Long short-term memory network of machine learning for compensating temperature error of a fiber optic gyroscope independent of the temperature sensor

Yin Cao; Wenyuan Xu; Bo Lin; Yuang Zhu; Fanchao Meng; Xiaoting Zhao; Jinmin Ding; Shuqin Lou; Xin Wang; Jingwen He; Xinzhi Sheng; Sheng Liang

doi:10.1364/AO.471762

Applied Optics
Vol. 61,
Issue 28,
pp. 8212-8222
(2022)
•https://doi.org/10.1364/AO.471762

Long short-term memory network of machine learning for compensating temperature error of a fiber optic gyroscope independent of the temperature sensor

Yin Cao, Wenyuan Xu, Bo Lin, Yuang Zhu, Fanchao Meng, Xiaoting Zhao, Jinmin Ding, Shuqin Lou, Xin Wang, Jingwen He, Xinzhi Sheng, and Sheng Liang

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Yin Cao, Wenyuan Xu, Bo Lin, Yuang Zhu, Fanchao Meng, Xiaoting Zhao, Jinmin Ding, Shuqin Lou, Xin Wang, Jingwen He, Xinzhi Sheng, and Sheng Liang, "Long short-term memory network of machine learning for compensating temperature error of a fiber optic gyroscope independent of the temperature sensor," Appl. Opt. 61, 8212-8222 (2022)

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Related Topics
Table of Contents Category
- Fiber Optics, Fiber Sensors, and Optical Communications
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: July 28, 2022
- Revised Manuscript: August 19, 2022
- Manuscript Accepted: September 1, 2022
- Published: September 21, 2022

Abstract

We present an artificial intelligence compensation method for temperature error of a fiber optic gyroscope (FOG). The difference from the existing methods is that the compensation model finally determined by this method only uses the FOG’s data to complete the regression prediction of the temperature error and eliminate the dependency on the temperature sensor. In the experimental stage, the proposed method performs temperature experiments with three varying trends of temperature heating, holding, and cooling and obtains sufficient output data sets of the FOG. Taking the output time series of the FOG as the input sample and based on the long short-term memory network of machine learning, the training, validation, and test of the model are completed. From the two perspectives of network learning ability and the improvement degree of the FOG’s performance, four indicators, including root mean square error, error cumulative distribution function, FOG bias stability, and Allan variance analysis are selected to evaluate the performance of the compensation model comprehensively. Compared with the existing methods using temperature information for prediction and compensation, the results show that the error compensation method without temperature information proposed can effectively improve the accuracy of the FOG and reduce the complexity of the compensation system. The work can also provide technical references for error compensation of other sensors.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Ref.	Data Utilization for Samples	Algorithm
[10]	(a) Temperature change rate	LSTM
[11]	(a) Temperature value	SVM (Support Vector Machine)
[12]	(a) Temperature value	BOA-GBDT (Bayesian optimization algorithm optimized gradient boosting tree)
[13]	(a) Temperature range; (b) temperature change rate; (c) effective refractive index; (d) angular velocity.	MLP (multilayer perceptron)
[14]	(a) Temperature value	RBF (radial basis function)
[15]	(a) Temperature value; (b) temperature change rate	ELM (extreme learning machine)
[16]	(a) Temperature value; (b) FOG’s output	LSTM
[17]	(a) Temperature value; (b) temperature change rate	RBF (radial basis function)
[18]	(a) Temperature value	BAS-GSA-HKSVM (beetle antennae search algorithm-gravitational search algorithm-hybrid kernel-based support vector machine)
[19]	(a) Temperature value; (b) temperature difference value	MLP (multilayer perceptron)
[20]	(a) Temperature value; (b) temperature change rate	EEMD-SVM (ensemble empirical mode decomposition-spport vector machine)
[21]	(a) Temperature change rate	LWT-FLP-ENN (lifting Wavelet transform-forward linear prediction -Elman neural network)
[22]	(a) Temperature difference value	EEMD-ELM (ensemble empirical mode decomposition-extreme learning machine)
[23]	(a) Temperature value	LS-SVR-AFSA (least square-support vector machine-artificial fish swarm algorithm)
[24]	(a) Temperature value; (b) temperature change rate; (c) temperature gradient	SVR (support vector regressor)
This Work	(a) FOG’s output	LSTM

