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浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (6): 1108-1117    DOI: 10.3785/j.issn.1008-973X.2021.06.011
交通工程、土木工程     
利用AR模型解决全相位技术数据长度限制
高向宇(),李杨龙()
北京工业大学 城市与工程安全减灾教育部重点实验室，北京 100124
Solving data length limit of all-phase technology by AR model
Xiang-yu GAO(),Yang-long LI()
Key Laboratory of Urban Security and Disaster Engineering, Beijing University of Technology, Beijing 100124, China
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摘要：

针对在建筑结构领域全相位技术中对数据长度的限制问题，提出使用基于自回归（AR）模型的数据外推方法（AREX），给出适用于全相位技术的AR模型定阶算法. 提出以有效频段最大能量集中为原则确定AR模型阶数的算法（ECC），与最终预测误差（FPE）、阿凯克信息准则（AIC）、贝叶斯信息准则（BIC）及奇异值差分谱准则（SVD）进行对比. 结果表明，ECC算法更适合AREX方法. 将原始信号及AREX方法与常见数据扩展方法的估计信号进行全相位处理，结果表明，AREX估计信号的波形和频谱的相似程度均优于其余方法. 将AREX方法用于建筑结构有限元分析数据和振动台试验信号的全相位数据处理，结果表明，AREX估计信号基本上可以等效原始信号结果，表明AREX可以解决全相位数据长度的限制问题.
关键词： 全相位技术;  数据扩展;  自回归模型;  定阶准则;  频率分析    
Abstract:

A data extrapolation method (AREX) based on autoregressive (AR) model was proposed aiming at the limitation of data length in all-phase technology in the field of building structure. An algorithm for determining the order of AR model suitable for all-phase technology was given. An algorithm based on the principle of energy concentration criterion (ECC) was proposed to determine the order of AR model . The algorithm was compared with the final prediction error (FPE), Akaike's information criterion (AIC), Bayesian information criterion (BIC) and difference spectrum theory of singular value (SVD). Results showed that ECC algorithm was more suitable for AREX method. The original signal and the estimation signal by AREX method and the other expansion method were processed in all-phase technology. Results showed that the similarity of the waveform and spectrum of the AREX estimated signal was better than that of other methods. AREX was applied to the all-phase data processing of actual finite element and shaking table test signals in the field of building structure. Results show that the AREX estimation signal can basically be equivalent to results of the original signal, indicating that AREX can solve the limitation of all-phase data length.
Key words: all-phase technology    data expansion    autoregressive model    order determination    frequency analysis
收稿日期: 2020-05-25 出版日期: 2021-07-30
CLC:  TU 317  
基金资助: 北京市自然科学基金资助项目（8141001）
作者简介: 高向宇（1959—），男，教授，从事结构工程及防灾减灾与防护工程的研究. orcid.org/0000-0002-6734-3097. E-mail： gaoxy@bjut.edu.cn
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高向宇
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引用本文:

高向宇,李杨龙. 利用AR模型解决全相位技术数据长度限制[J]. 浙江大学学报(工学版), 2021, 55(6): 1108-1117.

Xiang-yu GAO,Yang-long LI. Solving data length limit of all-phase technology by AR model. Journal of ZheJiang University (Engineering Science), 2021, 55(6): 1108-1117.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2021.06.011    或    https://www.zjujournals.com/eng/CN/Y2021/V55/I6/1108

参数 取值 参数 取值
A1 3 ${\phi _1}$ /rad ${\text{π}} /2$
A2 1 ${\phi _2}$ /rad ${\text{π}} /3$
A3 2 ${\phi _3}$ /rad ${\text{π}} /4$
f1 /Hz 12 fs /Hz 256
f2 /Hz 17 N 256
f3 /Hz 21 ? ?
表 1  构造参数取值
图 1  不同定阶准则下的AREX扩展数据波形图
图 2  不同定阶准则下AREX扩展数据apFFT幅值谱
图 3  不同定阶方法AREX波形相关系数
主频 Acc /%
OPT SVD ECC FPE AIC BIC
1阶 85 35 93 77 78 76
2阶 77 19 84 69 71 69
3阶 100 93 100 96 96 96
表 2  不同定阶方法apFFT频率识别正确率
图 4  最优阶数分布规律与SNR的关系
图 5  ECC阶数分布规律与SNR的关系
图 6  不同扩展方法的全相位波形
图 7  不同扩展方法的apFFT幅值谱
图 8  不同扩展方法全相位波形相关系数
主频 Acc /%
原始信号 DSAF ZP AREX
1阶 100 100 88 94
2阶 83 56 6 85
3阶 42 54 19 95
表 3  不同扩展方法apFFT频率识别正确率
图 9  工业厂房结构的有限元模型
图 10  结构自由衰减信号
图 11  自由衰减信号apFFT分析结果对比图
图 12  振动台结构试验模型
图 13  振动台结构白噪声试验信号
图 14  振动台信号apFFT分析结果的对比图
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