挠性陀螺EMD-ARIMA漂移模型设计与应用

蔡曜; 司玉辉; 王玉琢; 黄涛; 张亚静; 杨晓龙

doi:10.13700/j.bh.1001-5965.2022.0871

挠性陀螺EMD-ARIMA漂移模型设计与应用

doi: 10.13700/j.bh.1001-5965.2022.0871

西安航天精密机电研究所，西安 710100

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E-mail：615596667@qq.com

中图分类号: V241.5⁺59
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出版历程
- 收稿日期: 2022-10-30
- 录用日期: 2022-12-30
- 网络出版日期: 2023-02-27
- 整期出版日期: 2024-11-30

Design and application of EMD-ARIMA drift model for flexible gyro

Xi’an Aerospace Precision Mechatronics Institute，Xi’an 710100，China

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Corresponding author: E-mail：615596667@qq.com

摘要

摘要:
为降低挠性陀螺的漂移率，提高挠性陀螺的精度，基于经验模态分解（EMD）、求和自回归移动平均（ARIMA）2种信号处理工具，提出EMD-ARIMA漂移模型。设计野点剔除算子，避免EMD过程中出现过冲、欠冲问题；对本征模态函数（IMF）辨识进行讨论，制定各阶IMF的使用原则；设计自适应定阶寻优算子，避免依靠技术人员判读自相关图、偏自相关图进行ARIMA建模，实现对多个信号（或多阶IMF）进行EMD-ARIMA建模的批处理功能。将重构的拟合信号和原始信号进行对比。工程实践表明：最终重构的拟合信号较原始信号漂移率降低了12.8%；Allan方差各项误差源均降低，M_APE为3.6×10⁻³，R_MSE为5.1×10⁻³，残差趋于白噪声；漂移模型在挠性陀螺漂移建模中，具有同路重复性、两路一致性、不同个体通用性。
- 挠性陀螺 /
- 求和自回归移动平均模型 /
- 经验模态分解 /
- 野点剔除算子 /
- 自适应定阶寻优算子
Abstract:
In order to reduce the drift rate of the flexible gyro and improve the precision of the flexible gyro, EMD-ARIMA drift model was proposed based on empirical mode decomposition (EMD) and autoregressive integrated moving average (ARIMA) signal processing tools. The outfield removal operator is designed to avoid the overshoot and undershoot problems in the EMD process. The identification of the intrinsic mode function (IMF) is discussed, and the principles for the use of IMF at various levels are formulated. By depending on technical staff to interpret autocorrelation and partial autocorrelation graphs and to implement the batch processing function of EMD-ARIMA modeling for multiple signals (or multi-order IMFs), the adaptive order optimization operator is intended to avoid ARIMA modelling. Comparing the reconstructed fitting signal with the original signal, the engineering practice shows that the drift rate of the final reconstructed fitting signal is 12.8% lower than that of the original signal. All the error sources of Allan variance are reduced. Meanwhile, the M_APE is 3.6×10⁻³, and the R_MSE is 5.1×10⁻³. The drift model in flexible gyro drift modeling possesses the qualities of universality in many individuals, consistency in two ways, and repetition in one manner.
- flexible gyro /
- autoregressive integrated moving average model /
- empirical mode decomposition /
- outfield removal operator /
- adaptive order optimization operator

