CN113686354A - Resonant gyroscope temperature compensation method based on neural network algorithm - Google Patents

Resonant gyroscope temperature compensation method based on neural network algorithm Download PDF

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CN113686354A
CN113686354A CN202110861547.0A CN202110861547A CN113686354A CN 113686354 A CN113686354 A CN 113686354A CN 202110861547 A CN202110861547 A CN 202110861547A CN 113686354 A CN113686354 A CN 113686354A
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temperature
neural network
gyroscope
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neuron
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贾晨凯
赵鑫
孙文超
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707th Research Institute of CSIC
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/183—Compensation of inertial measurements, e.g. for temperature effects

Abstract

The invention relates to a resonant gyroscope temperature compensation method based on a neural network algorithm, which comprises the following steps: step 1, carrying out a temperature test on a resonant gyroscope, and sampling the output of the resonant gyroscope; step 2, carrying out comparative analysis, carrying out polynomial fitting on the gyro zero offset-temperature sample by using a least square method based on a polynomial model, and establishing a first-order polynomial model of which the zero offset changes along with the temperature; step 3, substituting the gyroscope and the temperature data recorded in the step 1 into the first-order polynomial model with the zero offset changing along with the temperature obtained by calculation in the step 2 to obtain gyroscope output data; and 4, training the network parameters by taking the gyroscope output data as sample input of the RBF neural network model to obtain a group of trained networks, and performing temperature compensation on the resonant gyroscope based on the RBF neural network model. The invention can compensate the material property changes of the gyro harmonic oscillator such as density, Young modulus, Poisson ratio and the like caused by temperature change.

Description

Resonant gyroscope temperature compensation method based on neural network algorithm
Technical Field
The invention belongs to the technical field of rate integral hemispherical resonant gyroscope inertial navigation systems, relates to a resonant gyroscope temperature compensation method, and particularly relates to a resonant gyroscope temperature compensation method based on a neural network algorithm.
Background
The traditional resonance gyroscope has the defects that the zero drift change of the gyroscope is aggravated and the precision of the gyroscope is greatly reduced due to the change of the temperature, which causes the change of the material properties of the gyroscope harmonic oscillator, such as density, Young modulus, Poisson ratio and the like.
When the gyro temperature error is compensated in the full temperature region, the least square method is used for fitting the polynomial model to perform temperature zero compensation on the spiral, the method can cause that the nonlinear characteristic of gyro zero offset changing along with the temperature is difficult to accurately express, and the temperature error compensation effect is not ideal.
Upon search, no prior art documents that are the same or similar to the present invention have been found.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a resonant gyroscope temperature compensation method based on a neural network algorithm, which is used for compensating material properties such as density, Young modulus, Poisson ratio and the like of a gyroscope harmonic oscillator caused by temperature change, so that the defects of aggravated zero drift change and great reduction of gyroscope precision caused by the temperature change are avoided.
The invention solves the practical problem by adopting the following technical scheme:
a resonant gyro temperature compensation method based on a neural network algorithm comprises the following steps:
step 1, carrying out a temperature test on a resonant gyroscope, and sampling the output of the resonant gyroscope;
step 2, carrying out comparative analysis, carrying out polynomial fitting on the gyro zero offset-temperature sample by using a least square method based on a polynomial model, and establishing a first-order polynomial model of which the zero offset changes along with the temperature;
step 3, substituting the gyroscope and the temperature data recorded in the step 1 into the first-order polynomial model with the zero offset changing along with the temperature obtained by calculation in the step 2 to obtain gyroscope output data;
and 4, training the network parameters by taking the gyroscope output data as sample input of the RBF neural network model to obtain a group of trained networks, and performing temperature compensation on the resonant gyroscope based on the RBF neural network model.
Further, the specific steps of step 1 include:
(1) performing temperature test at 20-35 deg.C for 20 hr, sampling gyroscope output at 250Hz
(2) After the data acquisition is finished, the gyro data and the temperature data are subjected to average smoothing processing for 100 seconds due to the excessive number of samples, namely, the average number of the data of each 25000 sampling points is taken as the gyro output and the temperature in the period of time.
