测试噪声是实际工程结构振动测试时难以避免的信号成分。当结构真实模态淹没于测试噪声之中时，传统的降噪方法往往将该部分真实模态与噪声一并消除，导致结构固有信息损失。本文提出一种能够适用于高背景噪声实测信号的降噪新方法，该方法建立在实测信号由一系列复指数信号成分的线性叠加基础之上，基于低阶状态空间模型将各复指数信号成分表征为一系列的极值及留数，并通过建立各复指数成分极值与频率的转换关系,并施加频率窗口从而分离预定频率区间的极值与留数向量，最终获得降噪后的重构信号。与传统的高阶模型相比，因采用低阶状态空间模型可以大大降低矩阵的条件数，数值稳定性更好。同时，将实测信号表示为一系列复指数信号成分，可以克服传统傅里叶分解技术的固定分辨率问题，通用性更广。文中首先选用一质量-弹簧-阻尼模型，通过构造不同信噪比的测试信号，开展了新方法降噪效果的研究。结果证实，信号的信噪比分别为40dB、30dB、20dB和10dB的噪声时，该方法都能有效消除信号的噪声。为进一步验证方法的有效性，文中选用一实际海洋平台实测加速度响应信号进行研究，结果表明实测信号消噪后的频率成分与已有测试结果基本一致，验证了方法的有效性。
Abstract
Noise is an unavoidable signal component in vibration testing of practical engineering structures. When true structural modes are submerged in noise, the traditional de-noising method may eliminate noise and parts of true modes to cause structural natural vibration information loss. Here, a new de-noising method suitable for test signals with high background noise was proposed. With this method, a measured signal was regarded as a linear superposition of a series of complex exponential signal components, and they were represented as a series of extreme values and residues based on a lower order state space model. The conversion relations between complex exponential components’ extreme values and frequencies were established. Imposing a frequency window, extreme values and residue vectors in a predetermined interval were separated to acquire a reconstructed signal after de-noising. It was shown that compared with the traditional higher order model, adopting a lower order state space model can reduce significantly a matrix’s conditioning number, and obtain a better numerical stability; representing a measured signal as a series of complex exponential signal components can overcome the intrinsic resolution problem of Fourier decomposition technique and have a wider generality. A mass-spring-damper model was firstly adopted, and test signals with different signal-noise ratios were constructed to study the new method’s de-noising effect. Results showed that when the SNRs of test signals are 40 dB, 30 dB, 20 dB and 10 dB, respectively, the new approach can effectively eliminate noise. To further verify the effectiveness of the proposed method, acceleration response signals of an actual offshore platform were collected. The results showed that after de-noising with the new method, the measured signals’ frequency components agree well with those of existing recorded data in 1994.
关键词
极值-留数分解 /
信号消噪 /
傅里叶变换 /
信号重构 /
模态识别
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Key words
pole-residue decomposition /
signal noise elimination /
Fourier transformation /
signal reconstruction /
modal identification
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