Abstract Motivated by practical needs to reduce data transmission payloads in wireless sensors for vibration-based monitoring of engineering structures, this paper proposes a novel approach for identifying resonant frequencies of white-noise excited structures using acceleration measurements acquired at rates significantly below the Nyquist rate. The approach adopts the deterministic co-prime sub-Nyquist sampling scheme, originally developed to facilitate telecommunication applications, to estimate the autocorrelation function of response acceleration time-histories of low-amplitude white-noise excited structures treated as realizations of a stationary stochastic process. Next, the standard multiple signal classification (MUSIC) spectral estimator is applied to the estimated autocorrelation function enabling the identification of structural natural frequencies with high resolution by simple peak picking in the frequency domain without posing any sparsity conditions to the signals. This is achieved by processing autocorrelation estimates without undertaking any (typically computationally expensive) signal reconstruction step in the time-domain, as required by various recently proposed in the literature sub-Nyquist compressive sensing-based approaches for structural health monitoring, while filtering out any broadband noise added during data acquisition. The accuracy and applicability of the proposed approach is first numerically assessed using computer-generated noise-corrupted acceleration time–history data obtained by a simulation-based framework examining white-noise excited structural systems with two closely-spaced modes of vibration carrying the same amount of energy, and a third isolated weakly excited vibrating mode. Further, damage detection potential of the developed method is numerically illustrated using a white-noise excited reinforced concrete 3-storey frame in a healthy and two damaged states caused by ground motions of increased intensity. The damage assessment relies on shifts in natural frequencies between the pre-earthquake and post-earthquake state. Overall, numerical results demonstrate that the considered approach can accurately identify structural resonances and detect structural damage associated with changes to natural frequencies as minor as 1% by sampling up to 78% below Nyquist rate for signal to noise ratio as low as 10dB. These results suggest that the adopted approach is robust and noise-immune while it can reduce data transmission requirements in acceleration wireless sensors for natural frequency identification and damage detection in engineering structures.

中文翻译：

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用于识别紧密间隔结构自然频率和震后损坏检测的压缩 MUSIC 谱方法

摘要 出于减少用于工程结构振动监测的无线传感器中数据传输有效载荷的实际需要，本文提出了一种新方法，用于使用以显着低于奈奎斯特速率的速率获取的加速度测量来识别白噪声激励结构的共振频率。该方法采用最初为促进电信应用而开发的确定性互质子奈奎斯特采样方案，以估计作为平稳随机过程实现的低振幅白噪声激励结构的响应加速时程的自相关函数。下一个，将标准多信号分类 (MUSIC) 频谱估计器应用于估计的自相关函数，通过在频域中进行简单的峰值拾取，能够以高分辨率识别结构自然频率，而不会对信号施加任何稀疏条件。这是通过处理自相关估计而不在时域中进行任何（通常计算成本高的）信号重建步骤来实现的，正如文献中最近提出的各种基于子奈奎斯特压缩传感的结构健康监测方法所要求的，同时过滤掉任何数据采集​​期间添加的宽带噪声。所提出方法的准确性和适用性首先使用计算机生成的噪声破坏加速度时程数据进行数值评估，该数据通过基于模拟的框架获得，检查白噪声激发的结构系统，其中两种紧密间隔的振动模式承载相同的量的能量，以及第三种孤立的弱激发振动模式。此外，使用白噪声激发的钢筋混凝土 3 层框架在健康和由强度增加的地面运动引起的两种损坏状态下，对所开发方法的损坏检测潜力进行了数值说明。损害评估依赖于震前和震后状态之间自然频率的变化。全面的，数值结果表明，所考虑的方法可以准确地识别结构共振，并通过在信噪比低至 10dB 的情况下以低于奈奎斯特率 78% 的频率进行采样，从而准确识别结构共振并检测与小至 1% 的自然频率变化相关的结构损坏。这些结果表明，所采用的方法具有鲁棒性和抗噪性，同时可以降低加速度无线传感器的数据传输要求，用于工程结构的固有频率识别和损伤检测。