Moreover, the first-order polynomial model of the zero offset variation with temperature in the step 2 is specifically:
Figure BDA0003185933200000021
G0＝k0+k1T+k2T2+...+knTn
in the formula: g0Is the gyro output, T is the ambient temperature,
Figure BDA0003185933200000022
is a fitting coefficient determined by least squares fitting.
Further, the specific steps of step 4 include:
(1) initializing neural network parameters, and giving values of eta and alpha and a value of iteration termination precision epsilon;
(2) calculating the value of the root mean square error RMS output by the network, if the RMS is less than or equal to epsilon, ending the training, otherwise, entering the step (3);
(3) carrying out iterative calculation of the weight, the central vector and the base width vector;
(4) and (4) returning to the step (2).
Moreover, the step 4, the step (1), comprises the following specific steps:
determining a network input vector X ═ X1,x2,…,xn]T；
② initializing central vector C of each neuron of hidden layerj＝[cj1,cj2,...,cjm]TThe K-means clustering method is generally used for solving；
Initializing hidden layer to output layer weight vector W ═ W1,w2,...,wm]Fitting and solving by using a least square method;
and fourthly, obtaining the initial value of the RBF network center parameter based on the above:
Figure BDA0003185933200000031
wherein, p is the total number of neurons in the hidden layer, j is 1, 2., p, maxi, mini are the maximum value and the minimum value of all input information of the ith characteristic in the training set respectively;
initializing the base width vector B of the networkj＝[bj1,bj2,...,bjm]TThe width vector influences the action range of the neuron on the input information, and the calculation method is as follows:
Figure BDA0003185933200000032
wherein, bfIn order to adjust the width coefficient, the value is less than 1, which is beneficial to improving the local response capability of the RBF neural network;
moreover, the calculation formula of the step 4, the step (2) is as follows:
Figure BDA0003185933200000033
moreover, the calculation formula of the step 4 and the step (3) is as follows:
Figure BDA0003185933200000034
Figure BDA0003185933200000035
Figure BDA0003185933200000036
wherein, cjm(t) is the tuning weight between the kth output neuron and the jth hidden layer neuron at the time of the tth iterative computation; bjm(t) and wkj(t) is the center vector and the base width vector of the jth hidden layer neuron for the ith input neuron at the time of the t iteration; eta is a learning factor;
e is an evaluation function of the RBF neural network:
Figure BDA0003185933200000041
wherein, OlkIs the expected output value of the kth output neuron at the ith input sample; y islkThe net output value of the kth output neuron at the ith input sample is obtained.
The invention has the advantages and beneficial effects that:
the invention considers that the RBF neural network model is adopted to compensate the temperature error of the resonant gyroscope and is compared with the first-order polynomial model compensation, thereby proving the effectiveness of the RBF neural network model in the application of the temperature error compensation of the resonant gyroscope.
Drawings
FIG. 1 is a block diagram of the RBF neural network of the present invention;
FIG. 2 is a graph comparing the output of a gyroscope after first-order polynomial compensation in accordance with the present invention;
FIG. 3 is a graph comparing the compensated gyro output of the RBF neural network of the present invention.
Detailed Description
The embodiments of the invention will be described in further detail below with reference to the accompanying drawings:
a resonant gyro temperature compensation method based on a neural network algorithm comprises the following steps:
step 1, carrying out a temperature test on a resonant gyroscope, and sampling the output of the resonant gyroscope;
the specific steps of the step 1 comprise:
(1) performing temperature test at 20-35 deg.C for 20 hr, sampling gyroscope output at 250Hz
(2) After the data acquisition is finished, the gyro data and the temperature data are subjected to average smoothing processing for 100 seconds due to the excessive number of samples, namely, the average number of the data of each 25000 sampling points is taken as the gyro output and the temperature in the period of time.
Step 2, carrying out comparative analysis, carrying out polynomial fitting on the gyro zero offset-temperature sample by using a least square method based on a polynomial model, and establishing a first-order polynomial model of which the zero offset changes along with the temperature;
the first-order polynomial model of the zero offset along with the temperature change in the step 2 specifically comprises the following steps:
Figure BDA0003185933200000051
G0＝k0+k1T+k2T2+...+knTn
in the formula: g0Is the gyro output, T is the ambient temperature,
Figure BDA0003185933200000052
is a fitting coefficient determined by least squares fitting.
