非线性自回归模型辨识及其在结构损伤识别中的应用

PDF(1428 KB)

振动与冲击 ›› 2017, Vol. 36 ›› Issue (20) : 118-124.

论文

马家欣1，许飞云1，黄凯2，黄仁1

作者信息 +

Nonlinear auto-regressive model identification and its application in structural damage detection

Ma Jiaxin1, Xu Feiyun1, Huang Kai2, Huang Ren1

Author information +

文章历史 +

摘要

分析了带有外部输入的线性/非线性自回归模型一般表达式（GNARX）与Volterra级数模型的相似之处，以及GNARX模型与带外部输入的自回归模型（ARX）之间的内在联系。根据GNARX模型结构特点，提出了一种基于参数离差率的结构剪枝算法，并用于模型结构辨识，通过数据仿真，验证了方法的可行性和有效性。最后，将GNARX模型结合提出的结构辨识方法，应用于钢板的损伤识别。结果显示，基于参数离差率的结构剪枝算法辨识GNARX模型结构，其损伤识别精度最高，体现了GNARX模型及其结构剪枝算法应用于结构损伤识别的优越性。

Abstract

The similarities between the general expression for the linear and nonlinear auto-regressive model with exogenous inputs (GNARX) and Volterra series model, and the internal links between GNARX and auto-regressive model with exogenous inputs (ARX) are analyzed. On the basis of the structure characteristics of GNARX model, a structure pruning algorithm based on parameters’ rate of standard deviation is proposed and applied to model structure identification for GNARX model. With data simulation, the feasibility and effectiveness of the method is verified. Finally, GNARX model together with the proposed structure identification method is applied to structural damage detection for steel plate. The results show that GNARX model, whose structure is identified with structure pruning algorithm based on parameters’ rate of standard deviation, has the highest identification accuracy of structural damage, which indicates the superiority of GNARX model and its structure pruning algorithm applied to structural damage detection.

导出引用

马家欣1，许飞云1，黄凯2，黄仁1. 非线性自回归模型辨识及其在结构损伤识别中的应用[J]. 振动与冲击, 2017, 36(20): 118-124

Ma Jiaxin1, Xu Feiyun1, Huang Kai2, Huang Ren1. Nonlinear auto-regressive model identification and its application in structural damage detection[J]. Journal of Vibration and Shock, 2017, 36(20): 118-124

参考文献

[1] Yan Y J, Cheng L, Wu Z Y, et al. Development in vibration-based structural damage detection technique [J]. Mechanical Systems and Signal Processing, 2007, 21(5): 2198-2211.
[2] 张俊哲. 无损检测技术及其应用[M]. 2版. 北京: 科学出版社, 2010.
[3] Jaishi B, Ren W X. Finite element model updating based on eigenvalue and strain energy residuals using multiobjective optimisation technique [J]. Mechanical Systems and Signal Processing, 2007, 21(5): 2295-2317.
[4] Hua X G, Ni Y Q, Ko J M. Adaptive regularization parameter optimization in output-error-based finite element model updating [J]. Mechanical Systems and Signal Processing, 2009, 23(3): 563-579.
[5] 杨叔子, 吴雅, 轩建平, 等. 时间序列分析的工程应用: 上册[M]. 2版. 武汉: 华中科技大学出版社, 2007.
[6] Moore S M, Lai J C S, Shankar K. ARMAX modal parameter identification in the presence of unmeasured excitation-II: Numerical and experimental verification [J]. Mechanical Systems and Signal Processing, 2007, 21(4): 1616-1641.
[7] 刁延松, 任红. 基于AR模型和因子分析的结构损伤预警研究[J]. 振动与冲击, 2014, 33(18): 115-119.
DIAO Yan-song, REN Hong. Study on the structural damage alarm based on AR model and factor analysis [J]. Journal of Vibration and Shock, 2014, 33(18): 115-119.
[8] de Lautour O R, Omenzetter P. Damage classification and estimation in experimental structures using time series analysis and pattern recognition [J]. Mechanical Systems and Signal Processing, 2010, 24(5): 1556-1569.
[9] Gul M, Catbas F N. Structural health monitoring and damage assessment using a novel time series analysis methodology with sensor clustering [J]. Journal of Sound and Vibration, 2011, 330(6): 1196-1210.
[10] 马家欣, 许飞云, 黄仁. 一种线性/非线性自回归模型及其在建模和预测中的应用[J]. 东南大学学报: 自然科学版, 2013, 43(3): 509-514.
MA Jia-xin, XU Fei-yun, HUANG Ren. A linear and nonlinear atuo-regressive model and its application in modeling and forecasting [J]. Journal of Southeast University: Natural Science Edition, 2013, 43(3): 509-514.
[11] Huang R, Xu F Y, Chen R W. General expression for liner and nonlinear time series models [J]. Frontiers of Mechanical Engineering in China, 2009, 4(1):15-24.
[12] Schetzen M. The Volterra and Wiener Theories of Nonlinear Systems [M]. New York: Wiley, 1980.
[13] Bernal D, Zonta D, Pozzi M. ARX residuals in damage detection [J]. Structural Control & Health Monitoring, 2012, 19(4): 535-547.
[14] 陈茹雯, 黄仁. 非线性时序模型在机械系统故障诊断中的应用[J]. 振动、测试与诊断, 2012, 32(1): 91-95.
CHEN Ru-wen, HUANG Ren. Fault diagnosis of mechanical system based on nonlinear time series model [J]. Journal of Vibration, Measurement & Diagnosis, 2012, 32(1):91-95.
[15] Karnin E D. A simple procedure for pruning back-propagation trained neural networks [J]. IEEE Transactions on Neural Networks, 1990, 1(2): 519-531.
[16] Akaike H. Maximum likelihood identification of Gaussian autoregressive moving average models [J]. Biometrika, 1973, 60(2): 255-265.
[17] Fukunage K, Narendra P M. A branch and bound algorithm for computing k-nearest neighbors [J]. IEEE Transactions on Computers, 1975, C-24 (7): 750-753.
[18] Pandya D H, Upadhyay S H, Harsha S P. Fault diagnosis of rolling element bearing with intrinsic mode function of acoustic emission data using APF-KNN [J]. Expert Systems with Application, 2013, 40 (10): 4137-4145.