基于FAST和Sobol指数法的雷达系统效能敏感性分析

doi:10.12305/j.issn.1001-506X.2024.02.20

Abstract

Abstract:

In order to rapidly improve the comprehensive efficiency of the air detection radar system at a low cost, the evaluation index system of the comprehensive efficiency is firstly establised, and then the establishment of the comprehensive effectiveness evaluation model is completed. Two global sensitivity analysis methods, including Fourier amplitudes sensitivity test (FAST) and Sobol index method based on variance principle, are selected to conduct sensitivity analysis on the established evaluation model from the perspectives of frequency domain and time domain respectively. In the sensitivity analysis based on FAST, the method of selecting the eigenfrequency set corresponding to the 21-dimensional input index is proposed. In the sensitivity analysis based on Sobol index method, the effects of the second-order and higher-order sensitivity indexes are considered. By comparing the analysis results of FAST and Sobol index method, it can be seen that the sensitivity analysis results obtained by the two methods have good consistency. Among them, power and frequency are the main influence indicators of the air detection radar, which can provide the reliability basis for the development and upgrade of the radar system.

Key words: radar system, effectiveness evaluation, sensitivity analysis, Fourier amplitudes sensitivity test (FAST), Sobol index method

CLC Number:

TP391.9

Tao HU, Liqun SHEN, Jingda ZHU, Chenghui SUN, Weifeng DONG. Sensitivity analysis of radar system effectiveness based on FAST and Sobol index method[J]. Systems Engineering and Electronics, 2024, 46(2): 561-569.

