Broadband displacement reconstruction method based on acceleration signal decomposition and regularization

CHEN Xinjun; LU Zhongrong; WANG Li

doi:10.13471/j.cnki.acta.snus.2022E053

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Broadband displacement reconstruction method based on acceleration signal decomposition and regularization

Research articles | 更新时间：2023-11-07

- Broadband displacement reconstruction method based on acceleration signal decomposition and regularization
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 62, Issue 5, Pages: 128-135(2023)
- 作者机构：
  
  中山大学航空航天学院，广东深圳 518107
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2022E053
  CLC： O329
- Published：25 September 2023，
  
  Published Online：19 June 2023，
  
  Received：05 November 2022，
  
  Accepted：07 April 2023
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陈信君,吕中荣,汪利.基于加速度信号分解和正则化的宽频位移重构方法[J].中山大学学报(自然科学版),2023,62(05):128-135.

CHEN Xinjun,LU Zhongrong,WANG Li.Broadband displacement reconstruction method based on acceleration signal decomposition and regularization[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(05):128-135.
陈信君,吕中荣,汪利.基于加速度信号分解和正则化的宽频位移重构方法[J].中山大学学报(自然科学版),2023,62(05):128-135. DOI： 10.13471/j.cnki.acta.snus.2022E053.

CHEN Xinjun,LU Zhongrong,WANG Li.Broadband displacement reconstruction method based on acceleration signal decomposition and regularization[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(05):128-135. DOI： 10.13471/j.cnki.acta.snus.2022E053.

摘要

实际工程应用中，位移测量通常需要设置参考点，导致大型结构的位移难以直接测量。为此，本文提出了一种基于加速度信号分解和正则化的位移重构新方法，直接利用易获取（无需参考点）、精度高的加速度数据来恢复结构的位移信息。首先，建立位移与加速度的离散线性方程，直接求解该方程得出，位移是加速度的二重积分。但由于直接积分对低频噪声十分敏感，导致出现低频漂移现象。因此在离散线性方程的基础上引入Tikhonov正则化，克服求解中的病态性，解决低频漂移问题。为了提高位移重构精度，还发展了基于重叠窗的位移重构方案，每个窗的区间长度应取信号主频周期的3倍左右。研究发现，该方法适合于单一主频（或窄频）加速度的位移重构，对宽频位移重构通常效果较差。为了提高宽频位移重构精度，本文进一步提出有限带宽信号分解方法，将宽频加速度信号分解为若干窄频信号，然后，利用正则化方法对每个窄频信号进行高精度的位移重构。最后，数值和实验算例结果表明，所提方法确实能从宽频加速度信号中准确重构出结构的位移响应。

Abstract

In practical engineering application， the displacement measurement usually needs to set reference points， which makes it difficult to directly measure the displacement of large structures. Therefore， this paper proposes a new method which directly uses easily accessible （no reference point needed） and highly precise acceleration data to recover the displacement of the structure. Firstly， the discrete linear equation between displacement and acceleration is established. Displacement is the double integral of acceleration by directly solving the equation. However， direct integration is very sensitive to low frequency noise， resulting in "low-frequency drift" phenomenon. Secondly， Tikhonov regularization is introduced on the basis of discrete linear equations to overcome the ill-posed problem and solve the "low-frequency drift" problem. In addition， in order to improve the accuracy of displacement reconstruction， a displacement reconstruction scheme based on overlapping windows is developed， and the interval length of each window should be about 3 times of the main frequency period of the signal. It is found that this method is suitable for the displacement reconstruction of acceleration at single main frequency （or narrow frequency）， but it is usually poor for broadband displacement reconstruction. In order to improve the accuracy of broadband displacement reconstruction， this paper further proposes a bandlimited signal decomposition method， which decomposes the broadband acceleration signal into several narrow frequency signals， and then uses the regularization method to reconstruct the displacement of each narrow frequency signal with high accuracy. Finally， numerical and experimental results show that the proposed method can accurately reconstruct the displacement of the structure from the broadband acceleration signal.

关键词

宽频位移重构低频漂移有限带宽信号分解正则化

Keywords

broadband displacement reconstructionlow-frequency driftbandlimited signal decompositionregularization

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