Spectral Richness PSO algorithm for parameter identification of dynamical systems under non-ideal excitation conditions[Formula presented]

This work proposes a new Particle Swarm Optimization (PSO) algorithm specifically designed for parameter identification of physical systems. The key feature of the proposed algorithm is that it takes into consideration the Spectral Richness of the signal used for exciting the system during the identification procedure. The Spectral Richness is essentially the number of spectral lines in the Fast Fourier Transform of a signal, and if this number is large, the variability of the parameter estimates produced by well-known PSO algorithms is small. However, low values of Spectral Richness may cause large variability of the parameter estimates. The proposed approach, which is termed as the Spectral Richness Particle Swarm Optimization (SR-PSO) algorithm, reduces the variability of the parameter estimates when using an excitation signal with a low value of Spectral Richness compared with state-of-the-art PSO algorithms, and maintains the same performance if the Spectral Richness is high. In a first case study, a set of real-time experiments applying excitation signals with different levels of Spectral Richness have been performed on a servomechanism in order to obtain several data sets. The acquired data from each excitation signal has been used to perform a parameter identification process using various algorithms including the classic PSO, the Linear Variable Weight Particle Swarm Optimization (LVW-PSO), the Linear Variable Constriction Factor Particle Swarm Optimization (LVCF-PSO), the state-of-the-art Fractional Order Regulated Particle Swarm Optimization (FOR-PSO) and the proposed Spectral Richness Particle Swarm Optimization (SR-PSO). The pertinence of the parameter estimates is also evaluated by designing and experimentally applying a model-based feedback control to the servomechanism. The proposed SR-PSO algorithm is also tested in a thermoelectric cooler model using numerical simulations. It is shown that the values of the identified parameters heavily depends on the kind of excitation signal applied to this system.