阅读说明：本技术 一种石英谐振差动式加速度计温度补偿方法 (Temperature compensation method for quartz resonance differential accelerometer ) 是由 周冠武 张庆红 李皎 康磊 于 2019-11-26 设计创作，主要内容包括：一种石英谐振差动式加速度计温度补偿方法,采集加速度计与温度传感器输出的频率信号f<Sub>1</Sub>、f<Sub>2</Sub>与温度信号T以及加速度a；计算不同温度下加速度计的静态数学模型的零偏K<Sub>0</Sub>、标度因数K<Sub>1</Sub>与二阶非线性系数K<Sub>2</Sub>,以f<Sub>1</Sub>、f<Sub>2</Sub>、T、a、K<Sub>0</Sub>、K<Sub>1</Sub>、K<Sub>2</Sub>组成数据源；选取在不同温度与加速度条件下的数据源作为初始样本数据,对样本数据进行预处理,并分为训练样本与验证样本；设置自增极限学习机相关参数；以样本数据作为自增极限学习机温度补偿模型的输入,进行模型学习与验证；输入预处理后的实测频率信号f<Sub>1</Sub>、f<Sub>2</Sub>与温度信号T进行模型预测；本发明不仅具有补偿速度快、隐层节点数自确定优点,而且具有加速度计标定功能。(A temperature compensation method for quartz resonance differential accelerometer includes collecting frequency signal f output by accelerometer and temperature sensor 1 、f 2 With temperature signal T and acceleration a; calculating zero offset K of static mathematical model of accelerometer at different temperatures 0 Scale factor K 1 And a second order nonlinear coefficient K 2 With f 1 、f 2 、T、a、K 0 、K 1 、K 2 Composing a data source; selecting data sources under different temperature and acceleration conditions as initial sample data, preprocessing the sample data, and dividing the sample data into training samples and verification samples; setting relevant parameters of a self-increment limit learning machine; taking sample data as input of a temperature compensation model of the self-increment extreme learning machine to carry out model learning and verification; inputting the preprocessed actual measurement frequency signal f 1 、f 2 Carrying out model prediction with the temperature signal T; the invention not only hasThe compensation speed is fast, the number of hidden nodes is self-determined, and the accelerometer calibration function is achieved.)

1. A temperature compensation method for a quartz resonant differential accelerometer is characterized by comprising the following steps:

step 1: acquiring frequency signals f output by an accelerometer and a temperature sensor in a required temperature compensation range and an acceleration measurement range₁、f₂With temperature signal T and acceleration a; calculating zero offset K of static mathematical model of accelerometer at different temperatures₀Scale factor K₁And a second order nonlinear coefficient K₂With f₁、f₂、T、a、K₀、K₁、K₂Composing a data source;

step 2: selecting data sources under different temperature and acceleration conditions as initial sample data, preprocessing the sample data, and dividing the sample data into training samples and verification samples; setting relevant parameters of a self-increment limit learning machine;

and step 3: taking sample data as input of a temperature compensation model of the self-increment extreme learning machine to carry out model learning and verification;

and 4, step 4: inputting the preprocessed actual measurement frequency signal f₁、f₂Model prediction is performed with the temperature signal T.

2. The method of claim 1, wherein the temperature compensation method comprises: the step 2 is to sample data (f)_i1、f_i2、T_i、a_i、K_i0、K_i0、K_i0) Each column ofCarrying out standardization treatment, and randomly extracting samples according to a ratio of 4:1 to divide training samples and verification samples; setting the number of nodes of an input layer and an output layer of the self-increment limit learning machine to be 3 and 4; number of hidden nodes

3. The method of claim 1, wherein the learning and verification process of the temperature compensation model of the self-boosting extreme learning machine of step 3 comprises the following steps:

step 3.1: given a training sample { (x)_i,t_i)|x_i＝[f_i1,f_i2,T_i],t_i＝[a_i,K_i0,K_i1,K_i2]I-1, …, M }, verify sample { (x } {._i,t′_i)|x′_i＝[f′_i1,f′_i2,T′_i],t′_i＝[a′_i,K′_i0,K′_i1,K′_i2]I ═ 1, …, N }; the residual error E of the training sample is t,verifying the residual error E 'of the sample as t',

step 3.2: judging the number of hidden nodes

step 3.3: adding a hidden node and updating the number of the hidden nodes

step 3.4: calculating the weight vector between the hidden layer node and the output layer node according to the training sample

step 3.5: computing and adding new nodes

Step 3.4: computing and adding new nodes

4. The method of claim 1, wherein the temperature compensation method comprises: the step 4 of predicting the temperature compensation model of the self-increment extreme learning machine comprises the following steps:

step 4.1: inputting measured frequency signal f₁、f₂Normalizing the temperature signal T according to the maximum value and the minimum value of each column of the sample