	Before Compensating	Compensated with Temperature Information	Compensated without Temperature Information
$S (^{\circ} / h)$	0.0476	0.0094	0.0049
$c$	——	5.05	9.68

		Compensated with Temperature Information		Compensated without Temperature Information
	Before Compensating	Noise	Descend	Noise	Descend
$Q$ (°)	$- 1.3923 \times 10^{- 6}$	$- 8.9742 \times 10^{- 7}$	35.54%	$7.6064 \times 10^{- 7}$	45.37%
$N_{A} (^{\circ} / h^{1 / 2})$	$1.4752 \times 10^{- 3}$	$1.3946 \times 10^{- 3}$	5.47%	$1.1429 \times 10^{- 3}$	22.53%
$B$ ( $^{\circ} / h$ )	$- 1.2764 \times 10^{- 2}$	$- 9.6566 \times 10^{- 3}$	24.34%	$- 1.3308 \times 10^{- 3}$	89.57%
$K_{R} (^{\circ} / h^{3 / 2})$	$4.6583 \times 10^{- 2}$	$3.2241 \times 10^{- 2}$	30.79%	$5.6341 \times 10^{- 3}$	87.91%
$R (^{\circ} / h^{2})$	$- 1.4028 \times 10^{- 2}$	$- 1.3954 \times 10^{- 3}$	90.05%	$- 2.4851 \times 10^{- 4}$	98.23%

Ref.	Data Utilization for Samples	Algorithm
[10]	(a) Temperature change rate	LSTM
[11]	(a) Temperature value	SVM (Support Vector Machine)
[12]	(a) Temperature value	BOA-GBDT (Bayesian optimization algorithm optimized gradient boosting tree)
[13]	(a) Temperature range; (b) temperature change rate; (c) effective refractive index; (d) angular velocity.	MLP (multilayer perceptron)
[14]	(a) Temperature value	RBF (radial basis function)
[15]	(a) Temperature value; (b) temperature change rate	ELM (extreme learning machine)
[16]	(a) Temperature value; (b) FOG’s output	LSTM
[17]	(a) Temperature value; (b) temperature change rate	RBF (radial basis function)
[18]	(a) Temperature value	BAS-GSA-HKSVM (beetle antennae search algorithm-gravitational search algorithm-hybrid kernel-based support vector machine)
[19]	(a) Temperature value; (b) temperature difference value	MLP (multilayer perceptron)
[20]	(a) Temperature value; (b) temperature change rate	EEMD-SVM (ensemble empirical mode decomposition-spport vector machine)
[21]	(a) Temperature change rate	LWT-FLP-ENN (lifting Wavelet transform-forward linear prediction -Elman neural network)
[22]	(a) Temperature difference value	EEMD-ELM (ensemble empirical mode decomposition-extreme learning machine)
[23]	(a) Temperature value	LS-SVR-AFSA (least square-support vector machine-artificial fish swarm algorithm)
[24]	(a) Temperature value; (b) temperature change rate; (c) temperature gradient	SVR (support vector regressor)
This Work	(a) FOG’s output	LSTM

	Before Compensating	Compensated with Temperature Information	Compensated without Temperature Information
$S (^{\circ} / h)$	0.0476	0.0094	0.0049
$c$	——	5.05	9.68

Step	Start $T$ (°C)	End $T$ (°C)	Variation Type	Duration (h)
1	Room $T$	−40	cooling	——
2	−40	−40	holding	2
3	−40	60	heating	2
4	60	60	holding	2
5	60	−40	cooling	2
6	−40	−40	holding	2
7	−40	60	heating	2
8	60	60	holding	2
9	60	−40	cooling	2
10	−40	−40	holding	2
11	−40	60	heating	2
12	60	room $T$	cooling	——

Abstract

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Equations (21)

Applied Optics