Nondetection, false alarm, and calibration insensitivity in kurtosis- and pseudofractal-based singularity detection

This work isolates cases of nondetection, false alarm, and insensitivity for a general class of problems dealing with the detection and characterization of existence, location, and extent of singularities embedded in signals or in their derivatives when employing kurtosis- and pseudofractal-based methods for the detection and characterization process. The nondetection, false alarm, and insensitivity for these methods are illustrated on an example problem of damage identification and calibration in beams where the singularity to be identified lies in the derivative of the measured signal. The findings are general, not constrained to linear systems, and are potentially applicable to a wide range of fields including engineering system identification, fault detection, health monitoring of mechanical and civil structures, sensor failure, aerospace engineering, and biomedical engineering.