Single and Multi-frequency Parameter Estimation by α SWIFT-DPLL Through Optimized MOPSO Algorithm

Purpose Vibration parameter estimation using a non-contact technique for industry applications, biomedical applications, condition monitoring of civil structures, and rotating machines. Methods An alpha sliding window infinite Fourier transform ( α SWIFT) based digital phase-locked loop (DPLL) is proposed to measure the vibration signal. The proposed DPLL is mainly comprised of a quadrature detector, which is derived from the α SWIFT structure, a moving averager unit, a controller unit, and a bi-quad oscillator. The α SWIFT structure provides inherent stability as the system poles always lie inside the unit circle and has high noise rejection capability due to narrow bandwidth at high values of time-constant. Further, the α SWIFT structure works on an exponential window function that gives higher weight to recent samples and also reduces the leakage effects. The Pareto front multi-objective particle swarm optimization (PF-MOPSO) algorithm is introduced in the DPLL for computing the controller gains. Three non-conflicting objective functions, namely amplitude error, phase error, and total harmonic distortion (THD) are considered in the PF-MOPSO algorithm to optimize the controller parameters. The bi-quad oscillator generates the variable pulses based on the extracted signal to synchronize the remaining units. Results The proposed DPLL is able to extract the multi-frequency components of the vibration parameter using a non-contact technique. The system is capable of measuring low frequencies up to 0.2 Hz and low amplitudes up to 0.06 mm. The proposed DPLL can also extract the vibration parameters up to the noise level of -2 dB.