PATH_IMAGE076
为L2范数；in,
Figure 879026DEST_PATH_IMAGE075
as the cost function,
Figure 28248DEST_PATH_IMAGE076
is the L2 norm;

S43、将样本标签

Figure 236375DEST_PATH_IMAGE073
和动态温度频率输入时间序列预测模型，使得预测值
Figure 205468DEST_PATH_IMAGE077
与样本标签
Figure 173555DEST_PATH_IMAGE073
差值最小，得到训练完成的时间序列预测模型。S43, label the sample
Figure 236375DEST_PATH_IMAGE073
and dynamic temperature frequency input time series forecasting model, making the predicted value
Figure 205468DEST_PATH_IMAGE077
with sample tags
Figure 173555DEST_PATH_IMAGE073
The difference is the smallest, and the trained time series forecasting model is obtained.

进一步地，所述步骤S6中计算硅谐振压力传感器的动态补偿后的压力的公式为：Further, the formula for calculating the dynamically compensated pressure of the silicon resonant pressure sensor in the step S6 is:

Figure 911704DEST_PATH_IMAGE078
Figure 911704DEST_PATH_IMAGE078

其中，

Figure 759574DEST_PATH_IMAGE079
为硅谐振压力传感器的动态补偿后的压力，
Figure 215963DEST_PATH_IMAGE080
为校准温度频率，
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为第
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个温度标定点下第
Figure 114485DEST_PATH_IMAGE004
个压力标定点所对应的标准化后的压力频率，
Figure 195573DEST_PATH_IMAGE039
和
Figure 873679DEST_PATH_IMAGE040
均为计数小标，
Figure 183569DEST_PATH_IMAGE041
为第
Figure 99573DEST_PATH_IMAGE042
个静态标定参数。in,
Figure 759574DEST_PATH_IMAGE079
is the dynamically compensated pressure of the silicon resonant pressure sensor,
Figure 215963DEST_PATH_IMAGE080
To calibrate the temperature frequency,
Figure DEST_PATH_IMAGE081
for the first
Figure 256250DEST_PATH_IMAGE003
temperature calibration point
Figure 114485DEST_PATH_IMAGE004
The normalized pressure frequency corresponding to a pressure calibration point,
Figure 195573DEST_PATH_IMAGE039
and
Figure 873679DEST_PATH_IMAGE040
Both are counting subscripts,
Figure 183569DEST_PATH_IMAGE041
for the first
Figure 99573DEST_PATH_IMAGE042
a static calibration parameter.

综上，本发明的有益效果为：本发明通过静态标定找到压力频率和温度频率与静态压力数据之间的静态标定参数，再通过动态标定，得到动态温度频率和动态压力频率；再通过样本标签与动态温度频率对时间序列预测模型进行训练，找到样本标签与动态温度频率间的对应参数关系，从而计算出校准温度频率，通过校准温度频率和静态标定参数去计算压力，作为硅谐振压力传感器的动态补偿后的压力，以解决硅谐振压力传感器压力值不准确的问题。In summary, the beneficial effects of the present invention are: the present invention finds the static calibration parameters between the pressure frequency and temperature frequency and the static pressure data through static calibration, and then obtains the dynamic temperature frequency and dynamic pressure frequency through dynamic calibration; Train the time series prediction model with the dynamic temperature frequency, find the corresponding parameter relationship between the sample label and the dynamic temperature frequency, thereby calculate the calibration temperature frequency, and calculate the pressure by calibrating the temperature frequency and static calibration parameters, as the silicon resonant pressure sensor Dynamically compensated pressure to solve the problem of inaccurate pressure values of silicon resonant pressure sensors.

附图说明Description of drawings

图1为一种硅谐振压力传感器的动态补偿方法的流程图。FIG. 1 is a flowchart of a dynamic compensation method for a silicon resonant pressure sensor.

具体实施方式Detailed ways

下面对本发明的具体实施方式进行描述，以便于本技术领域的技术人员理解本发明，但应该清楚，本发明不限于具体实施方式的范围，对本技术领域的普通技术人员来讲，只要各种变化在所附的权利要求限定和确定的本发明的精神和范围内，这些变化是显而易见的，一切利用本发明构思的发明创造均在保护之列。The specific embodiments of the present invention are described below so that those skilled in the art can understand the present invention, but it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes Within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.

本发明针对因外接温度二极管，而导致硅谐振传感器存在的温度跟随性问题，提供一种动态补偿方法。基于外置温度传感器阵列，通过静态标定找到压力频率和温度频率与静态压力数据之间的静态标定参数，再通过动态标定，得到动态温度频率和动态压力频率；再通过样本标签与动态温度频率对时间序列预测模型进行训练，找到样本标签与动态温度频率间的对应参数关系，从而计算出校准温度频率，通过校准温度频率和静态标定参数去计算压力，作为硅谐振压力传感器的动态补偿后的压力，以解决硅谐振压力传感器压力值不准确的问题。The invention provides a dynamic compensation method aiming at the temperature followability problem of the silicon resonant sensor caused by an external temperature diode. Based on the external temperature sensor array, the static calibration parameters between the pressure frequency and temperature frequency and static pressure data are found through static calibration, and then the dynamic temperature frequency and dynamic pressure frequency are obtained through dynamic calibration; and then the sample label is compared with the dynamic temperature frequency The time series prediction model is trained to find the corresponding parameter relationship between the sample label and the dynamic temperature frequency, so as to calculate the calibration temperature frequency, and calculate the pressure through the calibration temperature frequency and static calibration parameters, as the dynamic compensation pressure of the silicon resonant pressure sensor , to solve the problem of inaccurate pressure values of silicon resonant pressure sensors.

