基于相关证据推理规则的激光惯组健康评估

doi:10.7527/S1000-6893.2023.29453

Abstract

Abstract:

The Laser Inertial Measurement Unit （LIMU） is an important navigation unit for the complex equipment system， and its good health state is of great significance for ensuring safe and stable operation of the system. In the health assessment of LIMU， there exist the problems of imperfect assessment indicator system， inconsistent assessment framework， dependent assessment indicators and uncertain parameters of assessment model. Based on the analysis of working mechanism of LIMU， a health assessment indicator system is constructed， and a health assessment method of LIMU is proposed based on the Evidential Reasoning Rule with Dependent Evidence （ERR-DE）. Firstly， the concept of transformation matrix is proposed to achieve unified transformation of different assessment frameworks. Secondly， the coefficient of the variation-based weighting method is used to determine evidence weights， and the distance-based method is employed to determine evidence reliabilities. Then， based on the evidence reliability， a mechanism to determine the aggregation sequence of evidences is proposed， and an evidence dependence analysis method is proposed based on the Relative Total Dependence Coefficient （RTDC）. Based on the Evidential Reasoning Rule （ERR）， the ERR-DE is proposed. Furthermore， a parameter optimization model is constructed to determine the optimal assessment parameters and improve the assessment accuracy. The assessment algorithm is further summarized. Finally， the effectiveness of the proposed method is verified through a health assessment case study and comparative studies on a certain type of LIMU.

Key words: evidential reasoning rule, laser inertial measurement unit, health assessment, evidence dependence, parameter optimization

CLC Number:

V241.5

Shuaiwen TANG, You CAO, Peng ZHANG, Jiang JIANG. Health assessment of LIMU based on evidential reasoning rule with dependent evidence[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(12): 329453.

Figures/Tables 37

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig. 9

Table 1

Assessment grades and referential values of drift coefficients

参考值	小	中	大
$K 0 X$ /（（°）·h^-1）	-0.02	0	0.02
$K 0 Y$ /（（°）·h^-1）	0	0.03	0.06
$K 0 Z$ /（（°）·h^-1）	-0.04	-0.02	0
$K 1 X$ /（10^-6（"）·s^-1）	1	5	10
$K 1 Y$ /（10^-6（"）·s^-1）	2	10	20
$K 1 Z$ /（10^-6（"）·s^-1）	-5	0	5
$D 0 X$ /（10^-4g）	-9	-7	-5
$D 0 Y$ /（10^-3g）	6	7.5	9
$D 0 Z$ /（10^-3g）	2.3	2.4	2.5
$D 1 X$ /（s^-1·g^-1）	-0.8	0	0.8
$D 1 Y$ /（s^-1·g^-1）	-0.2	0	0.2
$D 1 Z$ /（s^-1·g^-1）	-0.2	0	0.2

Table 1

Table 2

Assessment grades and referential values of light intensity voltages

参考值	很弱	弱	中等	强	很强
$L X$ / V	-4.3	-4.26	-4.22	-4.18	-4.15
$L Y$ / V	-4.4	-4.3	-4.2	-4.1	-4
$L Z$ / V	-3.7	-3.67	-3.65	-3.62	-3.6

Table 2

Table 3

Assessment grades and referential values of temperature voltages

参考值	弱	中等	强
$T X$ / V	1.3	1.5	1.7
$T Y$ / V	1.3	1.5	1.7
$T Z$ / V	1.3	1.5	1.7

Table 3

Table 4

Fig.10

Fig.11

Fig.12

Table 5

Distance dependence of health indicators of LIMU

距离相关性	结果	距离相关性	结果	距离相关性	结果
$C (K 0 X, K 1 X)$	0.941 1	$C (K 0 Z, K 1 Z)$	0.693 9	$C (D 0 Y, D 1 Y)$	0.544 4
$C (K 0 X, L X)$	0.958 3	$C (K 0 Z, L Z)$	0.859 2	$C (D 0 Y, T Y)$	0.969 8
$C (K 1 X, L X)$	0.919 1	$C (K 1 Z, L Z)$	0.692 7	$C (D 1 Y, T Y)$	0.537 9
$C (K 0 Y, K 1 Y)$	0.897 0	$C (D 0 X, D 1 X)$	0.973 6	$C (D 0 Z, D 1 Z)$	0.602 5
$C (K 0 Y, L Y)$	0.900 2	$C (D 0 X, T X)$	0.981 4	$C (D 0 Z, T Z)$	0.947 4
$C (K 1 Y, L Y)$	0.933 9	$C (D 1 X, T X)$	0.974 1	$C (D 1 Z, T Z)$	0.624 5