And 3, substituting the gyroscope and the temperature data recorded in the step 1 into the first-order polynomial model with the zero offset changing along with the temperature obtained by calculation in the step 2 to obtain gyroscope output data:
G0＝33.74-339.17T
and 4, training the network parameters by taking the gyroscope output data as sample input of the RBF neural network model to obtain a group of trained networks, and performing temperature compensation on the resonant gyroscope based on the RBF neural network model.
The specific steps of the step 4 comprise:
(3) initializing neural network parameters, and giving values of eta and alpha and a value of iteration termination precision epsilon;
the step 4, the step (1), comprises the following specific steps:
determining a network input vector X ═ X1,x2,...,xn]T；
② initializing central vector C of each neuron of hidden layerj＝[cj1,cj2,...,cjm]TGenerally, a K-means clustering method is used for solving;
initializing hidden layer to output layer weight vector W ═ W1,w2,...,wm]Fitting and solving by using a least square method;
and fourthly, obtaining the initial value of the RBF network center parameter based on the above:
Figure BDA0003185933200000053
wherein, p is the total number of neurons in the hidden layer, j is 1, 2.. and p, max i, min i are respectively the maximum value and the minimum value of all input information of the ith characteristic in the training set;
initializing the base width vector B of the networkj＝[bj1,bj2,...,bjm]TThe width vector influences the action range of the neuron on the input information, and the calculation method is as follows:
Figure BDA0003185933200000061
wherein, bfIn order to adjust the width coefficient, the value is less than 1, which is beneficial to improving the local response capability of the RBF neural network;
(2) calculating the value of the root mean square error RMS output by the network, if the RMS is less than or equal to epsilon, finishing the training, otherwise, entering the step (3):
Figure BDA0003185933200000062
(3) carrying out iterative calculation of the weight, the central vector and the base width vector;
the calculation formula of the step 4 and the step (3) is as follows:
Figure BDA0003185933200000063
Figure BDA0003185933200000064
Figure BDA0003185933200000065
wherein, cjm(t) is the tuning weight between the kth output neuron and the jth hidden layer neuron at the time of the tth iterative computation; bjm(t) and wkj(t) is the center vector and the base width vector of the jth hidden layer neuron for the ith input neuron at the time of the t iteration; eta is a learning factor; e is an evaluation function of the RBF neural network:
Figure BDA0003185933200000066
wherein, OlkIs the expected output value of the kth output neuron at the ith input sample; y islkThe net output value of the kth output neuron at the ith input sample is obtained.
(4) And (4) returning to the step (2).
In this embodiment, a set of data is recorded by placing the gyroscope in an outdoor environment with naturally changing temperature, and the gyroscope data is subjected to temperature compensation by using a trained RBF neural network and a first-order polynomial of least square fitting, and the compensation effect is shown in fig. 2 and 3. Analysis data shows that the original gyro output standard deviation is 0.829 DEG/h, the gyro output standard deviation is 0.322 DEG/h after compensation based on the RBF neural network model, the gyro standard deviation is 0.371 DEG/h after compensation of the first-order polynomial model, the gyro output after compensation of the neural network is improved more than the polynomial compensation precision, the drift standard deviation is reduced by 61.16% after compensation, and the method has a certain engineering application value.
The working principle of the invention is as follows:
1. resonance gyroscope temperature error mechanism analysis
Under the action of the change of the elastic modulus of the material and the thermal stress, the relationship of the harmonic oscillator rigidity along with the change of the temperature can be expressed as follows:
K＝K0[1+(kt+λσaE0)(T-T0)]
in the formula: k, K0At temperatures T, T of harmonic oscillator0Stiffness in time; k is a radical oftIs the coefficient of the elastic modulus changing with the temperature; lambda [ alpha ]σThe proportionality coefficient of harmonic oscillator rigidity change caused by thermal stress; a is the coefficient of thermal expansion; e0Is the elastic modulus of the harmonic oscillator material at the temperature T. From this, the relationship between the resonance frequency and the temperature of the resonator is:
Figure BDA0003185933200000071
wherein f (T), f0At temperatures T, T of harmonic oscillator0The resonant frequency of time.