如图1所示，一种硅谐振压力传感器的动态补偿方法，包括以下步骤：As shown in Figure 1, a dynamic compensation method for a silicon resonant pressure sensor includes the following steps:

S1、对硅谐振压力传感器进行静态标定，得到静态标定参数、平均温度频率和标准化后的压力频率；S1. Perform static calibration on the silicon resonant pressure sensor to obtain static calibration parameters, average temperature frequency and standardized pressure frequency;

在本实施例中，步骤S1采用外置温度传感器阵列对硅谐振压力传感器进行静态标定。In this embodiment, step S1 uses an external temperature sensor array to statically calibrate the silicon resonant pressure sensor.

所述步骤S1包括以下分步骤：The step S1 includes the following sub-steps:

S11、在硅谐振压力传感器的全温范围内，选取多个温度标定点；S11. Select multiple temperature calibration points within the full temperature range of the silicon resonant pressure sensor;

在本实施例中，全温范围为[-55℃，85℃]。In this embodiment, the full temperature range is [-55°C, 85°C].

S12、在硅谐振压力传感器的全压范围内，选取多个压力标定点；S12. Select multiple pressure calibration points within the full pressure range of the silicon resonant pressure sensor;

在本实施例中，全压范围为[0kPa，130kPa]。In this embodiment, the total pressure range is [0kPa, 130kPa].

S13、在压力标定点和温度标定点下采集硅谐振压力传感器的静态四路温度频率、静态压力频率和静态压力数据；S13. Collect static four-way temperature frequency, static pressure frequency and static pressure data of the silicon resonant pressure sensor at the pressure calibration point and temperature calibration point;

S14、对静态四路温度频率取均值，得到平均温度频率；S14. Taking the average value of the static four temperature frequencies to obtain the average temperature frequency;

所述步骤S14中平均温度频率的计算公式为：The calculation formula of the average temperature frequency in the step S14 is:

Figure 85983DEST_PATH_IMAGE001
Figure 85983DEST_PATH_IMAGE001

其中，

Figure 516964DEST_PATH_IMAGE002
为第
Figure 879813DEST_PATH_IMAGE003
个温度标定点下第
Figure 197793DEST_PATH_IMAGE004
个压力标定点的平均温度频率，
Figure 355105DEST_PATH_IMAGE005
为第
Figure 211065DEST_PATH_IMAGE006
个温度标定点下第
Figure 112025DEST_PATH_IMAGE008
个压力标定点的静态第一路温度频率，
Figure 799358DEST_PATH_IMAGE009
为第
Figure 878304DEST_PATH_IMAGE010
个温度标定点下第
Figure 283877DEST_PATH_IMAGE011
个压力标定点的静态第二路温度频率，
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为第
Figure 264789DEST_PATH_IMAGE013
个温度标定点下第
Figure 967166DEST_PATH_IMAGE014
个压力标定点的静态第三路温度频率，
Figure 342259DEST_PATH_IMAGE015
为第
Figure 585021DEST_PATH_IMAGE013
个温度标定点下第
Figure 246947DEST_PATH_IMAGE016
个压力标定点的静态第四路温度频率。in,
Figure 516964DEST_PATH_IMAGE002
for the first
Figure 879813DEST_PATH_IMAGE003
temperature calibration point
Figure 197793DEST_PATH_IMAGE004
The average temperature frequency of a pressure calibration point,
Figure 355105DEST_PATH_IMAGE005
for the first
Figure 211065DEST_PATH_IMAGE006
temperature calibration point
Figure 112025DEST_PATH_IMAGE008
The static first channel temperature frequency of a pressure calibration point,
Figure 799358DEST_PATH_IMAGE009
for the first
Figure 878304DEST_PATH_IMAGE010
temperature calibration point
Figure 283877DEST_PATH_IMAGE011
The static second channel temperature frequency of a pressure calibration point,
Figure 722949DEST_PATH_IMAGE012
for the first
Figure 264789DEST_PATH_IMAGE013
temperature calibration point
Figure 967166DEST_PATH_IMAGE014
The static temperature frequency of the third pressure calibration point,
Figure 342259DEST_PATH_IMAGE015
for the first
Figure 585021DEST_PATH_IMAGE013
temperature calibration point
Figure 246947DEST_PATH_IMAGE016
The static fourth channel temperature frequency of a pressure calibration point.

