Abstract

Extracting relevant information from data has traditionally been achieved with Fourier analysis and Fourier-based methods that assume stationarity of data, with basis sets of sines and cosines used to represent the data series a priori. However, sines and cosines have constant amplitudes and frequencies, whereas the original data series would usually have amplitudes and frequencies that vary with time. A new method of analysis that is adaptive in nature, the Hilbert-Huang transform (HHT) has been developed. Rather than defining them a priori, basis sets are derived from the intrinsic time-scales of the data series through a sifting process called empirical mode decomposition (EMD); the bases are called intrinsic mode functions (IMF), which are usually almost orthogonal based on a defined index of orthogonality, and form a complete set by virtue of the fact the sum of the IMFs equals the original signal. There are no stationary assumptions in HHT; therefore, it is suitable for analyzing nonstationary systems. One important distinguishing feature between Fourier methods and HHT is that the former analyze data globally by averaging, while the latter analyzes locally. A 2-D version of the EMD, called bidimensional empirical mode decomposition (BEMD), has recently been developed; BEMD is used mostly in image-processing applications. This study explores the potential of HHT and BEMD in civil infrastructure systems and investigates how they can be incorporated into condition assessment and monitoring. It also includes a new theoretical development in EMD by which relevant IMFs are distinguished from IMFs that may have been generated by numerical errors, and which may not be quite relevant; these IMFs are distinguished using a stringent threshold that is dependent on the correlation coefficient between the IMFs and the original signal.