Spatial filtering and proper orthogonal decomposition of scanning laser Doppler vibrometry data for the nondestructive evaluation of frescoes

Recently, scanning laser Doppler vibrometry experiments have been conducted in order to identify structural faults in frescoes at the US Capitol. In these experiments, the artwork is subjected to force excitations over a range of frequencies and a laser vibrometer is used to measure the velocity response of the structure over an array of spatial locations. At each frequency, a two-dimensional spatial image of the force–velocity transfer function is obtained. Spatial locations that consistently exhibit large responses are indicative of potential regions of delamination. In this paper the use of proper orthogonal decomposition, also known as principle component analysis, to identify coherent features in the structural response and obtain a succinct representation of the data is described. It is shown that, for the fresco studied in this paper, the response can be characterized in terms of only a few proper orthogonal decomposition modes. Unfortunately, these modes are corrupted by spatially varying noise. This noise is a result of surface irregularities that affect the direction in which the incident laser beam is reflected, which in turn corrupts the measured response at those locations. Therefore, the use of spatial filtering techniques is also explored for removing this “speckle noise” from the measured force–velocity transfer functions prior to performing the proper orthogonal decomposition analysis. Wavelets are particularly well suited for this application because they decompose images into functions that are localized in the spatial and frequency domains. In this paper, several wavelet bases with differing properties are used to filter the scanning laser Doppler vibrometry images. In addition, wavenumber filters, which essentially act as low-pass filters, are also employed. While the results do not definitively show which filtering technique is most effective for this application, it is clear that both wavelet processing and wavenumber filtering can reduce speckle noise while retaining the salient physical features in the image data. Therefore, it is demonstrated that proper orthogonal decomposition analysis coupled with spatial filtering is an effective tool for analyzing scanning laser Doppler vibrometry data in fault detection applications.