S15、对平均温度频率和静态压力频率进行标准化处理，得到标准化后的温度频率和压力频率；S15. Standardize the average temperature frequency and static pressure frequency to obtain standardized temperature frequency and pressure frequency;

所述步骤S15中标准化后的温度频率的计算公式为：The calculation formula of the normalized temperature frequency in the step S15 is:

Figure 182542DEST_PATH_IMAGE017
Figure 182542DEST_PATH_IMAGE017

其中，

Figure 47861DEST_PATH_IMAGE018
为第
Figure 94314DEST_PATH_IMAGE003
个温度标定点下第
Figure 610746DEST_PATH_IMAGE004
个压力标定点所对应的标准化后的温度频率，
Figure 467975DEST_PATH_IMAGE019
为第
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个温度标定点下第
Figure 388843DEST_PATH_IMAGE004
个压力标定点的平均温度频率，
Figure 963044DEST_PATH_IMAGE020
为
Figure 974862DEST_PATH_IMAGE021
个平均温度频率
Figure 814774DEST_PATH_IMAGE022
的均值，
Figure 203030DEST_PATH_IMAGE023
为
Figure 694054DEST_PATH_IMAGE021
个平均温度频率
Figure 876773DEST_PATH_IMAGE024
的标准差，
Figure 953050DEST_PATH_IMAGE025
为温度标定点或压力标定点的数量；in,
Figure 47861DEST_PATH_IMAGE018
for the first
Figure 94314DEST_PATH_IMAGE003
temperature calibration point
Figure 610746DEST_PATH_IMAGE004
The normalized temperature frequency corresponding to a pressure calibration point,
Figure 467975DEST_PATH_IMAGE019
for the first
Figure 804278DEST_PATH_IMAGE003
temperature calibration point
Figure 388843DEST_PATH_IMAGE004
The average temperature frequency of a pressure calibration point,
Figure 963044DEST_PATH_IMAGE020
for
Figure 974862DEST_PATH_IMAGE021
average temperature frequency
Figure 814774DEST_PATH_IMAGE022
the mean value of
Figure 203030DEST_PATH_IMAGE023
for
Figure 694054DEST_PATH_IMAGE021
average temperature frequency
Figure 876773DEST_PATH_IMAGE024
standard deviation of
Figure 953050DEST_PATH_IMAGE025
is the number of temperature calibration points or pressure calibration points;

所述步骤S15中标准化后的压力频率的计算公式为：The calculation formula of the normalized pressure frequency in the step S15 is:

Figure 82680DEST_PATH_IMAGE026
Figure 82680DEST_PATH_IMAGE026

其中，

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为第
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个温度标定点下第
Figure 580023DEST_PATH_IMAGE004
个压力标定点所对应的标准化后的压力频率，
Figure 326394DEST_PATH_IMAGE028
为第
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个温度标定点下第
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个压力标定点的静态压力频率，
Figure 336441DEST_PATH_IMAGE029
为
Figure 73453DEST_PATH_IMAGE030
个静态压力频率
Figure 878729DEST_PATH_IMAGE031
的均值，
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为
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个静态压力频率
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的标准差。in,
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for the first
Figure 781832DEST_PATH_IMAGE003
temperature calibration point
Figure 580023DEST_PATH_IMAGE004
The normalized pressure frequency corresponding to a pressure calibration point,
Figure 326394DEST_PATH_IMAGE028
for the first
Figure 526431DEST_PATH_IMAGE003
temperature calibration point
Figure 50953DEST_PATH_IMAGE004
The static pressure frequency of a pressure calibration point,
Figure 336441DEST_PATH_IMAGE029
for
Figure 73453DEST_PATH_IMAGE030
static pressure frequency
Figure 878729DEST_PATH_IMAGE031
the mean value of
Figure 574152DEST_PATH_IMAGE032
for
Figure 612516DEST_PATH_IMAGE033
static pressure frequency
Figure 684377DEST_PATH_IMAGE034
standard deviation of .

S16、根据标准化后的温度频率、标准化后的压力频率和静态压力数据，构建第一压力温度模型；S16. Construct a first pressure-temperature model according to the normalized temperature frequency, the normalized pressure frequency, and the static pressure data;

所述步骤S16中第一压力温度模型为：In the step S16, the first pressure-temperature model is:

Figure 344159DEST_PATH_IMAGE035
Figure 344159DEST_PATH_IMAGE035

其中，

Figure 679326DEST_PATH_IMAGE036
为第
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个温度标定点下第
Figure 549379DEST_PATH_IMAGE004
个压力标定点的静态压力数据，
Figure 578515DEST_PATH_IMAGE037
为第
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个温度标定点下第
Figure 110920DEST_PATH_IMAGE004
个压力标定点所对应的标准化后的压力频率，
Figure 524583DEST_PATH_IMAGE038
为第
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个温度标定点下第
Figure 85195DEST_PATH_IMAGE004
个压力标定点所对应的标准化后的温度频率，
Figure 805020DEST_PATH_IMAGE039
和
Figure 287954DEST_PATH_IMAGE040
均为计数小标，
Figure 26103DEST_PATH_IMAGE041
为第
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个静态标定参数。in,
Figure 679326DEST_PATH_IMAGE036
for the first
Figure 673827DEST_PATH_IMAGE003
temperature calibration point
Figure 549379DEST_PATH_IMAGE004
Static pressure data of pressure calibration points,
Figure 578515DEST_PATH_IMAGE037
for the first
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temperature calibration point
Figure 110920DEST_PATH_IMAGE004
The normalized pressure frequency corresponding to a pressure calibration point,
Figure 524583DEST_PATH_IMAGE038
for the first
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temperature calibration point
Figure 85195DEST_PATH_IMAGE004
The normalized temperature frequency corresponding to a pressure calibration point,
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and
Figure 287954DEST_PATH_IMAGE040
Both are counting subscripts,
Figure 26103DEST_PATH_IMAGE041
for the first
Figure 670711DEST_PATH_IMAGE042
a static calibration parameter.