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图 1 野点剔除算子流程

Figure 1. Flow of outlier elimination operator

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图 2 EMD流程

Figure 2. Flow of EMD

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图 3 各阶IMF有效信息占比示意图

Figure 3. Schematic diagram of effective information ratio of each order of IMF

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图 4 自适应定阶寻优算子流程

Figure 4. Flow of adaptive order optimization operator

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图 5 EMD分解结果

Figure 5. Empirical mode decomposition results

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图 6 漂移序列对比

Figure 6. Drift sequence comparison

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图 7 Allan方差曲线

Figure 7. Allan variance curve

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图 8 实测序列与预测序列的对比

Figure 8. Comparison between measured sequence and predicted sequence

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表 1 各阶IMF对应的最优模型

Table 1. Optimal models corresponding to each order of IMF

${\text{IMF}}$阶数	p	d	q	A_IC	$ {\phi _1} $	$ {\phi _2} $	$ {\theta _1} $	$ \sigma _\varepsilon ^2 $	$ I_{\mathrm{MF}} $标准差	$ I_{\mathrm{MF}}^{{\mathrm{Fit}}} $标准差	M_APE	R_MSE
1	1	0	1	−12.9	−0.82	0	−1.00	2.4×10⁻⁶	1.6×10⁻³	1.2×10⁻⁵	1.2	1.6×10⁻³
2	2	0	0	−15.4	1.72	−0.88	0	2.1×10⁻⁷	2.4×10⁻³	5.3×10⁻⁴	2.4	2.5×10⁻³
3	2	0	0	−18.5	1.95	−0.99	0	9.0×10⁻⁹	3.1×10⁻³	2.6×10⁻³	5.2	3.4×10⁻³
4	2	0	0	−22.4	1.99	−1.00	0	1.8×10⁻¹⁰	3.0×10⁻³	2.9×10⁻³	2.5×10⁻¹	2.3×10⁻³
5	2	1	0	−32.3	2.00	−1.00	0	9.7×10⁻¹⁵	2.0×10⁻³	1.7×10⁻³	1.3	5.2×10⁻⁴
6	2	1	0	−37.4	2.00	−1.00	0	5.8×10⁻¹⁷	1.9×10⁻³	1.9×10⁻³	1.5×10⁻¹	9.9×10⁻⁵
7	2	0	0	−33.9	2.00	−1.00	0	1.8×10⁻¹⁵	1.7×10⁻³	1.7×10⁻³	5.1×10⁻²	1.3×10⁻⁵
8	2	1	0	−47.6	2.00	−1.00	0	2.1×10⁻²¹	2.4×10⁻³	2.4×10⁻³	3.9×10⁻³	2.4×10⁻⁶
9	2	1	0	−54.4	2.00	−1.00	0	2.3×10⁻²⁴	2.4×10⁻³	2.4×10⁻³	1.3×10⁻⁴	9.7×10⁻⁸

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表 2 量化对比汇总表

Table 2. Summary of quantitative comparison table

序列	标准差/ 10⁻³mV	漂移率/ ((°)·h⁻¹)	零偏不稳定性/ ((°)·h⁻¹)	角速率游走/ ((°)·h^−3/2)	速率斜坡/ ((°)·h⁻²)	M_APE	R_MSE
原始序列	7.8	0.78	20.5	1960	271000
A_R(1)模型拟合序列	2.2	0.22	5.0	468	64900	4.9×10⁻³	7.1×10⁻³
A_R(2)模型拟合序列	2.3	0.23	5.3	487	67500	4.9×10⁻³	7.0×10⁻³
EMD-ARIMA漂移序列	6.8	0.68	18.1	1020	75300	3.6×10⁻³	5.1×10⁻³

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表 3 实测序列与预测序列的量化对比汇总

Table 3. Summary of quantitative comparison between measured and predicted sequences

序列	均值/mV	标准差/mV	漂移率/((°)·h⁻¹)	零偏不稳定性/ ((°)·h⁻¹)	角速率游走/ ((°)·h^−3/2）	速率斜坡/ ((°)·h⁻²）	M_APE	R_MSE
实测序列	1.115	6.86×10⁻³	0.686	22.8	1990	276000
预测序列	1.121	2.84×10⁻³	0.284	3.71	151	9300	6.5×10⁻³	9.0×10⁻³

