基于区间数学方法的结构参数识别

宋海洋

doi:10.21656/1000-0887.440319

基于区间数学方法的结构参数识别

doi: 10.21656/1000-0887.440319

宋海洋^{1, 2, ,}

1.
东北电力大学建筑工程学院，吉林吉林 132012
2.
东北电力大学吉林省电力基础设施安全评估与灾害防治重点实验室，吉林吉林 132012

基金项目:

吉林省教育厅科学技术研究项目 JJKH20230143KJ

详细信息

通讯作者:
宋海洋(1986—)，男，高级工程师，博士，硕士生导师(通讯作者. E-mail: paper2021@163.com)

中图分类号: O347.1
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- 被引次数: 0
出版历程
- 收稿日期: 2023-10-22
- 修回日期: 2024-01-29
- 刊出日期: 2024-05-01

Structural Parameter Identification Based on the Interval Mathematics Method

SONG Haiyang^{1, 2
, ,}

1.
School of Civil Engineering and Architecture, Northeast Electric Power University, Jilin, Jilin 132012, P.R.China
2.
Key Lab of Electric Power Infrastructure Safety Assessment and Disaster Prevention of Jilin Province, Northeast Electric Power University, Jilin, Jilin 132012, P.R.China

摘要

摘要: 统计能量分析方法是目前处理结构高频振动的有效方法之一，在航空、航天、船舶和机械等领域得到了广泛的应用. 内损耗因子和耦合损耗因子是统计能量分析方法中非常重要的两个结构参数，这些参数可以利用试验测量得到的外部输入功率和结构模态能量通过理论方法识别出来. 传统的统计能量分析参数识别方法没有考虑输入功率和模态能量的测量误差对识别结果的影响，识别结果精度较低，难以满足工程需要. 该研究将区间数学方法应用于统计能量分析的参数识别，提出了一种可以考虑模态能量测量误差和输入功率测量误差的参数识别方法，揭示了模态能量和输入功率的测量误差对参数识别的影响规律，提高参数识别的准确性. 该文的研究内容可以为后续的结构设计和安全性分析提供参考.
- 区间数学 /
- 参数识别 /
- 统计能量分析 /
- 结构振动
Abstract: The statistical energy analysis (SEA) method was popularly employed to handle the high-frequency dynamics problems in many engineering fields such as aerospace and shipping. The damping loss factor and coupling loss factor were the major parameters in the SEA theory, and they can usually be identified with the measured external input power and structural modal energy. The measurement errors of the input power and modal energy were not considered in the traditional parameter identification, where the accuracy of the identified results was relatively low. The interval mathematics method was applied to the parameter identification in this study, and the measurement errors of the input power and modal energy were fully considered. The effects of the measurement errors on the parameter identification were revealed, and the accuracy of the identified results was improved. The work can be helpful for the structure design and safety analysis.
- interval mathematics /
- parameter identification /
- statistical energy analysis /
- structural vibration

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图 1 统计能量分析子系统间的能量耗散和能量传输

Figure 1. Energy dissipation and energy transfer between SEA subsystems

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图 2 统计能量分析模型第m次激励效果图

Figure 2. The mth excitation on the SEA model

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图 3 分析流程图

Figure 3. The analytical process of the full text

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图 4 两壳耦合结构

Figure 4. The 2-shell coupling structure

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图 5 耦合损耗因子区间η₁₂^I

Figure 5. The coupling loss factor interval η₁₂^I

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图 6 内损耗因子区间η₁^I

Figure 6. The damping loss factor interval η₁^I

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图 7 六板耦合结构

Figure 7. The composite structure with 6 plates

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图 8 每个子系统的外部输入功率

Figure 8. The exterior input power of each subsystem

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图 9 每个子系统的模态能量

Figure 9. The modal energy caused by the exterior input power

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图 10 两钢板耦合结构的振动试验^[16]

Figure 10. The vibration experiment of 2 connected steel plates^[16]

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表 1 每个子系统的外部输入功率

Table 1. The exterior input power of each subsystem

f/Hz	P_{1, 1}/W	P_{2, 1}/W	P_{1, 2}/W	P_{2, 2}/W
1 000	0.150	0.020	0.012	0.170
2 000	0.300	0.050	0.025	0.350
3 000	0.600	0.100	0.050	0.700
4 000	1.500	0.250	0.125	1.750