S17、采用最小二乘法对第一压力温度模型进行求解，得到静态标定参数。S17. Solving the first pressure-temperature model by using the least squares method to obtain static calibration parameters.

S2、对硅谐振压力传感器进行动态标定，得到动态温度频率和动态压力频率；S2. Perform dynamic calibration on the silicon resonant pressure sensor to obtain dynamic temperature frequency and dynamic pressure frequency;

所述步骤S2具体为：在随机变化的温度条件下，采集多个压力标定点下连续多次的硅谐振压力传感器的动态温度频率和动态压力频率。The step S2 specifically includes: under a randomly changing temperature condition, collecting the dynamic temperature frequency and the dynamic pressure frequency of the silicon resonant pressure sensor for multiple consecutive times at multiple pressure calibration points.

S3、根据静态标定的平均温度频率、标准化后的压力频率和动态标定的动态压力频率，构建样本标签；S3. Construct a sample label according to the statically calibrated average temperature frequency, the standardized pressure frequency, and the dynamically calibrated dynamic pressure frequency;

所述步骤S3包括以下分步骤：The step S3 includes the following sub-steps:

S31、根据静态标定过程中的标准化后的压力频率和平均温度频率，构建第二温度压力模型；S31. Construct a second temperature and pressure model according to the standardized pressure frequency and average temperature frequency in the static calibration process;

S32、采用最小二乘法对第二温度压力模型进行求解，得到温度压力系数；S32. Using the least square method to solve the second temperature and pressure model to obtain the temperature and pressure coefficient;

所述步骤S32中第二温度压力模型为：The second temperature and pressure model in the step S32 is:

Figure 330362DEST_PATH_IMAGE043
Figure 330362DEST_PATH_IMAGE043

其中，

Figure 633299DEST_PATH_IMAGE044
为第
Figure 822359DEST_PATH_IMAGE003
个温度标定点下第
Figure 372289DEST_PATH_IMAGE004
个压力标定点的平均温度频率，
Figure 315975DEST_PATH_IMAGE045
为第
Figure 891443DEST_PATH_IMAGE003
个温度标定点下第
Figure 674024DEST_PATH_IMAGE004
个压力标定点所对应的标准化后的压力频率，
Figure 660435DEST_PATH_IMAGE046
、
Figure 825837DEST_PATH_IMAGE047
和
Figure 923106DEST_PATH_IMAGE048
为温度压力系数，具体的
Figure 181699DEST_PATH_IMAGE048
为第一温度压力系数，
Figure 339010DEST_PATH_IMAGE047
为第二温度压力系数，
Figure 991709DEST_PATH_IMAGE046
为第三温度压力系数；in,
Figure 633299DEST_PATH_IMAGE044
for the first
Figure 822359DEST_PATH_IMAGE003
temperature calibration point
Figure 372289DEST_PATH_IMAGE004
The average temperature frequency of a pressure calibration point,
Figure 315975DEST_PATH_IMAGE045
for the first
Figure 891443DEST_PATH_IMAGE003
temperature calibration point
Figure 674024DEST_PATH_IMAGE004
The normalized pressure frequency corresponding to a pressure calibration point,
Figure 660435DEST_PATH_IMAGE046
,
Figure 825837DEST_PATH_IMAGE047
and
Figure 923106DEST_PATH_IMAGE048
is the temperature pressure coefficient, specifically
Figure 181699DEST_PATH_IMAGE048
is the first temperature pressure coefficient,
Figure 339010DEST_PATH_IMAGE047
is the second temperature pressure coefficient,
Figure 991709DEST_PATH_IMAGE046
is the third temperature pressure coefficient;

S33、根据温度压力系数和动态标定的动态压力频率，得到样本标签。S33. Obtain a sample label according to the temperature-pressure coefficient and the dynamically calibrated dynamic pressure frequency.

所述步骤S33中样本标签公式为：The sample label formula in the step S33 is:

Figure 95931DEST_PATH_IMAGE049
Figure 95931DEST_PATH_IMAGE049

其中，

Figure 533997DEST_PATH_IMAGE050
为第
Figure 862210DEST_PATH_IMAGE004
个压力标定点下第
Figure 2204DEST_PATH_IMAGE051
次采集所对应的样本标签，
Figure 706855DEST_PATH_IMAGE052
、
Figure 999427DEST_PATH_IMAGE053
和
Figure 498541DEST_PATH_IMAGE054
为温度压力系数，
Figure 125832DEST_PATH_IMAGE055
为第
Figure 571857DEST_PATH_IMAGE004
个压力标定点下第
Figure 968203DEST_PATH_IMAGE051
次采集的硅谐振压力传感器的动态压力频率。in,
Figure 533997DEST_PATH_IMAGE050
for the first
Figure 862210DEST_PATH_IMAGE004
pressure calibration point
Figure 2204DEST_PATH_IMAGE051
The sample label corresponding to the second collection,
Figure 706855DEST_PATH_IMAGE052
,
Figure 999427DEST_PATH_IMAGE053
and
Figure 498541DEST_PATH_IMAGE054
is the temperature pressure coefficient,
Figure 125832DEST_PATH_IMAGE055
for the first
Figure 571857DEST_PATH_IMAGE004
pressure calibration point
Figure 968203DEST_PATH_IMAGE051
The dynamic pressure frequency of the silicon resonant pressure sensor acquired for the second time.