Step 4.2: computing output of a self-augmented extreme learning machine

Step 4.3: performing inverse normalization processing on the output result of the incremental extreme learning machine_max-X_min)+X_minObtaining the acceleration a and the zero offset K₀Scale factor K₁And a second order nonlinear coefficient K₂。

Technical Field

The invention belongs to the technical field of quartz acceleration sensors, and particularly relates to a temperature compensation method for a quartz resonance differential accelerometer.

Background

The accelerometer is one of key elements of an inertial navigation system, is widely applied to the fields of aerospace, automobiles, consumer electronics and the like, and the performance of the accelerometer directly determines the navigation accuracy. The quartz resonance differential accelerometer is a micro-mechanical accelerometer processed by using MEMS technology and outputs digital frequency signals. The double-end-fixed quartz tuning fork mainly comprises two identical double-end-fixed quartz tuning forks, a sensitive mass block, a mounting base and a damper. When the accelerometer is subjected to acceleration in a sensitive direction, the sensitive mass block is subjected to axial inertia force with the magnitude of F ═ ma, one tuning fork is subjected to tensile force, the resonant frequency of the tuning fork is increased, and the other tuning fork is subjected to acceleration, the resonant frequency of the tuning fork is decreased; the difference between the frequencies of the two differentially arranged tuning forks is thus proportional to the axial force F, i.e. to the acceleration. The quartz resonance differential accelerometer has the advantages of strong anti-interference capability, high sensor precision, high sensitivity and the like; meanwhile, the differential structure can greatly reduce the interference of temperature fluctuation on the accelerometer. However, errors are inevitably generated in the manufacturing and assembling processes of the accelerometer, so that the temperature drift amounts of the two quartz tuning forks are slightly different. The temperature compensation of the accelerometer has important practical value because the influence of temperature on the output of the sensor can be reduced by improving the machining and assembling precision, but the influence of temperature cannot be completely eliminated.

In order to reduce and compensate the influence of temperature on the accelerometer, two methods, namely hardware and software, are commonly used at present to realize temperature compensation, and the influence of temperature on parameters such as the scale factor, zero offset and linearity of the accelerometer is reduced. The hardware compensation method mainly comprises the thermal design of an accelerometer, the design of a temperature compensation structure, a thermosensitive magnetic shunt compensation method of a torquer and a circuit compensation method. From the perspective of engineering application, the hardware compensation cost is high, and the period is long; software compensation is often performed by building an accurate temperature compensation model. The software compensation method mainly comprises polynomial fitting, a wavelet network, a vector machine and a back propagation neural network. Therefore, the method for establishing the static temperature model of the accelerometer and the software temperature compensation model by researching the rule of the influence of the temperature on the output of the accelerometer is an important method for improving the accuracy of the accelerometer.

Disclosure of Invention

In order to improve the adaptability of the parameter configuration of the software compensation technology, the invention aims to provide a temperature compensation method of a quartz resonance differential accelerometer, which has the advantages of high calculation speed, high precision and no parameter configuration.

In order to achieve the purpose, the invention adopts the technical scheme that:

a temperature compensation method for a quartz resonant differential accelerometer comprises the following steps:

step 1: acquiring frequency signals f output by an accelerometer and a temperature sensor in a required temperature compensation range and an acceleration measurement range₁、f₂With temperature signal T and acceleration a; calculating zero offset K of static mathematical model of accelerometer at different temperatures₀Scale factor K₁And a second order nonlinear coefficient K₂With f₁、f₂、T、a、K₀、K₁、K₂Composing a data source;

step 2: selecting data sources under different temperature and acceleration conditions as initial sample data, preprocessing the sample data, and dividing the sample data into training samples and verification samples; setting relevant parameters of a self-increment limit learning machine;

and step 3: taking sample data as input of a temperature compensation model of the self-increment extreme learning machine to carry out model learning and verification;

and 4, step 4: inputting the preprocessed actual measurement frequency signal f₁、f₂Model prediction is performed with the temperature signal T.

