A Comparison of Evolutionary Computation Techniques for IIR Model Identification

Abstract

System identification is a complex optimization problem which has recently attracted the attention in the field of science and engineering. In particular, the use of infinite impulse response (IIR) models for identification is preferred over their equivalent FIR (finite impulse response) models since the former yield more accurate models of physical plants for real world applications. However, IIR structures tend to produce multimodal error surfaces whose cost functions are significantly difficult to minimize. Evolutionary computation techniques (ECT) are used to estimate the solution to complex optimization problems. They are often designed to meet the requirements of particular problems because no single optimization algorithm can solve all problems competitively. Therefore, when new algorithms are proposed, their relative efficacies must be appropriately evaluated. Several comparisons among ECT have been reported in the literature. Nevertheless, they suffer from one limitation: their conclusions are based on the performance of popular evolutionary approaches over a set of synthetic functions with exact solutions and well-known behaviors, without considering the application context or including recent developments. This study presents the comparison of various evolutionary computation optimization techniques applied to IIR model identification. Results over several models are presented and statistically validated.

Flower Pollination Algorithm for Multimodal Optimization

“…In case of 6 J , the algorithms CSA, DCGA, MGSA and MGSA present a poor performance; however, the FSDE, CDE, RM and MFPA algorithms have been able to detect all optima. For function 7 f , the MFPA, CDE and ES algorithms detect most of the optima whereas the rest of the methods reach different performance levels. By analyzing the MPR index in Table 2, MFPA has obtained the best score for all the multimodal problems.…”

“…These techniques provide a theoretical guarantee of finding the global optimum assuming some theoretical suppositions about objective function such as the unimodality 5,6 . However, most of the practical optimization problems tend to generate multimodal surfaces maintaining several local and global optima 7 . Under such conditions, the use of classical methods faces great difficulties in finding an acceptable solution due the existence of several optima in the objective function.…”

Swarm and evolutionary computing algorithms for system identification and filter design: A comprehensive review

“…Even though there are concerns on stability, this property of IIR filters have made them a popular candidate for practical system identification and filter design (Cuevas et al, 2014). In a basic IIR system identification task, mod-4 elling of a practical system is attempted using an adaptive IIR filter.…”

“…CSA was used for the design of a fractional delay IIR filter in (Kumar and Rawat, 2015). In (Cuevas et al, 2014), performance of CSA, flower pollination algorithm (FPA), electromagnetism-like optimization (EM), PSO and ABC were compared for equal and reduced order IIR modelling. Even though CSA was shown to provide accurate modelling in comparison with PSO, ABC, and EM, it failed to outperform FPA.…”

“…The error surface in most of the system identification scenarios discussed above is multimodal and thus a conventional gradient descent approach may converge to a sub-optimal solution (Cuevas et al, 2014). In an endeavour to overcome this limitation of traditional gradient descent algorithm based system identification methods, the system identification task may be formulated as an optimization problem that can be solved using a structured stochastic search strategy like swarm and evolutionary computing algorithms.…”