S4、采用样本标签和动态标定的动态温度频率对时间序列预测模型进行训练，得到训练完成的时间序列预测模型；S4. Using the sample label and the dynamically calibrated dynamic temperature frequency to train the time series prediction model to obtain the trained time series prediction model;

所述步骤S4包括以下分步骤：Described step S4 comprises following sub-steps:

S41、构建时间序列预测模型，得到样本标签

Figure 386021DEST_PATH_IMAGE056
的预测值
Figure 500608DEST_PATH_IMAGE057
：S41. Construct a time series prediction model and obtain sample labels
Figure 386021DEST_PATH_IMAGE056
predicted value of
Figure 500608DEST_PATH_IMAGE057
:

Figure 812641DEST_PATH_IMAGE058
Figure 63493DEST_PATH_IMAGE059
Figure 812641DEST_PATH_IMAGE058
Figure 63493DEST_PATH_IMAGE059

其中，

Figure 107673DEST_PATH_IMAGE057
为样本标签
Figure 460288DEST_PATH_IMAGE056
的预测值，
Figure 841591DEST_PATH_IMAGE060
为时间序列预测模型找到参数间对应关系的函数，其函数括号内的参数为第
Figure 415791DEST_PATH_IMAGE061
个压力标定点下多次采集的动态温度频率，
Figure 427610DEST_PATH_IMAGE062
为第
Figure 267521DEST_PATH_IMAGE063
路第
Figure 531143DEST_PATH_IMAGE065
个压力标定点下第
Figure 318707DEST_PATH_IMAGE066
次采集的动态温度频率，
Figure 767006DEST_PATH_IMAGE067
为第
Figure 77901DEST_PATH_IMAGE063
路第
Figure 269848DEST_PATH_IMAGE065
个压力标定点下第
Figure 897270DEST_PATH_IMAGE068
次采集的动态温度频率，
Figure 516470DEST_PATH_IMAGE069
为第
Figure 330973DEST_PATH_IMAGE063
路第
Figure 61032DEST_PATH_IMAGE065
个压力标定点下第
Figure 261069DEST_PATH_IMAGE070
次采集的动态温度频率，
Figure 785591DEST_PATH_IMAGE071
；in,
Figure 107673DEST_PATH_IMAGE057
Label the sample
Figure 460288DEST_PATH_IMAGE056
predicted value of
Figure 841591DEST_PATH_IMAGE060
It is a function to find the corresponding relationship between parameters for the time series forecasting model, and the parameters in the function brackets are the first
Figure 415791DEST_PATH_IMAGE061
The dynamic temperature frequency collected multiple times under a pressure calibration point,
Figure 427610DEST_PATH_IMAGE062
for the first
Figure 267521DEST_PATH_IMAGE063
roadside
Figure 531143DEST_PATH_IMAGE065
pressure calibration point
Figure 318707DEST_PATH_IMAGE066
The dynamic temperature frequency of the second acquisition,
Figure 767006DEST_PATH_IMAGE067
for the first
Figure 77901DEST_PATH_IMAGE063
roadside
Figure 269848DEST_PATH_IMAGE065
pressure calibration point
Figure 897270DEST_PATH_IMAGE068
The dynamic temperature frequency of the second acquisition,
Figure 516470DEST_PATH_IMAGE069
for the first
Figure 330973DEST_PATH_IMAGE063
roadside
Figure 61032DEST_PATH_IMAGE065
pressure calibration point
Figure 261069DEST_PATH_IMAGE070
The dynamic temperature frequency of the second acquisition,
Figure 785591DEST_PATH_IMAGE071
;

S42、构建代价函数，度量预测值

Figure 274341DEST_PATH_IMAGE072
与样本标签
Figure 293244DEST_PATH_IMAGE073
差值，其中，代价函数为：S42. Construct a cost function and measure the predicted value
Figure 274341DEST_PATH_IMAGE072
with sample tags
Figure 293244DEST_PATH_IMAGE073
difference, where the cost function is:

Figure 347788DEST_PATH_IMAGE074
Figure 347788DEST_PATH_IMAGE074

其中，

Figure 574370DEST_PATH_IMAGE075
为代价函数，
Figure 347154DEST_PATH_IMAGE076
为L2范数；in,
Figure 574370DEST_PATH_IMAGE075
as the cost function,
Figure 347154DEST_PATH_IMAGE076
is the L2 norm;

S43、将样本标签

Figure 901238DEST_PATH_IMAGE073
和动态温度频率输入时间序列预测模型，使得预测值
Figure DEST_PATH_IMAGE082
与样本标签
Figure 810289DEST_PATH_IMAGE073
差值最小，得到训练完成的时间序列预测模型。S43, label the sample
Figure 901238DEST_PATH_IMAGE073
and dynamic temperature frequency input time series forecasting model, making the predicted value
Figure DEST_PATH_IMAGE082
with sample tags
Figure 810289DEST_PATH_IMAGE073
The difference is the smallest, and the trained time series forecasting model is obtained.

S5、采用训练完成的时间序列预测模型计算校准温度频率；S5. Calculating the calibration temperature frequency using the trained time series prediction model;

S6、根据校准温度频率、静态标定参数和标准化后的压力频率，计算硅谐振压力传感器的动态补偿后的压力。S6. Calculate the dynamically compensated pressure of the silicon resonant pressure sensor according to the calibrated temperature frequency, the static calibration parameter and the standardized pressure frequency.

