Temporal and Spatial Filtering Techniques for Scanning Laser DopplerVibrometry in Delamination Detection in Frescoes

摘要

In recent studies, Scanning Laser Doppler Vibrometry (SLDV) experiments have been conducted to identifyrnstructural faults in frescoes at the US Capitol. In these experiments, a laser vibrometer measures the velocityrnresponse of the structure over an array of spatial locations to force excitations over a range of frequencies. Atrneach frequency, a two-dimensional spatial image of the force-velocity transfer function is obtained. Spatialrnlocations that consistently exhibit large responses are indicative of potential regions of delamination. ProperrnOrthogonal Decomposition (POD), also known as Principle Component Analysis (PCA), is used to identifyrncoherent features in the structural response and obtain a succinct representation of the data. While this approachrnhas been shown to successfully enable the representation of the fresco response in terms of only a few PODrnmodes, these modes are corrupted by spatially-varying noise. This noise is a result of surface irregularities thatrnaffect the direction in which the incident laser beam is reflected, which in turn corrupts the measured response atrnthose locations. Thus, it is desirable to remove this "speckle noise" from the measured force-velocity transferrnfunctions prior to performing POD analysis. The purpose of this paper is to explore wavelet-based and wavernnumber filtering techniques for the denoising of SLDV images. Wave number filters essentially act as spatial lowpassrnfilters while wavelets decompose images in terms of functions that are localized in the time and frequencyrndomains. A number of different wavelet bases are employed for image denoising in this paper including the Haarrnbasis, single-generator biorthogonal wavelets, and piecewise-linear orthonormal multiwavelets. These basesrnhave differing collections of desirable properties for the application at hand, and their performance is compared tornthat of both mild and strong wave number filters. Finally, the paper compares POD results obtained using the rawrndata, the wavelet-denoised data, and wave number filtered data. While the results do not definitively show whichrndenoising technique is most effective for this application, it is clear that both wavelet denoising and wave numberrnfiltering are capable of reducing speckle noise while retaining important physical features in the image data.rnTherefore, this paper demonstrates that denoising, coupled with POD analysis, is an effective tool for faultrndetection.