A novel phase performance evaluation method for particle swarm optimization algorithms using velocity-based state estimation.

•It explores a velocity-based state estimation (VSE) method, which can estimate the real-time state of PSO variants with flexibility and less computation.•It provides a novel phase performance evaluation based on VSE, which includes phase identification method and three kinds of phase performance indicators.•It evaluates six main PSOs, and design hybrid algorithm experiments to verify the characteristics of algorithms.