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表 2 带有±3%测量误差的外部输入功率

Table 2. The exterior input power with ±3% measurement errors

f/Hz	P_{1, 1}^I/W	P_{2, 1}^I/W	P_{1, 2}^I/W	P_{2, 2}^I/W
1 000	[0.145 50, 0.154 50]	[0.019 40, 0.020 60]	[0.011 64, 0.012 36]	[0.164 90, 0.175 10]
2 000	[0.291 00, 0.309 00]	[0.048 50, 0.051 50]	[0.024 25, 0.025 75]	[0.332 50, 0.367 50]
3 000	[0.582 00, 0.618 00]	[0.097 00, 0.103 00]	[0.048 50, 0.051 50]	[0.679 00, 0.721 00]
4 000	[1.455 00, 1.545 00]	[0.242 50, 0.257 50]	[0.121 25, 0.128 75]	[1.697 50, 1.802 50]

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表 3 每个子系统的模态能量

Table 3. The modal energy of each subsystem

f/Hz	e_{1, 1}/J	e_{2, 1}/J	e_{1, 2}/J	e_{2, 2}/J
1 000	1 300	450	300	750
2 000	1 500	600	400	1 000
3 000	2 300	900	600	1 500
4 000	4 600	1 800	1 200	3 000

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表 4 带有±3%测量误差的模态能量

Table 4. The modal energy with ±3% measurement errors

f/Hz	e_{1, 1}^I/J	e_{2, 1}^I/J	e_{1, 2}^I/J	e_{2, 2}^I/J
1 000	[1 261, 1 339]	[437, 463]	[291, 309]	[728, 772]
2 000	[1 455, 1 545]	[582, 618]	[388, 412]	[970, 1 030]
3 000	[2 231, 2 369]	[873, 927]	[582, 618]	[1 455, 1 545]
4 000	[4 462, 4 738]	[1 746, 1 854]	[1 164, 1 236]	[2 910, 3 090]

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表 5 识别出的参数区间

Table 5. Identified parameter intervals of the composite structure

f/Hz	η₁^I	η₁₃^I	η₁₆^I
1 000	[0.081 8, 0.084 2]	[0.004 4, 0.008 8]	[0.002 5, 0.004 1]

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表 6 第一次试验测量得到的输入功率和模态能量

Table 6. The measured input power and modal energy in the 1st test

f/Hz	subsystem 1		subsystem 2
f/Hz	input power P/W	modal energy e/J	input power P/W	modal energy e/J
1 000	3.20×10^－11	5.06×10^－7	0	3.22×10^－7
2 000	2.39×10^－11	1.022×10^－6	0	5.500×10^－8

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表 7 第二次试验测量得到的输入功率和模态能量

Table 7. The measured input power and modal energy in the 2nd test

f/Hz	subsystem 1		subsystem 2
f/Hz	input power P/W	modal energy e/J	input power P/W	modal energy e/J
1 000	0	4.57×10^－9	7.90×10^－13	4.52×10^－8
2 000	0	1.65×10^－10	7.962×10^－14	6.34×10^－9

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表 8 由传统方法识别的参数结果^[16]

Table 8. Traditional identification results of SEA parameters^[16]

f/Hz	η₁	η₂	η₁₂	η₂₁
1 000	0.08	0.004	0.009 0	0.007 0
2 000	0.03	0.007	0.000 8	0.000 4

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表 9 参数区间的识别结果

Table 9. Identified parameter intervals of 2 connected steel plates

f/Hz	η₁^I	η₂^I	η₁₂^I	η₂₁^I
1 000	[0.075 08, 0.084 92]	[0.003 75, 0.004 25]	[0.007 85, 0.010 16]	[0.006 10, 0.007 89]
2 000	[0.028 25, 0.031 75]	[0.006 60, 0.007 39]	[0.000 69, 0.000 91]	[0.000 35, 0.000 45]

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参考文献(16)

