Triggering expectation and residual excitation of distributed random decrement technique

A distributing process is proposed for Random Decrement Technique (RDT), to accurate modal identification. Impulse response can be extracted from random response, whose signal is overlap-averaged under Gaussian white noise excitation. With better understanding of initial condition, RDT can be improved with triggering expectation and residual excitation. Firstly, the initial condition is defined as the expectation of random response on instants of triggering time series. Response of unit initial condition can be calculated from Random Decrement (RD) signals, using matrix equations generated from multiple RD processes; this response also keeps a unique expression for a particular system. Secondly, the key of RDT error can be the residual excitation, which refers to the residue of random excitation after RD process. Importantly, the influence of residual excitation declines with increased overlap-averaging times. This modified RDT might be used to obtain impulse response from random response, and its error can be estimated.