所述步骤S6中计算硅谐振压力传感器的动态补偿后的压力的公式为：The formula for calculating the dynamically compensated pressure of the silicon resonant pressure sensor in the step S6 is:

Figure 676613DEST_PATH_IMAGE078
Figure 676613DEST_PATH_IMAGE078

其中，

Figure 202273DEST_PATH_IMAGE079
为硅谐振压力传感器的动态补偿后的压力，
Figure 562978DEST_PATH_IMAGE080
为校准温度频率，
Figure 795376DEST_PATH_IMAGE081
为第
Figure 98182DEST_PATH_IMAGE003
个温度标定点下第
Figure 579979DEST_PATH_IMAGE004
个压力标定点所对应的标准化后的压力频率，
Figure 993642DEST_PATH_IMAGE039
和
Figure 893596DEST_PATH_IMAGE040
均为计数小标，
Figure 367303DEST_PATH_IMAGE041
为第
Figure 539658DEST_PATH_IMAGE042
个静态标定参数。in,
Figure 202273DEST_PATH_IMAGE079
is the dynamically compensated pressure of the silicon resonant pressure sensor,
Figure 562978DEST_PATH_IMAGE080
To calibrate the temperature frequency,
Figure 795376DEST_PATH_IMAGE081
for the first
Figure 98182DEST_PATH_IMAGE003
temperature calibration point
Figure 579979DEST_PATH_IMAGE004
The normalized pressure frequency corresponding to a pressure calibration point,
Figure 993642DEST_PATH_IMAGE039
and
Figure 893596DEST_PATH_IMAGE040
Both are counting subscripts,
Figure 367303DEST_PATH_IMAGE041
for the first
Figure 539658DEST_PATH_IMAGE042
a static calibration parameter.

Claims (2)