Table 5

Fig.13

Fig.14

Fig.15

Table 6

Constraints on referential values of drift coefficients

约束	小	中	大
$K 0 X$ /（（°）/h）	［-0.03，-0.01］	［-0.01，0.01］	［0.01，0.03］
$K 0 Y$ /（（°）/h）	［-0.01，0.01］	［0.01，0.05］	［0.05，0.07］
$K 0 Z$ /（（°）/h）	［-0.05，-0.03］	［-0.03，-0.01］	［-0.01，0.01］
$K 1 X$ /（10^-6（"）·s^-1）	［0，3］	［3，7］	［7，12］
$K 1 Y$ /（10^-6（"）·s^-1）	［0，8］	［8，15］	［15，30］
$K 1 Z$ /（10^-6（"）·s^-1）	［-6，-3］	［-3，3］	［3，6］
$D 0 X$ /（10^-4g）	［-10，-8］	［-8，-6］	［-6，-4］
$D 0 Y$ /（10^-3g）	［0，7］	［7，8］	［8，10］
$D 0 Z$ /（10^-3g）	［0，2.35］	［2.35，2.45］	［2.45，2.55］
$D 1 X$ /（s^-1·g^-1））	［-1，-0.5］	［-0.5，0.5］	［0.5，1］
$D 1 Y$ /（s^-1·g^-1））	［-0.3，-0.1］	［-0.1，0.1］	［0.1，0.3］
$D 1 Z$ /（s^-1·g^-1））	［-0.3，-0.1］	［-0.1，0.1］	［0.1，0.3］

Table 6

Table 7

Constraints on referential values of light intensity voltages

约束	很弱	弱	中等	强	很强
$L X$ /V	［-4.32，-4.28］	［-4.28，-4.24］	［-4.24，-4.2］	［-4.2，-4.16］	［-4.16，-4.12］
$L Y$ /V	［-4.45，-4.35］	［-4.35，-4.25］	［-4.25，-4.15］	［-4.15，-4.05］	［-4.05，-3.95］
$L Z$ /V	［-3.72，-3.68］	［-3.68，-3.66］	［-3.66，-3.64］	［-3.64，-3.61］	［-3.61，-3.58］

Table 7

Table 8

Constraints on referential values of temperature voltages

约束	弱	中等	强
$T X$ /V	［1.2，1.4］	［1.4，1.6］	［1.6，1.8］
$T Y$ /V	［1.2，1.4］	［1.4，1.6］	［1.6，1.8］
$T Z$ /V	［1.2，1.4］	［1.4，1.6］	［1.6，1.8］

Table 8

Table 9

Optimal weights of intermediate indicators

指标	$X L G$	$Y L G$	$Z L G$	$X Q F A$	$Y Q F A$	$Z Q F A$
权重	0.263 3	0.157 0	0.196 3	0.1531	0.05	0.180 3

Table 9

Table 10

Table 11

Optimal referential values of drift coefficients

参考值	小	中	大
$K 0 X$ /（（°）·h^-1）	-0.018 1	0.006 8	0.014 4
$K 0 Y$ /（（°）·h^-1）	-7×10^-5	0.027 3	0.059 3
$K 0 Z$ /（（°）·h^-1）	-0.04	-0.023 9	-0.000 6
$K 1 X$ /（10^-6（"）·s^-1）	1.78	5.27	9.5
$K 1 Y$ /（10^-6（"）·s^-1）	3.57	11.3	22.5
$K 1 Z$ /（10^-6（"）·s^-1）	-4.42	1.84	4.31
$D 0 X$ /（10^-4g）	-8.94	-7.09	-5.03
$D 0 Y$ /（10^-3g）	3.5	7.5	8.9
$D 0 Z$ /（10^-3g）	1.2	2.4	2.5
$D 1 X$ /（s^-1·g^-1）	-0.73	0.14	0.70
$D 1 Y$ /（s^-1·g^-1）	-0.19	0.02	0.21
$D 1 Z$ /（s^-1·g^-1）	-0.14	0.01	0.18

Table 11

Table 12

Optimal referential values of light intensity voltages

参考值	很弱	弱	中等	强	很强
$L X$ /V	-4.3	-4.26	-4.22	-4.18	-4.14
$L Y$ /V	-4.4	-4.3	-4.2	-4.1	-4
$L Z$ /V	-3.7	-3.67	-3.65	-3.625	-3.595

Table 12

Table 13

Optimal referential values of temperature voltages

参考值	弱	中等	强
$T X$ /V	1.301 2	1.498 7	1.700 4
$T Y$ /V	1.300 8	1.498 6	1.699 6
$T Z$ /V	1.300 6	1.496 4	1.694 8

