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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (6): 1108-1117    DOI: 10.3785/j.issn.1008-973X.2021.06.011
    
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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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     
Received: 25 May 2020      Published: 30 July 2021
CLC:  TU 317  
  TN 911  
Fund:  北京市自然科学基金资助项目（8141001）
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Xiang-yu GAO
Yang-long LI
Cite this article:

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.

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


利用AR模型解决全相位技术数据长度限制

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 
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 ? ?
Tab.1 Values of construction parameter
Fig.1 Waveforms of AREX extended data under different order criteria
Fig.2 ApFFT amplitude spectrum of AREX extended data under different fixed order criteria
Fig.3 Correlation coefficients of AREX waveforms with different order determination methods
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
Tab.2 Correct rate of apFFT frequency recognition with different order determination methods
Fig.4 Relationship between distribution law of optimal order and SNR
Fig.5 Relationship between distribution law of ECC order and SNR
Fig.6 All-phase waveforms of different expansion methods
Fig.7 ApFFT amplitude spectrum of different expansion methods
Fig.8 Correlation coefficients of all-phase waveforms with different expansion methods
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
Tab.3 Correct rate of apFFT frequency recognition with different expansion methods
Fig.9 Finite element model of industrial plant structure
Fig.10 Structural free attenuation signal
Fig.11 Comparison of apFFT analysis results of free attenuation signals
Fig.12 Shaking table structure test model
Fig.13 White noise signal of shaking table structure
Fig.14 Comparison of apFFT analysis results of shaking table signals
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