1.一种硅谐振压力传感器的动态补偿方法，其特征在于，包括以下步骤：1. A dynamic compensation method for a silicon resonant pressure sensor, characterized in that, comprising the following steps: S1、对硅谐振压力传感器进行静态标定，得到静态标定参数、平均温度频率和标准化后的压力频率；S1. Perform static calibration on the silicon resonant pressure sensor to obtain static calibration parameters, average temperature frequency and standardized pressure frequency; S2、对硅谐振压力传感器进行动态标定，得到动态温度频率和动态压力频率；S2. Perform dynamic calibration on the silicon resonant pressure sensor to obtain dynamic temperature frequency and dynamic pressure frequency; S3、根据静态标定的平均温度频率、标准化后的压力频率和动态标定的动态压力频率，构建样本标签；S3. Construct a sample label according to the statically calibrated average temperature frequency, the standardized pressure frequency, and the dynamically calibrated dynamic pressure frequency; S4、采用样本标签和动态标定的动态温度频率对时间序列预测模型进行训练，得到训练完成的时间序列预测模型；S4. Using the sample label and the dynamically calibrated dynamic temperature frequency to train the time series prediction model to obtain the trained time series prediction model; S5、采用训练完成的时间序列预测模型计算校准温度频率；S5. Calculating the calibration temperature frequency using the trained time series prediction model; S6、根据校准温度频率、静态标定参数和标准化后的压力频率，计算硅谐振压力传感器的动态补偿后的压力；S6. Calculate the dynamically compensated pressure of the silicon resonant pressure sensor according to the calibrated temperature frequency, the static calibration parameters and the standardized pressure frequency; 所述步骤S1包括以下分步骤：The step S1 includes the following sub-steps: S11、在硅谐振压力传感器的全温范围内，选取多个温度标定点；S11. Select multiple temperature calibration points within the full temperature range of the silicon resonant pressure sensor; S12、在硅谐振压力传感器的全压范围内，选取多个压力标定点；S12. Select multiple pressure calibration points within the full pressure range of the silicon resonant pressure sensor; S13、在压力标定点和温度标定点下采集硅谐振压力传感器的静态四路温度频率、静态压力频率和静态压力数据；S13. Collect static four-way temperature frequency, static pressure frequency and static pressure data of the silicon resonant pressure sensor at the pressure calibration point and temperature calibration point; S14、对静态四路温度频率取均值，得到平均温度频率；S14. Taking the average value of the static four temperature frequencies to obtain the average temperature frequency; S15、对平均温度频率和静态压力频率进行标准化处理，得到标准化后的温度频率和压力频率；S15. Standardize the average temperature frequency and static pressure frequency to obtain standardized temperature frequency and pressure frequency; S16、根据标准化后的温度频率、标准化后的压力频率和静态压力数据，构建第一压力温度模型；S16. Construct a first pressure-temperature model according to the normalized temperature frequency, the normalized pressure frequency, and the static pressure data; S17、采用最小二乘法对第一压力温度模型进行求解，得到静态标定参数；S17. Using the least squares method to solve the first pressure-temperature model to obtain static calibration parameters; 所述步骤S14中平均温度频率的计算公式为：The calculation formula of the average temperature frequency in the step S14 is:
Figure FDA0003825169660000021
Figure FDA0003825169660000021
 其中，
Figure FDA0003825169660000024
为第i个温度标定点下第j个压力标定点的平均温度频率，
Figure FDA0003825169660000025
为第i个温度标定点下第j个压力标定点的静态第一路温度频率，
Figure FDA0003825169660000026
为第i个温度标定点下第j个压力标定点的静态第二路温度频率，
Figure FDA0003825169660000027
为第i个温度标定点下第j个压力标定点的静态第三路温度频率，
Figure FDA0003825169660000028
为第i个温度标定点下第j个压力标定点的静态第四路温度频率；in,
Figure FDA0003825169660000024
is the average temperature frequency of the jth pressure calibration point under the ith temperature calibration point,
Figure FDA0003825169660000025
is the static first-way temperature frequency of the j-th pressure calibration point under the i-th temperature calibration point,
Figure FDA0003825169660000026
is the static temperature frequency of the second channel at the j-th pressure calibration point under the i-th temperature calibration point,
Figure FDA0003825169660000027
is the static temperature frequency of the third channel at the j-th pressure calibration point under the i-th temperature calibration point,
Figure FDA0003825169660000028
is the static fourth channel temperature frequency of the jth pressure calibration point under the ith temperature calibration point; 所述步骤S15中标准化后的温度频率的计算公式为：The calculation formula of the normalized temperature frequency in the step S15 is:
Figure FDA0003825169660000022
Figure FDA0003825169660000022
 其中，
Figure FDA0003825169660000029
为第i个温度标定点下第j个压力标定点所对应的标准化后的温度频率，
Figure FDA00038251696600000210
为第i个温度标定点下第j个压力标定点的平均温度频率，
Figure FDA00038251696600000211
为I*I个平均温度频率
Figure FDA00038251696600000212
的均值，
Figure FDA00038251696600000213
为I*I个平均温度频率
Figure FDA00038251696600000214
的标准差，I为温度标定点或压力标定点的数量；in,
Figure FDA0003825169660000029
is the normalized temperature frequency corresponding to the jth pressure calibration point under the ith temperature calibration point,
Figure FDA00038251696600000210
is the average temperature frequency of the jth pressure calibration point under the ith temperature calibration point,
Figure FDA00038251696600000211
I*I average temperature frequency
Figure FDA00038251696600000212
the mean value of
Figure FDA00038251696600000213
I*I average temperature frequency
Figure FDA00038251696600000214
The standard deviation of , I is the number of temperature calibration points or pressure calibration points; 所述步骤S15中标准化后的压力频率的计算公式为：The calculation formula of the normalized pressure frequency in the step S15 is:
Figure FDA0003825169660000023
Figure FDA0003825169660000023
 其中，
Figure FDA00038251696600000215
为第i个温度标定点下第j个压力标定点所对应的标准化后的压力频率，
Figure FDA0003825169660000032
为第i个温度标定点下第j个压力标定点的静态压力频率，
Figure FDA0003825169660000033
为I*I个静态压力频率
Figure FDA0003825169660000034
的均值，
Figure FDA0003825169660000035
为I*I个静态压力频率
Figure FDA0003825169660000036
的标准差；in,
Figure FDA00038251696600000215
is the normalized pressure frequency corresponding to the jth pressure calibration point under the ith temperature calibration point,
Figure FDA0003825169660000032
is the static pressure frequency of the jth pressure calibration point under the ith temperature calibration point,
Figure FDA0003825169660000033
I*I static pressure frequency
Figure FDA0003825169660000034
the mean value of
Figure FDA0003825169660000035
I*I static pressure frequency
Figure FDA0003825169660000036
standard deviation of 所述步骤S16中第一压力温度模型为：In the step S16, the first pressure-temperature model is:
Figure FDA0003825169660000031
Figure FDA0003825169660000031
 其中，
Figure FDA0003825169660000037
为第i个温度标定点下第j个压力标定点的静态压力数据，