Table 13

Fig.16

Table 14

Assessment grades and referential values of light intensity voltages

参考值	弱	中等	强
$L X$ /V	-4.275	-4.22	-4.165
$L Y$ /V	-4.35	-4.2	-4.05
$L Z$ /V	-3.685	-3.65	-3.61

Table 14

Table 15

Constraints on referential values of light intensity voltages

约束	弱	中等	强
$L X$ /V	［-4.3，-4.25］	［-4.25，-4.2］	［-4.2，-4.15］
$L Y$ /V	［-4.4，-4.3］	［-4.3，-4.1］	［-4.1，-4］
$L Z$ /V	［-3.7，-3.67］	［-3.67，-3.63］	［-3.63，-3.6］

Table 15

Fig.17

Table 16

Fig.18

Table 17

Fig.19

Table 18

References 31

1	ZHOU Z J， NING P Y， WANG J， et al. An evidential reasoning rule-based quality state assessment method of complex systems considering feature selection［J］. IEEE Transactions on Instrumentation and Measurement， 2023， 72： 2510513.
2	CHEN L Y， ZHOU Z J， HU C H， et al. Performance evaluation of complex systems using evidential reasoning approach with uncertain parameters［J］. Chinese Journal of Aeronautics， 2021， 34（1）： 194-208.
3	ZHURAVLEV V P， PERELVAEV S E， BODUNOV B P， et al. New-generation small-size solid-state wave gyroscope for strapdown inertial navigation systems of unmanned aerial vehicle［C］∥2019 26th Saint Petersburg International Conference on Integrated Navigation Systems （ICINS）. Piscataway： IEEE Press， 2019： 1-3.
4	邵世纲，杨泽萱，邢冠楠，等. 国外主要战略导弹系列化发展及技术共用研究［J］. 宇航总体技术， 2017， 1（3）： 24-32.
	SHAO S G， YANG Z X， XING G N， et al. Research on serialization and technology sharing of foreign major strategic missiles［J］. Astronautical Systems Engineering Technology， 2017， 1（3）： 24-32 （in Chinese）.
5	谢冉. 复杂系统建模方法综述［J］. 现代防御技术， 2020， 48（3）： 31-36， 68.
	XIE R. Survey of complex system modeling methods［J］. Modern Defence Technology， 2020， 48（3）： 31-36， 68 （in Chinese）.
6	李永满. 某型激光陀螺捷联惯组测试系统设计［D］. 哈尔滨：哈尔滨工业大学， 2013.
	LI Y M. The test system design on the measurement unit of laser gyro strapdown inertial［D］. Harbin： Harbin Institute of Technology， 2013 （in Chinese）.
7	董春梅，任顺清，陈希军，等. 激光陀螺捷联惯导系统的模观测标定方法［J］. 红外与激光工程， 2018， 47（9）： 0917007.
	DONG C M， REN S Q， CHEN X J， et al. Calibration method for the laser gyro strapdown inertial navigation system based on norm-observation［J］. Infrared and Laser Engineering， 2018， 47（9）： 0917007 （in Chinese）.
8	王堃，徐兵华，孟凡军. 激光捷联惯组失效模式分析及性能评估方法研究［J］. 航空精密制造技术， 2020， 56（6）： 11-14.
	WANG K， XU B H， MENG F J. Failure mode analysis and performance evaluation of laser strapdown inertial unit［J］. Aviation Precision Manufacturing Technology， 2020， 56（6）： 11-14 （in Chinese）.
9	王易南，闫杰. 基于卫星和星敏感器的冗余激光惯组在轨标定［J］. 飞行器测控学报， 2016， 35（5）： 358-364.
	WANG Y N， YAN J. On-orbit calibration method for redundant inertial measurement units by satellite and star sensors［J］. Journal of Spacecraft TT&C Technology， 2016， 35（5）： 358-364 （in Chinese）.
10	王子超，范会迎，谢元平，等. 捷联惯导系统复杂误差参数系统级标定方法［J］. 红外与激光工程， 2022， 51（7）： 3788/IRLA20210499.
	WANG Z C， FAN H Y， XIE Y P， et al. System-level calibration method for complex error coefficients of strapdown inertial navigation system［J］. Infrared and Laser Engineering， 2022， 51（7）： 3788/IRLA20210499 （in Chinese）.
11	罗睿，李鹏，于玲燕. 一种考虑加表不对称误差的冗余惯组标定方法［J］. 中国惯性技术学报， 2023， 31（2）： 114-120.
	LUO R， LI P， YU L Y. A calibration method for redundant IMU considering accelerometer asymmetric error［J］. Journal of Chinese Inertial Technology， 2023， 31（2）： 114-120 （in Chinese）.
12	吴克雄，王振华. 基于专家系统和数据驱动的健康评估分析方法［J］. 黑龙江科学， 2019， 10（16）： 64-65.
	WU K X， WANG Z H. Health assessment and analysis method based on expert system and data driven［J］. Heilongjiang Science， 2019， 10（16）： 64-65 （in Chinese）.
13	陈雷雨，周志杰，唐帅文，等. 融合多元信息的武器装备性能评估方法［J］. 系统工程与电子技术， 2020， 42（7）： 1527-1533.
	CHEN L Y， ZHOU Z J， TANG S W， et al. Weapon equipment performance evaluation method with multi-information fusion［J］. Systems Engineering and Electronics， 2020， 42（7）： 1527-1533 （in Chinese）.
