## 6 Conclusions  
In this study, a hybrid optimization method called HPSO-QN was proposed to accurately identify the mechanical parameters of flexible 2 MM drive systems using PSO methods. The research consisted of the following key aspects:  
* Literature review: A comprehensive review of existing methods for parameter identification in two-mass drive systems was conducted to establish the background for the proposed research. * System modeling and control: An accurate dynamic model of the two-mass drive system was developed, and a hysteresis current controller was implemented to aid in the mechanical identification process. * Hybrid optimization method: The proposed hybrid PSO method, known as HPSO-QN, was implemented to identify the mechanical parameters of the 2 MM drive system. Its effectiveness was evaluated using experimental data, and the HPSO-QN MLSM method exhibited the best performance in terms of accuracy and efficiency. The following conclusions can be drawn from the results:  
* The HPSO-QN MLSM method achieved the lowest cost function value of \(2.32\times 10^{-6}\) with five independent runs. \begin{table}
\begin{tabular}{c c} \hline \hline
**PSO Methods** & **Time (minutes)** \\ \hline SPSO & 30.22 \\ HPSO-QN SM & 161.31 \\ HPSO-QN SLSM & 175.65 \\ HPSO-QN MLSM & 468.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Computation time for the proposed methods. Figure 7: Simulation response using estimated parameters compared with measured speeds (motor and load side). * The standard deviation values demonstrated the robustness of the HPSO-QN methods, with the HPSO-QN MLSM method having the lowest values for most parameters. The motor-side Coulomb friction parameter showed the lowest standard deviation of 0.0028 among all identified parameters. * Comparing the proposed methods, the HPSO-QN MLSM method proved to be the most effective in terms of _Fcost_, indicating its accuracy in parameter estimation. The HPSO-QN SM method achieved the lowest cost function value of 0.18% for load-side Coulomb friction. * The absolute percentage error (APE) values indicated that the HPSO-QN methods, particularly MLSM, exhibited low errors in estimating mechanical parameters and friction coefficients compared to the standard method. Possible future directions include the following:
* Exploring more realistic friction models, such as the [PERSON] and LuGre models, to improve the estimation of viscous friction coefficients with higher APE values. * Applying the HPSO-QN method for parameter estimation in other dynamic systems, such as battery and supercapacitor models. This could help in improving the accuracy of models used in energy systems and electric vehicles. * Evaluating the impact of the HPSO-QN methods on the performance of control systems in real-world applications, such as robotics and automotive systems. * Extending the HPSO-QN method to incorporate global optimization techniques, specifically multi-objective optimization, to optimize multiple objectives simultaneously. * Extending the HPSO-QN method to estimate parameters in more complex systems, such as three-mass model systems, to capture additional dynamics. * Utilizing the HPSO-QN method in problems of machine learning and deep learning, where high-dimensional parameter space is prevalent, which could enhance the efficiency of hyperparameter tuning. * Investigating the potential of integrating deep learning methods with the HPSO-QN approach to enhance parameter estimation accuracy and developing hybrid models that combine data-driven and physics-based approaches. In conclusion, the proposed HPSO-QN methods offer a promising solution for accurately estimating the mechanical parameters of 2 MM systems, providing reliable and consistent results compared to other methods. Moreover, the general optimization capabilities of the HPSO-QN method indicate its potential applicability in a wide range of fields beyond mechanical systems, including energy systems, machine learning, and more.