Figure FDA0003825169660000038
为第i个温度标定点下第j个压力标定点所对应的标准化后的压力频率，
Figure FDA0003825169660000039
为第i个温度标定点下第j个压力标定点所对应的标准化后的温度频率，a和b均为计数小标，kab为第a*b个静态标定参数；in,
Figure FDA0003825169660000037
is the static pressure data of the jth pressure calibration point under the ith temperature calibration point,
Figure FDA0003825169660000038
is the normalized pressure frequency corresponding to the jth pressure calibration point under the ith temperature calibration point,
Figure FDA0003825169660000039
is the normalized temperature frequency corresponding to the j-th pressure calibration point under the i-th temperature calibration point, a and b are count subscales, and k ab is the a*b-th static calibration parameter; 所述步骤S3包括以下分步骤：The step S3 includes the following sub-steps: S31、根据静态标定过程中的标准化后的压力频率和平均温度频率，构建第二温度压力模型；S31. Construct a second temperature and pressure model according to the standardized pressure frequency and average temperature frequency in the static calibration process; S32、采用最小二乘法对第二温度压力模型进行求解，得到温度压力系数；S32. Using the least square method to solve the second temperature and pressure model to obtain the temperature and pressure coefficient; S33、根据温度压力系数和动态标定的动态压力频率，得到样本标签；S33. Obtain the sample label according to the temperature-pressure coefficient and the dynamically calibrated dynamic pressure frequency; 所述步骤S32中第二温度压力模型为：The second temperature and pressure model in the step S32 is:
Figure FDA00038251696600000310
Figure FDA00038251696600000310
 其中，
Figure FDA00038251696600000312
为第i个温度标定点下第j个压力标定点的平均温度频率，
Figure FDA00038251696600000311
为第i个温度标定点下第j个压力标定点所对应的标准化后的压力频率，a2j、a1j和a0j为温度压力系数；in,
Figure FDA00038251696600000312
is the average temperature frequency of the jth pressure calibration point under the ith temperature calibration point,
Figure FDA00038251696600000311
is the normalized pressure frequency corresponding to the j-th pressure calibration point under the i-th temperature calibration point, a 2j , a 1j and a 0j are temperature and pressure coefficients; 所述步骤S33中样本标签公式为：The sample label formula in the step S33 is:
Figure FDA0003825169660000046
Figure FDA0003825169660000046
 其中，
Figure FDA0003825169660000047
为第j个压力标定点下第n次采集所对应的样本标签，a2j、a1j和a0j为温度压力系数，
Figure FDA0003825169660000048
为第j个压力标定点下第n次采集的硅谐振压力传感器的动态压力频率；in,
Figure FDA0003825169660000047
is the sample label corresponding to the nth collection at the jth pressure calibration point, a 2j , a 1j and a 0j are the temperature and pressure coefficients,
Figure FDA0003825169660000048
is the dynamic pressure frequency of the silicon resonant pressure sensor collected for the nth time at the jth pressure calibration point; 所述步骤S4包括以下分步骤：Described step S4 comprises following sub-steps: S41、构建时间序列预测模型，得到样本标签
Figure FDA0003825169660000049
的预测值
Figure FDA0003825169660000041
S41. Construct a time series prediction model and obtain sample labels
Figure FDA0003825169660000049
predicted value of
Figure FDA0003825169660000041
Figure FDA0003825169660000042
Figure FDA0003825169660000042
 其中，
Figure FDA0003825169660000043
为样本标签
Figure FDA00038251696600000410
的预测值，Pre(·)为时间序列预测模型找到参数间对应关系的函数，其函数括号内的参数为第j个压力标定点下多次采集的动态温度频率，
Figure FDA00038251696600000411
为第k路第j个压力标定点下第n次采集的动态温度频率，
Figure FDA00038251696600000412
为第k路第j个压力标定点下第n-1次采集的动态温度频率，
Figure FDA00038251696600000413
为第k路第j个压力标定点下第n-2次采集的动态温度频率，k＝1，2，3，4in,
Figure FDA0003825169660000043
Label the sample
Figure FDA00038251696600000410
The predicted value of , Pre( ) is a function to find the corresponding relationship between parameters for the time series prediction model, and the parameters in the function brackets are the dynamic temperature frequency collected multiple times under the jth pressure calibration point,
Figure FDA00038251696600000411
is the dynamic temperature frequency collected for the nth time at the jth pressure calibration point of the kth road,
Figure FDA00038251696600000412
is the dynamic temperature frequency collected for the n-1th time at the jth pressure calibration point of the kth road,
Figure FDA00038251696600000413
It is the dynamic temperature frequency collected for the n-2th time at the jth pressure calibration point of the kth road, k=1, 2, 3, 4 S42、构建代价函数，度量预测值
Figure FDA0003825169660000044
与样本标签
Figure FDA00038251696600000414
差值，其中，代价函数为：S42. Construct a cost function and measure the predicted value
Figure FDA0003825169660000044
with sample tags
Figure FDA00038251696600000414
difference, where the cost function is:
Figure FDA0003825169660000045
Figure FDA0003825169660000045
 其中，Cost为代价函数，L2为L2范数；Among them, Cost is the cost function, and L 2 is the L2 norm; S43、将样本标签
Figure FDA00038251696600000415
和动态温度频率输入时间序列预测模型，使得预测值
Figure FDA0003825169660000051
与样本标签
Figure FDA0003825169660000054
差值最小，得到训练完成的时间序列预测模型；S43, label the sample
Figure FDA00038251696600000415
and dynamic temperature frequency input time series forecasting model, making the predicted value
Figure FDA0003825169660000051
with sample tags
Figure FDA0003825169660000054
The difference is the smallest, and the trained time series forecasting model is obtained; 所述步骤S6中计算硅谐振压力传感器的动态补偿后的压力的公式为：The formula for calculating the dynamically compensated pressure of the silicon resonant pressure sensor in the step S6 is:
Figure FDA0003825169660000052
Figure FDA0003825169660000052
 其中，P为硅谐振压力传感器的动态补偿后的压力，
Figure FDA0003825169660000053
为校准温度频率，
Figure FDA0003825169660000055
为第i个温度标定点下第j个压力标定点所对应的标准化后的压力频率，a和b均为计数小标，kab为第a*b个静态标定参数。Among them, P is the pressure after dynamic compensation of the silicon resonant pressure sensor,
Figure FDA0003825169660000053
To calibrate the temperature frequency,
Figure FDA0003825169660000055
is the normalized pressure frequency corresponding to the j-th pressure calibration point under the i-th temperature calibration point, a and b are count subscales, and k ab is the a*b-th static calibration parameter. 2.根据权利要求1所述的硅谐振压力传感器的动态补偿方法，其特征在于，所述步骤S2具体为：在随机变化的温度条件下，采集多个压力标定点下连续多次的硅谐振压力传感器的动态温度频率和动态压力频率。2. The dynamic compensation method of the silicon resonant pressure sensor according to claim 1, characterized in that, the step S2 is specifically: under randomly changing temperature conditions, collecting silicon resonant multiple times consecutively under a plurality of pressure calibration points Dynamic temperature frequency and dynamic pressure frequency of the pressure sensor.
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