Intrinsic Spatio-Temporal Resolution Analysis of Nondestructive Impact Diagnostic Force Ensembles and Collocated Accelerations in a Composite Beam Structure

Several ensembles of sweeping diagnostic impulsive forces were measured in a unidirectional carbon-epoxy composite beam modified locally with a soft viscoelastic patch. The spatial uniformity of the typical ensemble of diagnostic signals is addressed by a systematic spatio-temporal coherence analysis in terms of proper orthogonal decomposition (POD) modes. All samples of spanning ensembles are strongly dominated by the same POD mode characterized by a nearly uniform spatial modulation and a sharp triangular pulse time modulation. The higher POD modes have small amounts of energy. They possess an important statistics property: their spatial modulation mean value is nearly zero with standard deviation nearly identical to the nearly uniform value of the dominant POD mode. The nearly uniform spatial distribution of the dominant POD mode is a fuzzy picture of the ideal or nominal one where the impact-generated diagnostic forces should have a time waveform independent of the site of impact. Despite this energy content deficiency, the ensemble of acceleration signals acquired at a fixed point while the beam is excited by an ensemble of sweeping diagnostic forces has very robust POD modal structure. The POD modes show in a clear manner the presence of a soft viscoelastic patch simulating mass modifications. The POD-based coherence analysis of ensembles of diagnostic forces generated in this practical problem is potentially useful for a real-time verification-inspection of the integrity of networks of embedded and surface-mounted actuators and sensors.