Figures/Tables 11

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References 31

1	HAN W , TANG Z Y , ZHU Z B . Method of target tracking with Doppler blind zone constraint[J]. Journal of Systems Engineering and Electronics, 2013, 24 (6): 889- 898. doi: 10.1109/JSEE.2013.00103
2	ACCARDO D , FASANO G , FORLENZA L , et al. Flight test of a radar-based tracking system for UAS sense and avoid[J]. IEEE Trans. Aerospace and Electronic Systems, 2013, 49 (2): 1139- 1160. doi: 10.1109/TAES.2013.6494404
3	王国恩, 李仙茂, 厉春生. 海上舰机综合雷达对抗侦察效能分析[J]. 电子信息对抗技术, 2016, 31 (6): 69- 75.
	WANG G E , LI X M , LI C S . Comprehensive radar countermeasure reconnaissance effectiveness analysis of the warship and aircraft on sea[J]. Electronic Information Warfare Technology, 2016, 31 (6): 69- 75.
4	滕俊, 郭万海, 崔超. 防空作战中相控阵雷达信息综合保障效能分析[J]. 舰船电子工程, 2011, 31 (8): 63-66, 75.
	TENG J , GUO W H , CUI C . Analysis of the phased array radar's integrated information support effectiveness in air defense[J]. Ship Electronic Engineering, 2011, 31 (8): 63-66, 75.
5	胡国庭, 李侠, 王万磊, 等. 地空导弹系统近方雷达情报保障效能评估[J]. 空军雷达学院学报, 2006, 20 (1): 5-7, 17.
	HU G T , LI X , WANG W L , et al. Assessment of intelligence support effectiveness of close-in radar for surface-to-air missile system[J]. Electronic Information Warfare Technology, 2006, 20 (1): 5-7, 17.
6	SALTELLI A . Making best use of model evaluations to compute sensitivity indices[J]. Computer Physics Communications, 2002, 145 (2): 280- 297. doi: 10.1016/S0010-4655(02)00280-1
7	BORGONOVO E , PECCATI L . Uncertainty and global sensitivity analysis in the evaluation of investment projects[J]. International Journal of Production Economics, 2005, 104 (1): 62- 73.
8	SONG X M , KONG F Z , ZHAN C S , et al. Parameter identification and global sensitivity analysis of Xin'anjiang model using meta-modeling approach[J]. Water Science and Engineering, 2013, 6 (1): 1- 17.
9	FREY H C , PATIL S R . Identification and review of sensitivity analysis methods[J]. Risk Analysis, 2002, 22 (3): 553- 578. doi: 10.1111/0272-4332.00039
10	MASSMANN C , HOLZMANN H . Analysis of the behavior of a rainfall-runoff model using three global sensitivity analysis methods evaluated at different temporal scales[J]. Journal of Hydrology, 2012, 475, 97- 110. doi: 10.1016/j.jhydrol.2012.09.026
11	CONNOR J D , SUMMERS D , REGAN C , et al. Sensitivity analysis in economic evaluation of payments for water and carbon ecosystem services[J]. Ecosystem Services, 2022, 54, 101416. doi: 10.1016/j.ecoser.2022.101416
12	LIU C , LIN D T , FAN J J , et al. Evaluation of housing price control policies based on a sensitivity analysis and nonstationary Markov chain simulation: empirical evidence from China[J]. Emerging Markets Finance and Trade, 2021, 57 (2): 311- 321. doi: 10.1080/1540496X.2018.1517644
13	WELI S S , VIGH L G . Blast reliability assessment and sensitivity analysis of steel MRFs equipped with NiTi SMA bolts[J]. Engineering Structures, 2023, 286, 116137. doi: 10.1016/j.engstruct.2023.116137
14	DENG G M , FAN D W , ZHANG B F , et al. Sensitivity analysis of large body of control parameters in machine learning control of a square-back Ahmed body[J]. Proceedings of the Royal Society A, 2023, 479 (2269): 20220280. doi: 10.1098/rspa.2022.0280
15	NAKAYAMA T , WANG Q , OKADERA T . Sensitivity analysis and parameter estimation of anthropogenic water uses for quantifying relation between groundwater overuse and water stress in Mongolia[J]. Ecohydrology & Hydrobiology, 2021, 21 (3): 490- 500.
16	MAMAT N , MOHD R S F , HAMZAH F B . Enhancement of water quality index prediction using support vector machine with sensitivity analysis[J]. Frontiers in Environmental Science, 2023, doi: 10.3389/fenvs.2022.1061835
17	李红祺. 随机平衡设计傅里叶振幅敏感性分析方法和拓展傅里叶振幅敏感性分析方法在陆面过程模式敏感性分析中的应用探索[J]. 物理学报, 2015, 64 (6): 403- 409.
	LI H Q . Applications of random balance design Fourier amplitude sensitivity test and extend Fourier amplitude sensitivity test in the parameter sensitivity analysis of land surface process model[J]. Acta Physica Sinica, 2015, 64 (6): 403- 409.
18	潘星, 张振宇, 张艳梅, 等. 基于Sobol敏感性分析的装备体系保障效能评估[J]. 系统工程与电子技术, 2021, 43 (2): 390- 398.
	PAN X , ZHANG Z Y , ZHANG Y M , et al. Equipment SoS support effectiveness evaluation based on Sobol sensitivity analy- sis[J]. System Engineering and Electronics, 2021, 43 (2): 390- 398.
19	MARTIN H K , STEFFEN P . Choosing the appropriate sensitivity analysis method for building energy model-based investigations[J]. Energy & Buildings, 2016, 130, 166- 176.
20	SONG Y , WEI T , EDUARD C , et al. Comparison of sensitivity analysis methods in building energy assessment[J]. Procedia Engineering, 2016, 146, 174- 181. doi: 10.1016/j.proeng.2016.06.369
21	KE Y . Research on the effectiveness evaluation model of the prison physical protection system based on grey analytic hierarchy process[J]. Security and Communication Networks, 2017, 2017, 1- 9.
22	CAO X Y , WANG Y D , SHI Z Y . Research on the maintenance effectiveness evaluation of electronic information equipment[J]. Journal of Physics: Conference Series, 2021, 1739, 012043. doi: 10.1088/1742-6596/1739/1/012043
23	赵日强, 安实, 麦强, 等. 基于ADC法的防空导弹武器系统效能建模[J]. 系统工程与电子技术, 2020, 42 (9): 2003- 2012.
	ZHAO R Q , AN S , MAI Q , et al. Effectiveness modeling of air defense missile weapon system based on ADC method[J]. System Engineering and Electronics, 2020, 42 (9): 2003- 2012.
24	张光义, 赵玉洁. 相控阵雷达技术[M]. 北京: 电子工业出版社, 2006.
	ZHANG G Y , ZHAO Y J . Phased array radar technology[M]. Beijing: Electronic Industry Press, 2006.
25	ZHANG Z , WANG C X , YANG H Y , et al. Broadband radar absorbing composites: spatial scale effect and environmental adaptability[J]. Composites science and Technology, 2020, 197, 108262.
26	HESS R A , VETTER T K , WELLS S R . Design and evaluation of a damage-tolerant flight control system[J]. Proc. of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2005, 219 (4): 341- 359. doi: 10.1243/095441005X7259
27	田清清, 李卫兵, 吴春霖, 等. 基于德尔菲法的感控投入成本测量指标体系构建[J]. 现代预防医学, 2023, 50 (3): 501- 508.
	TIAN Q Q , LI W B , WU C L , et al. The construction of cost measurement index system for hospital infection control inputs based on Delphi method[J]. Modern Preventive Medicine, 2023, 50 (3): 501- 508.
28	WEI C , ZENG X J , WANG Z G , et al. Construction and research on the evaluation system of university curriculum teaching quality based on analytic hierarchy process[J]. Curriculum and Teaching Methodology, 2022, 5 (12): 10- 17.
29	XU C G , GERTNER G Z . A general first-order global sensiti-vity analysis method[J]. Reliability Engineering & System Safety, 2008, 93 (7): 1060- 1071.
30	SCHAIBLT J H , SHULER K E . Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. Ⅱ Applications[J]. Journal of Chemical Physics, 1973, 59 (8): 3879- 3888.
31	KUCHERENKO S , ZUNIGA M M , TARANTOLA S , et al. Metamodelling and global sensitivity analysis of models with dependent variables[J]. AIP Conference Proceedings, 2011, 1389 (1): 1913- 1913.

