# Orthogonal Floating Search Algorithms: From The Perspective of Nonlinear System Identification

## TL;DR

This paper introduces an orthogonal floating search framework for nonlinear system structure selection, enhancing existing algorithms by integrating orthogonal space concepts and ERR metrics, and demonstrating improved performance on benchmark systems.

## Contribution

It adapts floating search algorithms with orthogonal space and ERR metrics, eliminating nesting effects and improving nonlinear system identification.

## Key findings

- Framework effectively identifies correct system structures.
- Existing feature selection methods can be tailored for nonlinear systems.
- Demonstrated improved performance on benchmark nonlinear systems.

## Abstract

The present study proposes a new Orthogonal Floating Search framework for structure selection of nonlinear systems by adapting the existing floating search algorithms for feature selection. The proposed framework integrates the concept of orthogonal space and consequent Error-Reduction-Ratio (ERR) metric with the existing floating search algorithms. On the basis of this framework, three well-known feature selection algorithms have been adapted which include the classical Sequential Forward Floating Search (SFFS), Improved sequential Forward Floating Search (IFFS) and Oscillating Search (OS). This framework retains the simplicity of classical Orthogonal Forward Regression with ERR (OFR-ERR) and eliminates the nesting effect associated with OFR-ERR. The performance of the proposed framework has been demonstrated considering several benchmark non-linear systems. The results show that most of the existing feature selection methods can easily be tailored to identify the correct system structure of nonlinear systems.