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表 4 EMD-ARIMA漂移模型信息汇总

Table 4. Summary of EMD-ARIMA drift model information

小时数	IMF总阶数	IMF阶数	p	d	q	$ {\phi _1} $	$ {\phi _2} $	$ {\theta _1} $	$ {\theta _2} $	$ {\theta _3} $	$ \sigma _\varepsilon ^2 $
第2小时	8	1	2	0	3	−0.50	−0.75	−0.53	−0.59	0.30	2.3×10⁻⁶
		2	2	0	0	1.75	−0.88	0	0	0	2.3×10⁻⁷
		3	2	0	0	1.95	−0.99	0	0	0	8.7×10⁻⁹
		4	2	0	0	1.99	−1.00	0	0	0	2.0×10⁻¹⁰
		5	2	1	0	2.00	−1.00	0	0	0	7.7×10⁻¹⁵
		6	2	1	0	2.00	−1.00	0	0	0	1.9×10⁻¹⁷
		7	2	1	0	2.00	−1.00	0	0	0	1.1×10⁻¹⁹
		8	2	1	0	2.00	−1.00	0	0	0	1.2×10⁻²²
第3小时	8	1	1	0	1	0.72	0	0.81	0	0	2.8×10⁻⁶
		2	2	0	0	1.73	−0.86	0	0	0	2.9×10⁻⁷
		3	2	0	0	1.95	−0.99	0	0	0	9.9×10⁻⁹
		4	2	0	0	1.99	−1.00	0	0	0	1.6×10⁻¹⁰
		5	2	1	0	2.00	−1.00	0	0	0	9.3×10⁻¹⁵
		6	2	1	0	2.00	−1.00	0	0	0	2.7×10⁻¹⁷
		7	2	1	0	2.00	−1.00	0	0	0	2.5×10⁻²⁰
		8	2	0	0	2.00	−1.00	0	0	0	2.1×10⁻¹⁸
第4小时	9	1	1	0	1	0.70	0	0.82	0	0	2.7×10⁻⁶
		2	2	0	0	1.75	−0.86	0	0	0	2.8×10⁻⁷
		3	2	0	0	1.96	−0.99	0	0	0	1.2×10⁻⁸
		4	2	1	0	1.99	−1.00	0	0	0	3.1×10⁻¹²
		5	2	1	0	2.00	−1.00	0	0	0	7.5×10⁻¹⁵
		6	2	1	0	2.00	−1.00	0	0	0	8.7×10⁻¹⁸
		7	2	1	0	2.00	−1.00	0	0	0	4.3×10⁻²⁰
		8	2	1	0	2.00	−1.00	0	0	0	2.4×10⁻²²
		9	2	1	0	2.00	−1.00	0	0	0	7.1×10⁻²⁷

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表 5 220024#Y路EMD-ARIMA漂移模型

Table 5. 220024# Y-channel EMD-ARIMA drift model

小时数	IMF总阶数	IMF阶数	p	d	q	$ {\phi _1} $	$ {\phi _2} $	$ {\theta _1} $	$ {\theta _2} $	$ {\theta _3} $	$ \sigma _\varepsilon ^2 $
1	8	1	1	0	3	−0.83	0	−0.82	0.46	0.32	2.8×10⁻⁶
		2	2	0	0	1.77	−0.91	0	0	0	2.4×10⁻⁷
		3	2	0	0	1.96	−0.99	0	0	0	5.7×10⁻⁹
		4	2	0	0	1.99	−1.00	0	0	0	1.2×10⁻¹⁰
		5	2	1	0	2.00	−1.00	0	0	0	3.2×10⁻¹⁵
		6	2	1	0	2.00	−1.00	0	0	0	6.2×10⁻¹⁸
		7	2	0	0	2.00	−1.00	0	0	0	6.5×10⁻¹⁶
		8	2	1	0	2.00	−1.00	0	0	0	5.6×10⁻²³

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表 6 210073#X路EMD-ARIMA漂移模型

Table 6. 210073# X-channel EMD-ARIMA drift model

小时数	IMF总阶数	IMF阶数	p	d	q	$ {\phi _1} $	$ {\phi _2} $	$ \sigma _\varepsilon ^2 $
1	10	1	2	0	0	0.05	−0.19	2.2×10⁻⁵
		2	2	0	0	1.70	−0.84	3.0×10⁻⁶
		3	2	0	0	1.94	−0.98	1.1×10⁻⁷
		4	2	0	0	1.99	−1.00	1.7×10⁻⁹
		5	2	1	0	2.00	−1.00	4.4×10⁻³
		6	2	0	0	2.00	−1.00	5.8×10⁻³
		7	2	0	0	2.00	−1.00	7.3×10⁻¹⁵
		8	2	0	0	2.00	−1.00	2.2×10⁻¹⁶
		9	2	0	0	2.00	−1.00	4.8×10⁻¹⁷
		10	2	1	0	2.00	−1.00	6.0×10⁻²⁴

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