It is known that, when the temperature changes, the resonance frequency of the resonator changes, and the output accuracy of the resonance gyro decreases.
2. RBF neural network model
An Artificial Neural Network (ANN) is a Network formed by widely interconnecting processing units, has a strong nonlinear mapping capability, and is widely applied in the fields of pattern recognition, information processing, system modeling and the like due to its unique information processing capability. The RBF neural network has good capability of approximating any nonlinear function and expressing the inherent difficultly-analyzed regularity of the system, and has extremely high learning convergence rate.
The network structure of the RBF neural network is shown in fig. 1, and it is a three-layer feedforward network: the first layer is an input layer and consists of signal source nodes; the second layer is a hidden layer, the number of hidden units depends on the requirements of the described problems, and the transform function RBF of the hidden units is a nonlinear function with symmetrical centers, which is radially symmetrical and attenuated; the third layer is the output layer, which responds to the action of the input mode.
The RBF neural network specifically comprises the following working steps:
determining parameters to be solved by algorithm
1) Determining a network input vector X ═ X1,x2,...,xn]T；
2) Initializing neuron center vectors C of hidden layerj＝[cj1,cj2,...,cjm]TGenerally, a K-means clustering method is used for solving;
3) initializing hidden-layer-to-output-layer weight vector W ═ W1,w2,...,wm]Fitting and solving by using a least square method;
4) the initial value of the RBF network central parameter obtained based on the above is as follows:
Figure BDA0003185933200000081
wherein, p is the total number of neurons in the hidden layer, j is 1, 2.
5) Initializing the base width vector B of the networkj＝[bj1,bj2,...,bjm]TThe width vector influences the action range of the neuron on the input information, and the calculation method is as follows:
Figure BDA0003185933200000082
wherein, bfThe value of the width modulation coefficient is less than 1, which is beneficial to improving the local response capability of the RBF neural network
(II) calculating the output value h of the jth neuron of the hidden layerj
H＝[h1,h2,...,hm]TIs a radial basis vector, whichMiddle hjFor the gaussian basis function:
Figure BDA0003185933200000083
in the formula: i | · | | represents the euclidean norm; cj＝[cj1,cj2,...,cjm]TIs the central vector of the jth node of the network; b ═ B1,b2,...,bm]TIs a vector of the base width of the network, bjThe larger the hidden layer has, the larger the range of influence on the input vector, and the better the smoothness between neurons.
(III) computing the output Y of the output layer neurons
Y＝[y1,y2,...,ym]T
Figure BDA0003185933200000091
Wherein, wkjIs the weight between the kth neuron of the output layer and the jth neuron of the hidden layer.
(iv) weight vector W ═ W1,w2,...,wm]Is calculated iteratively
The RBF neural network weight vector training method is a gradient descent method. The parameters of the center vector, the base width vector and the weight vector are adaptively adjusted to the optimal values through learning, and the algorithm is as follows:
Figure BDA0003185933200000092
Figure BDA0003185933200000093
Figure BDA0003185933200000094
wherein, cjm(t) is the tuning weight between the kth output neuron and the jth hidden layer neuron at the time of the tth iterative computation; bjm(t) and wkj(t) is the center vector and the base width vector of the jth hidden layer neuron for the ith input neuron at the time of the t iteration; eta is a learning factor; e is an evaluation function of the RBF neural network:
Figure BDA0003185933200000095
wherein, OlkIs the expected output value of the kth output neuron at the ith input sample; y islkThe net output value of the kth output neuron at the ith input sample is obtained.
It should be emphasized that the examples described herein are illustrative and not restrictive, and thus the present invention includes, but is not limited to, those examples described in this detailed description, as well as other embodiments that can be derived from the teachings of the present invention by those skilled in the art and that are within the scope of the present invention.

