SYSTEM IDENTIFICATION BASED ON THE DISTRIBUTION OF TIME BETWEEN ZERO CROSSINGS

A new method for system identification is proposed that is based on fitting the theoretical probability density function (PDF) for the time between zero crossings to a measured distribution of the crossing interval times. Using the theory first developed by Rice, an approximate closed-form expression for the probability density of the time between zero crossings of a linear single-degree-of-freedom system subject to a white noise excitation is obtained. The PDF is a function of the natural frequency and damping ratio of the system, and is accurate for a lightly damped system for time intervals up to the natural period of the system. To estimate the system natural frequency and damping ratio, the PDF is fitted to a histogram of measured crossing interval times, using the Levenberg–Marquardt non-linear least-squares technique. The approach is demonstrated using simulated data for systems with natural frequencies of 0·5, 1·0 and 2·0 Hz and damping ratios of 1, 2·5, 5 and 10%. The method is found to provide good results for the full range of system parameters studied, with errors in the predicted frequency of less than 1·5% and errors in the predicted damping ratio, on an average, less than 7%. The new method is intended to take advantage of technology that now exists in advanced low cost, battery operated, stand-alone instrumentation systems, and will be particularly beneficial in studies of large civil structures.