能力层	权重	指标层	权重	全局权重
空域探测能力	0.320 4	多目标处理性能	0.200 0	0.064 1
		最大作用距离	0.400 0	0.128 2
		方位观察范围	0.200 0	0.064 1
		俯仰观察范围	0.200 0	0.064 1
目标测量能力	0.242 6	距离测量精度	0.250 0	0.060 6
		方位角测量精度	0.250 0	0.060 6
		俯仰角测量精度	0.250 0	0.060 6
		速度测量精度	0.250 0	0.060 7
抗干扰能力	0.124 7	抗主瓣干扰性能	0.249 2	0.031 1
		抗副瓣干扰性能	0.326 9	0.040 8
		频率捷变	0.141 3	0.017 6
		频率分集	0.141 3	0.017 6
		旁瓣相消	0.141 3	0.017 6
数据处理能力	0.164 7	数据处理速度	0.400 0	0.065 9
		数据容量	0.200 0	0.032 9
		系统识别技术	0.400 0	0.065 9
生存与适应能力	0.147 6	系统可靠性	0.500 0	0.073 8
		环境适应性	0.250 0	0.036 9
		抗毁伤性	0.250 0	0.036 9

指标类型	x₀	y₀	x₁	y₁
效益型	不满意值	0	满意值	1
成本型	满意值	1	不满意值	0

指标	典型值
同时处理目标数目/架	600
发射机平均功率/kW	80
天线有效孔径/m²	7
信号重复周期/s	0.005
雷达系统损耗/dB	4.5
信噪比/dB	12
工作频率/GHz	2.1
俯仰观察范围/(°)	30
雷达信号带宽/kHz	300
半功率点水平宽度/(°)	1
半功率点垂直宽度/(°)	5
频率捷变/分	85
频率分集/分	80
旁瓣相消/分	85
数据处理速度/分	80
数据容量/分	85
系统识别技术/分	80
平均无故障时间/h	600
平均维修时间/h	20
环境适应性/分	80
抗毁伤性/分	85

参数个数	拟合方程	拟合程度
15	y=-2.85x²+100.08x+76.55	0.998 3
16	y=-2.69x²+91.02x+57.39	0.998 8
17	y=-2.67x²+85.21x+3.56	0.998 3
18	y=-2.66x²+79.67x+14.89	0.997 7
19	y=-2.46x²+70.48x+4.88	0.998 7

指标i	指标j	二阶交互效应指数
平均维修时间	平均无故障时间	0.000 945
工作频率	天线有效孔径面积	0.000 451
信噪比	雷达系统损耗	0.000 361
工作频率	信噪比	0.000 298
信噪比	天线有效孔径面积	0.000 262
信噪比	发射机平均功率	0.000 134
工作频率	发射机平均功率	0.000 120
半功率点垂直宽度	信噪比	0.000 075
雷达信号带宽	信噪比	0.000 045
雷达系统损耗	发射机平均功率	0.000 041

Sensitivity analysis of radar system effectiveness based on FAST and Sobol index method

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指标名称	FAST主效应	Sobol主效应	Sobol全效应
同时处理目标数目	0.053 6	0.053 2	0.053 2
发射机平均功率	0.210 3	0.212 6	0.212 5
天线有效孔径面积	0.091 7	0.091 4	0.092 0
信号重复周期	0.023 0	0.024 1	0.024 2
雷达系统损耗	0.024 5	0.025 2	0.024 8
信噪比	0.011 9	0.013 6	0.013 8
工作频率	0.157 1	0.156 4	0.157 1
俯仰观察范围	0.037 2	0.036 4	0.036 4
雷达信号带宽	0.013 4	0.014 5	0.014 5
半功率点水平宽度	0.013 2	0.013 7	0.013 7
半功率点垂直宽度	0.003 3	0.003 2	0.003 2
频率捷变	0.008 1	0.008 1	0.008 1
频率分集	0.007 2	0.006 2	0.006 2
旁瓣相消	0.008 1	0.008 3	0.008 3
数据处理速度	0.100 5	0.099 5	0.099 5
数据容量	0.028 3	0.027 6	0.027 6
系统识别技术	0.100 5	0.099 4	0.099 4
平均无故障时间	0.019 5	0.017 9	0.018 9
平均维修时间	0.019 3	0.019 8	0.020 8
环境适应性	0.031 5	0.031 9	0.031 9
抗毁伤性	0.035 6	0.035 2	0.035 2

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