Data source (f) in step 1₁、f₂T, a) collecting according to the temperature and acceleration measuring range by adopting the principle of equal interval; at the same temperature T, according to the formula f₁-f₂＝K₀+K₁*a+K₂*a²And a data source (f)_i1、f_i2、a_i) And calculating K by least squares₀、K₁、K₂。

Said step (c) is2 for sample data (f)_i1、f_i2、T_i、a_i、K_i0、K_i1、K_i2) Each column in (1) adopts

Carrying out standardization treatment, and randomly extracting samples according to a ratio of 4:1 to divide training samples and verification samples; setting the number of nodes of an input layer and an output layer of the self-increment limit learning machine to be 3 and 4; number of hidden nodes

Excitation function thereof

Or f (x) sin (x); setting the error precision epsilon and the maximum node number of the self-increasing hidden layer which need to be reached after temperature compensation

The learning and verification process of the temperature compensation model of the self-increment extreme learning machine in the step 3 comprises the following steps:

step 3.1: given a training sample { (x)_i,t_i)|x_i＝[f_i1,f_i2,T_i],t_i＝[a_i,K_i0,K_i1,K_i2]I-1, …, M }, verify sample { (x } {._i,t′_i)|x′_i＝[f′_i1,f′_i2,T′_i],t′_i＝[a′_i,K′_i0,K′_i1,K′_i2]I ═ 1, …, N }; the residual error E of the training sample is t,

verifying the residual error E 'of the sample as t',

step 3.2: judging the number of hidden nodes

Whether or not less than

And | E' | is greater than epsilon, if the condition is met, then go to step 3.3, otherwise end the temperature compensation;

step 3.3: adding a hidden node and updating the number of the hidden nodes

For weight vector between input layer and newly-added hidden layer node

And adding hidden layer node threshold

A random assignment is made, with a range of (0,1),

the number of hidden nodes;

step 3.4: calculating the weight vector between the hidden layer node and the output layer node according to the training sample

To train the activation vector of the new node of the sample,

step 3.5: computing and adding new nodes

Residual error of post-training samples

Step (ii) of3.4: computing and adding new nodes

Residual error of post-verification sample

And go to step 3.2.

And 4, step 4: inputting the preprocessed actual measurement frequency signal f₁、f₂The process of carrying out the self-increment extreme learning machine temperature compensation model prediction with the temperature signal T comprises the following steps:

step 4.1: inputting measured frequency signal f₁、f₂With the temperature signal T, performing standardization processing

To obtain

Step 4.2: computing output of a self-augmented extreme learning machine

Step 4.3: performing inverse normalization processing on the output result of the incremental extreme learning machine_max-X_min)+X_min。

The temperature compensation method can be used for a quartz resonance differential accelerometer measuring device or system, a data source is collected when the temperature calibration system is measured by acceleration, and sample data is selected to carry out temperature compensation model learning and verification of the self-increment extreme learning machine.

Drawings

FIG. 1 is a flow chart of a temperature compensation method for a self-increment extreme learning machine according to the present invention.

FIG. 2 is a learning flow chart of the temperature compensation model of the auto-increment limit learning machine of the present invention.

FIG. 3 is a flow chart of the application of the temperature compensation model of the incremental learning machine of the present invention.

Detailed Description

The following detailed description of the embodiments of the invention refers to the accompanying drawings.