[1]	李征宇, 王薇, 陈强. 基于能量法的高频冲击载荷下机械结构振动特性研究[J]. 船舶电子对抗, 2023, 46(5): 103-107. https://www.cnki.com.cn/Article/CJFDTOTAL-JCDZ202305021.htm LI Zhengyu, WANG Wei, CHEN Qiang. Research into mechanical structural vibration characteristics under high-frequency impact load based on energy method[J]. Shipboard Electronic Countermeasure, 2023, 46(5): 103-107. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JCDZ202305021.htm
[2]	王小峰, 崔东泽, 张鸿, 等. 带气膜阻尼悬臂平板振动特性的统计能量分析[J]. 机械设计与制造, 2023(12): 7-12. doi: 10.3969/j.issn.1001-3997.2023.12.002 WANG Xiaofeng, CUI Dongze, ZHANG Hong, et al. Statistical energy analysis on vibration characteristics of cantilever plate with air film damper[J]. Machinery Design & Manufacture, 2023(12): 7-12. (in Chinese) doi: 10.3969/j.issn.1001-3997.2023.12.002
[3]	沈重, 陈忠明. 基于有限元-统计能量分析混合法座舱噪声特性研究[J]. 噪声与振动控制, 2022, 42(5): 200-203. doi: 10.3969/j.issn.1006-1355.2022.05.033 SHEN Zhong, CHEN Zhongming. Study on noise characteristics of airplane cockpits based on FEM-SEA hybrid method[J]. Noise and Vibration Control, 2022, 42(5): 200-203. (in Chinese) doi: 10.3969/j.issn.1006-1355.2022.05.033
[4]	赵欣棠, 徐恬. 基于图论和统计能量分析的船舶舱室噪声传递路径[J]. 船舶设计通讯, 2021(162): 38-44. https://www.cnki.com.cn/Article/CJFDTOTAL-CBSJ2021S1009.htm ZHAO Xintang, XU Tian. Transfer path of ship cabin noise based on graph theory and statistical energy analysis[J]. Journal of Ship Design, 2021(162): 38-44. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CBSJ2021S1009.htm
[5]	张捷, 姚丹, 王瑞乾, 等. 基于试验统计能量分析的高速列车车内噪声预测方法[J]. 铁道学报, 2020, 42(11): 45-52. doi: 10.3969/j.issn.1001-8360.2020.11.007 ZHANG Jie, YAO Dan, WANG Ruiqian, et al. An approach for interior noise prediction of high-speed trains based on experimental statistical energy analysis[J]. Journal of the China Railway Society, 2020, 42(11): 45-52. (in Chinese) doi: 10.3969/j.issn.1001-8360.2020.11.007
[6]	张政, 许孟辉. 基于改进区间摄动分析的统计能量分析法[J]. 噪声与振动控制, 2019, 39(6): 25-29. doi: 10.3969/j.issn.1006-1355.2019.06.005 ZHANG Zheng, XU Menghui. Statistical energy analysis method based on improved interval perturbation analysis[J]. Noise and Vibration Control, 2019, 39(6): 25-29. (in Chinese) doi: 10.3969/j.issn.1006-1355.2019.06.005
[7]	DELANGHE K, SAS P. Statistical analysis of the power injection method[J]. Journal of the Aacoustical Society of America, 1996, 100(1): 294-303. doi: 10.1121/1.415915
[8]	CHEN Q, FEI Q G, LI Y B, et al. Prediction of statistical energy analysis parameters in thermal environment[J]. Journal of Spacecraft and Rockets, 2019, 56(3): 687-694. doi: 10.2514/1.A34181
[9]	秦朝红, 任方, 韩丽, 等. 飞行器典型结构中频分析参数识别及建模技术研究[J]. 强度与环境, 2014, 41(5): 38-44. https://www.cnki.com.cn/Article/CJFDTOTAL-QDHJ201405007.htm QIN Chaohong, REN Fang, HAN Li, et al. Parameter identification and modeling method for mid-frequency environment prediction of typical structure[J]. Structure and Environment Engineering, 2014, 41(5): 38-44. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-QDHJ201405007.htm
[10]	高群涛, 姚熊亮, 崔洪斌. 结构辐射噪声统计能量分析中参数的灰色预测[J]. 哈尔滨工程大学学报, 2006, 27(1): 48-52. https://www.cnki.com.cn/Article/CJFDTOTAL-HEBG200601009.htm GAO Quntao, YAO Xiongliang, CUI Hongbin. Prediction of statistical energy analysis parameter in structure diffused noise[J]. Journal of Harbin Engineering University, 2006, 27(1): 48-52. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HEBG200601009.htm
[11]	DING W Z, LI X H, YANG H, et al. Utilizing statistical information for interval analysis: a method for analyzing the interval uncertainty of line-of-sight measurement error of space-borne observation platforms[J]. IEEE Access, 2020, 8: 67868-67886. doi: 10.1109/ACCESS.2020.2982421
[12]	GUO X M, MA H, ZHANG X F, et al. Uncertain frequency responses of clamp-pipeline systems using an interval-based method[J]. IEEE Access, 2020, 8: 29370-29384.
[13]	ZHAO J Z, YAO G F, LIU R Y, et al. Interval analysis of the eigenvalues of closed-loop control systems with uncertain parameters[J]. Actuators, 2020, 9(2): 31.
[14]	ZHOU Y T, JIANG C, HAN X. Interval and subinterval analysis methods of the structural analysis and their error estimations[J]. International Journal of Computational Methods, 2006, 3(2): 229-244.
[15]	LYON R H, DEJONG R G. Theory and Applications of Statistical Energy Analysis[M]. 2nd ed. The MIT Press, 1995.
[16]	MAO B Y, XIE S L, XU M L, et al. Simulated and experimental studies on identification of impact load with the transient statistical energy analysis method[J]. Mechanical Systems and Signal Processing, 2014, 46: 307-324.