14	WANG J， ZHOU Z J， HU C H， et al. An evidential reasoning rule considering parameter uncertainty［J］. IEEE Transactions on Aerospace and Electronic Systems， 2022， 58（2）： 1391-1404.
15	YANG J B， XU D L. Evidential reasoning rule for evidence combination［J］. Artificial Intelligence， 2013， 205： 1-29.
16	周志杰，唐帅文，胡昌华，等. 证据推理理论及其应用［J］. 自动化学报， 2021， 47（5）： 970-984.
	ZHOU Z J， TANG S W， HU C H， et al. Evidential reasoning theory and its applications［J］. Acta Automatica Sinica， 2021， 47（5）： 970-984 （in Chinese）.
17	ZHOU M， LIU X B， CHEN Y W， et al. Evidential reasoning rule for MADM with both weights and reliabilities in group decision making［J］. Knowledge-Based Systems， 2018， 143： 142-161.
18	KONG G L， XU D L， YANG J B， et al. Evidential reasoning rule-based decision support system for predicting ICU admission and in-hospital death of trauma［J］. IEEE Transactions on Systems， Man， and Cybernetics： Systems， 2021， 51（11）： 7131-7142.
19	ZHANG B C， ZHANG A X， HU G Y， et al. Reliability assessment of train control and management system based on evidential reasoning rule and covariance matrix adaptation evolution strategy algorithm［J］. ISA Transactions， 2021， 116： 129-138.
20	TANG S W， ZHOU Z J， HU C H， et al. A new evidential reasoning rule-based safety assessment method with sensor reliability for complex systems［J］. IEEE Transactions on Cybernetics， 2022， 52（5）： 4027-4038.
21	YANG J B. Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties［J］. European Journal of Operational Research， 2001， 131（1）： 31-61.
22	唐帅文，周志杰，姜江，等. 考虑扰动的无人机集群协同态势感知一致性评估［J］. 航空学报， 2020， 41（S2）： 724233.
	TANG S W， ZHOU Z J， JIANG J， et al. Consistency assessment of cooperative situation awareness of UAV cluster considering disturbance［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（S2）： 724233 （in Chinese）.
23	LIU P D， LI Y， ZHANG X H， et al. A multiattribute group decision-making method with probabilistic linguistic information based on an adaptive consensus reaching model and evidential reasoning［J］. IEEE Transactions on Cybernetics， 2023， 53（3）： 1905-1919.
24	ZHAO F J， ZHOU Z J， HU C H， et al. A new evidential reasoning-based method for online safety assessment of complex systems［J］. IEEE Transactions on Systems， Man， and Cybernetics： Systems， 2018， 48（6）： 954-966.
25	DENG J X， DENG Y， CHEONG K H. Combining conflicting evidence based on Pearson correlation coefficient and weighted graph［J］. International Journal of Intelligent Systems， 2021， 36（12）： 7443-7460.
26	YAO S Y， YANG J B， XU D L， et al. Probabilistic modeling approach for interpretable inference and prediction with data for sepsis diagnosis［J］. Expert Systems with Applications， 2021， 183： 115333.
27	ZHOU J， SU X Y， QIAN H. Research on fusion of dependent evidence based on Kendall correlation coefficient［C］∥Proceedings of the 4th International Conference on Computer Science and Application Engineering. New York： ACM， 2020： 1-5.
28	JIANG W. A correlation coefficient for belief functions［J］. International Journal of Approximate Reasoning， 2018， 103： 94-106.
29	YAGER R R. On the fusion of non-independent belief structures［J］. International Journal of General Systems， 2009， 38（5）： 505-531.
30	ZHANG P， ZHOU Z J， TANG S W， et al. On the evidential reasoning rule for dependent evidence combination［J］. Chinese Journal of Aeronautics， 2023， 36（5）： 306-327.
31	SZÉKELY G J， RIZZO M L， BAKIROV N K. Measuring and testing dependence by correlation of distances［J］. The Annals of Statistics， 2007， 35（6）： 2769-2794.

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Health assessment of LIMU based on evidential reasoning rule with dependent evidence

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