Claims (7)

1. A resonance gyro temperature compensation method based on a neural network algorithm is characterized in that: the method comprises the following steps:
step 1, carrying out a temperature test on a resonant gyroscope, and sampling the output of the resonant gyroscope;
step 2, carrying out comparative analysis, carrying out polynomial fitting on the gyro zero offset-temperature sample by using a least square method based on a polynomial model, and establishing a first-order polynomial model of which the zero offset changes along with the temperature;
step 3, substituting the gyroscope and the temperature data recorded in the step 1 into the first-order polynomial model with the zero offset changing along with the temperature obtained by calculation in the step 2 to obtain gyroscope output data;
and 4, training the network parameters by taking the gyroscope output data as sample input of the RBF neural network model to obtain a group of trained networks, and performing temperature compensation on the resonant gyroscope based on the RBF neural network model.
2. The method for compensating the temperature of the resonant gyroscope based on the neural network algorithm according to claim 1, wherein the method comprises the following steps: the specific steps of the step 1 comprise:
(1) performing temperature test at 20-35 deg.C for 20 hr, sampling gyroscope output at 250Hz
(2) After the data acquisition is finished, the gyro data and the temperature data are subjected to average smoothing processing for 100 seconds due to the excessive number of samples, namely, the average number of the data of each 25000 sampling points is taken as the gyro output and the temperature in the period of time.
3. The method for compensating the temperature of the resonant gyroscope based on the neural network algorithm according to claim 1, wherein the method comprises the following steps: the first-order polynomial model of the zero offset along with the temperature change in the step 2 specifically comprises the following steps:
Figure FDA0003185933190000011
G0＝k0+k1T+k2T2+...+knTn
in the formula: g0Is the gyro output, T is the ambient temperature,
Figure FDA0003185933190000012
is a fitting coefficient determined by least squares fitting.
4. The method for compensating the temperature of the resonant gyroscope based on the neural network algorithm according to claim 1, wherein the method comprises the following steps: the specific steps of the step 4 comprise:
(1) initializing neural network parameters, and giving values of eta and alpha and a value of iteration termination precision epsilon;
(2) calculating the value of the root mean square error RMS output by the network, if the RMS is less than or equal to epsilon, ending the training, otherwise, entering the step (3);
(3) carrying out iterative calculation of the weight, the central vector and the base width vector;
(4) and (4) returning to the step (2).
5. The method for compensating the temperature of the resonant gyroscope based on the neural network algorithm, according to claim 4, is characterized in that: the step 4, the step (1), comprises the following specific steps:
determining a network input vector X ═ X1,x2,...,xn]T；
② initializing central vector C of each neuron of hidden layerj＝[cj1,cj2,...,cjm]TGenerally, a K-means clustering method is used for solving;
initializing hidden layer to output layer weight vector W ═ W1,w2,...,wm]Fitting and solving by using a least square method;
and fourthly, obtaining the initial value of the RBF network center parameter based on the above:
Figure FDA0003185933190000021
wherein, p is the total number of neurons in the hidden layer, j is 1, 2., p, maxi, mini are the maximum value and the minimum value of all input information of the ith characteristic in the training set respectively;
initializing the base width vector B of the networkj＝[bj1,bj2,...,bjm]TThe width vector influences the action range of the neuron on the input information, and the calculation method is as follows:
Figure FDA0003185933190000022
wherein, bfIn order to adjust the width coefficient, the value is less than 1, which is beneficial to improving the local response capability of the RBF neural network.
6. The method for compensating the temperature of the resonant gyroscope based on the neural network algorithm, according to claim 4, is characterized in that: the calculation formula of the step 4 and the step (2) is as follows:
Figure FDA0003185933190000031
7. the method for compensating the temperature of the resonant gyroscope based on the neural network algorithm, according to claim 4, is characterized in that: the calculation formula of the step 4 and the step (3) is as follows:
Figure FDA0003185933190000032
Figure FDA0003185933190000033
Figure FDA0003185933190000034
wherein, cjm(t) is the tuning weight between the kth output neuron and the jth hidden layer neuron at the time of the tth iterative computation; bjm(t) and wkj(t) is the center vector and the base width vector of the jth hidden layer neuron for the ith input neuron at the time of the t iteration; eta is a learning factor;
e is an evaluation function of the RBF neural network:
Figure FDA0003185933190000035
wherein, OlkIs the expected output value of the kth output neuron at the ith input sample; y islkThe net output value of the kth output neuron at the ith input sample is obtained.
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