Referring to fig. 1, a temperature compensation method for a quartz resonant differential accelerometer includes the following steps:

step 1: the quartz resonant differential accelerometer is collected at different temperatures (within working temperature range), such as-40 deg.C, -30 deg.C, … deg.C, 80 deg.C]Lower applied acceleration a (accelerometer measurement range), e.g., -1g, -0.7g, …,1g]Frequency signal f output by accelerometer₁、f₂The temperature sensor outputs a signal T; according to the data set [ f ] at the same temperature T₁,f₂,a]Calculating a static mathematical model f of the accelerometer at the temperature by using a least square method₁-f₂＝K₀+K₁*a+K₂*a²Zero offset K of₀Scale factor K₁And a second order nonlinear coefficient K₂(ii) a Finally obtaining data sources [ f ] at different temperatures₁、f₂、T、a、K₀、K₁、K₂]；

Step 2: selecting data sources under different temperature and acceleration conditions as initial sample data, preprocessing the sample data, and dividing the sample data into training samples and verification samples; setting relevant parameters of a self-increment limit learning machine;

selecting data sources under different temperature and acceleration conditions as sample data, and selecting the sample according to an equal interval principle, wherein the temperature interval is-10 ℃ (wherein-40 ℃ and 80 ℃ are required to be selected), and the acceleration interval is 0.3g (wherein-1 g and 1g are required to be selected); for each column of sample data

Carrying out standardization treatment, and randomly dividing the standard sample into a training sample and a verification sample according to a sample number ratio of 4: 1; setting the input layer (frequency signal f) of the extreme learning machine₁、f₂Temperature signal T)The number of nodes of the hidden layer and the output layer is 3, 0 and 4 (acceleration a and zero offset K)₀Scale factor K₁Second order nonlinear coefficient K₂) Excitation function of hidden layer node

The precision required to be achieved after temperature compensation is set to be epsilon 0.001 and the maximum node number of the self-increasing hidden layer

And step 3: taking sample data as input of a temperature compensation model of the self-increment extreme learning machine to carry out model learning and verification;

referring to fig. 2, the learning and verification process of the temperature compensation model of the incremental learning machine includes the following steps:

step 3.1: given a training sample { (x)_i,t_i)|x_i＝[f_i1,f_i2,T_i],t_i＝[a_i,K_i0,K_i1,K_i2]I-1, …, M }, verify sample { (x } {._i,t′_i)|x′_i＝[f′_i1,f′_i2,T′_i],t′_i＝[a′_i,K′_i0,K′_i1,K′_i2]I ═ 1, …, N }; the residual error E of the training sample is t,

verifying the residual error E 'of the sample as t',

step 3.2: judging the number of hidden nodes

Whether or not less thanAnd | E' | is greater than epsilon, if the condition is met, then go to step 3.3, otherwise end the temperature compensation;

step 3.3: adding a hidden node and updating the number of the hidden nodes

For weight vector between input layer and newly-added hidden layer nodeAnd adding hidden layer node threshold

A random assignment is made, with a range of (0,1),

the number of hidden nodes;

step 3.4: calculating the weight vector between the hidden layer node and the output layer node according to the training sample

To train the activation vector of the new node of the sample,

step 3.5: calculating new hidden layer node

Residual error of post-training samples

Step 3.4: calculating new hidden layer node

Residual error of post-verification sample

And go to step 3.2.

And 4, step 4: inputting the preprocessed actual measurement frequency signal f₁、f₂The process of carrying out the self-increment extreme learning machine temperature compensation model prediction with the temperature signal T comprises the following steps:

referring to fig. 3, the prediction process of the temperature compensation model of the auto-augmented limit learning machine includes the following steps:

step 4.1: inputting measured frequency signal f₁、f₂Normalizing the temperature signal T according to the maximum value and the minimum value of each column of the sample

To obtain

Step 4.2: computing output of a self-augmented extreme learning machine

Step 4.3: performing inverse normalization processing on the output result of the incremental extreme learning machine_max-X_min)+X_minObtaining the acceleration a and the zero offset K₀Scale factor K₁And a second order nonlinear coefficient K₂。

The invention utilizes data sources acquired by a quartz resonance differential accelerometer temperature calibration system at different temperatures as sample data to establish a quartz resonance differential accelerometer temperature compensation model based on an auto-increment limit learning machine. In order to meet the requirements of optimal precision and quick compensation, the number of hidden nodes of the extreme learning machine is self-determined in a self-increasing mode; in the training process, the weight of the nodes of the self-increment hidden layer is randomly assigned with the threshold value, and the weight of the nodes of the output layer is solved through error calculation. The model can be remodeled by changing sample data and judging conditions of the self-increasing node so as to adapt to the temperature compensation requirements of accelerometers with different ranges under the influence of different temperatures, and zero point and nonlinear compensation are simultaneously carried out.