Model identification of ventilation air pump utilizing Ridge-momentum regression and Grid-based structure optimization

Historically, the world has endured numerous respiratory pandemics, with the recent COVID-19 outbreak underscoring the significant importance of respiratory equipment and mechanical ventilators being no exception. Despite long-standing efforts in control and modeling system research, mechanical ventilators, especially the air generation unit, remain a significant challenge due to various factors and uncertainties (e.g., model structure, order selection, time-varying parameters, etc.). This paper presents a novel approach for identifying ARMA models, specifically in ventilation pumps, using Ridge regression modified with momentum (Ridge-M) and a grid search-based joint optimization strategy. The proposed algorithm effectively estimates model coefficients while simultaneously selecting the optimal AR and MA orders along with time-delay parameters. By integrating momentum into Ridge regression, the estimation process gains stability and improved convergence, particularly in handling abrupt system changes. The grid search framework ensures robust model selection by systematically evaluating candidate structures using the Akaike Information Criterion (AIC). Experimental validation with multiple input functions, including ramp and multistep signals, demonstrates that Ridge-M achieves superior performance in capturing dynamic system behaviors. Ridge-M reduces the root mean squared error (RMSE) by 2.7% on average across multistep inputs for both scenarios compared to recursive least squares and 6.8% compared to standard Ridge regression. However, standard Ridge outperforms Ridge-M for ramp inputs for both scenarios, reducing RMSE by 0.7%, indicating that momentum can slow adaptation to gradual variations. Nonetheless, Ridge-M achieves the lowest overall average RMSE (31.6236) compared to RLS (34.1499) and standard Ridge regression (32.0247), confirming its superior balance between stability and adaptability in model identification. This work offers a lightweight and stable method that is well-suited for embedded applications where data is noisy, the system is time-varying, and computational resources are limited.