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The vibratory response of buildings and machines carries key information that can be exploited to infer their operating conditions and to diagnose failures. Moreover, since vibration signatures observed from the exterior surfaces of structures are intrinsically linked to the type of machinery operating inside of them, the ability to monitor vibrations remotely can facilitate the detection and identification of the machinery. Recently, synthetic aperture radar (SAR) has proven to be a versatile tool capable of performing vibrometry and high-precision vibration-estimation algorithms have been developed for reconstructing surface vibration waveforms from SAR images. However, these algorithms tend to be computationally demanding and, in addition, require knowledge of the exact location of the object a priori. This renders their use as unpractical for exploratory applications. This paper focuses on the detection of vibrating objects by exploiting the phase modulation that a vibration causes in the received slow-time SAR data. Two different vibration detection schemes are investigated. The first scheme is data-driven and utilizes features extracted with the help of the discrete fractional Fourier transform (DFrFT) to feed a random-forest detector. The second scheme is model-based, and uses a probabilistic model of the slow-time SAR signal, the Karhunen-Loeve expansion, and a likelihood-ratio detector. The proposed detection algorithms are tested using both simulated and real SAR data. Our results show that both detection schemes can be used to achieve high-performance vibrating-object detectors.
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