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.
Citation: Cong Toai Truong, Trung Dat Phan, Van Tu Duong, Huy Hung Nguyen, Tan Tien Nguyen. Model identification of ventilation air pump utilizing Ridge-momentum regression and Grid-based structure optimization[J]. Mathematical Biosciences and Engineering, 2025, 22(8): 2020-2038. doi: 10.3934/mbe.2025074
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.
| [1] |
D. Graupe, D. J. Krause, J. B. Moore, J. B. Moore, Identification of autoregressive Moving-average parameters of time series, IEEE Transact Automat Control, 20 (1975), 104–107. https://doi.org/10.1109/TAC.1975.1100855 doi: 10.1109/TAC.1975.1100855
|
| [2] |
H. Djouadi, K. Ouari, Y. Belkhier, H. Lehouche, M. Bajaj, V. Blazek, Improved robust model predictive control for PMSM using backstepping control and incorporating integral action with experimental validation, Results Eng., 23 (2024), 102416. https://doi.org/10.1016/j.rineng.2024.102416 doi: 10.1016/j.rineng.2024.102416
|
| [3] |
N. M. Alyazidi, A. F. Bawazir, A. S. Al-Dogail, Robust integral sliding mode control for pressure management in multi-phase flow systems Discrete-time control Integral sliding mode control (ISMC) Multi-phase flow systems (MPFS) Pressure regulation Hammerstein model Nonlinear dynamics System identification, Results Eng., 25 (2024), 104024. https://doi.org/10.1016/j.rineng.2025.104024 doi: 10.1016/j.rineng.2025.104024
|
| [4] |
W. Fan, J. Xiong, Successive over relaxation for model-free LQR control of discrete-time Markov jump systems, Automatica, 171 (2024), 111919. https://doi.org/10.1016/j.automatica.2024.111919 doi: 10.1016/j.automatica.2024.111919
|
| [5] |
J. Xu, M. Wang, G. Zhang, Trajectory tracking control of an underactuated unmanned underwater vehicle synchronously following mother submarine without velocity measurement, Adv. Mechan. Eng., 7 (2015), 1–11. https://doi.org/10.1177/1687814015595340 doi: 10.1177/1687814015595340
|
| [6] |
Q. D. Le, Q. M. Lam, M. N. Huynh, H. H. Nguyen, V. T. Duong, Hardware-in-the-Loop simulation for online identification of Lithium-ion battery model parameters and state of charge estimation, Results Eng., 25 (2025), 104509. https://doi.org/10.1016/j.rineng.2025.104509 doi: 10.1016/j.rineng.2025.104509
|
| [7] |
S. Ekinci, D. Izci, Enhancing ⅡR system identification: Harnessing the synergy of gazelle optimization and simulated annealing algorithms, e-Prime – Adv. Electr. Eng. Electron. Energy, 5 (2023), 100225. https://doi.org/10.1016/j.prime.2023.100225 doi: 10.1016/j.prime.2023.100225
|
| [8] |
S. K V, D. G, S. M. Sulthan, Adaptive Particle Swarm Optimization based improved modeling of Solar Photovoltaic module for parameter determination, e-Prime – Adv. Electr. Eng. Electron. Energy, 8 (2024), 100621. https://doi.org/10.1016/j.prime.2024.100621 doi: 10.1016/j.prime.2024.100621
|
| [9] |
A. Srivastava, An application of kho-Kho optimization algorithm to estimation parameter of permanent magnet synchronous machine, e-Prime – Adv. Electr. Eng. Electron. Energy, 6 (2023), 100309. https://doi.org/10.1016/J.PRIME.2023.100309 doi: 10.1016/J.PRIME.2023.100309
|
| [10] |
B. P. Adedeji, Energy parameter modeling in plug-in hybrid electric vehicles using supervised machine learning approaches, e-Prime – Adv. Electr. Eng. Electron. Energy, 8 (2024), 100584. https://doi.org/10.1016/J.PRIME.2024.100584 doi: 10.1016/J.PRIME.2024.100584
|
| [11] |
Y. Tang, H. Ding, X. Shan, X. Wang, Application of the novel three-stage DEA model to evaluate total-factor energy efficiency: A case study based on 30 provinces and 8 comprehensive economic zones of China, Results Eng., 20 (2023), 101417. https://doi.org/10.1016/j.rineng.2023.101417 doi: 10.1016/j.rineng.2023.101417
|
| [12] |
M. Rayati, R. Nasiri, and M. N. Ahmadabadi, Improving muscle force distribution model using reflex excitation: Toward a model-based exoskeleton torque optimization approach, IEEE Transact Neural Syst. Rehab. Eng., 31 (2023), 720–728. https://doi.org/10.1109/TNSRE.2022.3230795 doi: 10.1109/TNSRE.2022.3230795
|
| [13] |
C. Remlinger, C. Alasseur, M. Brière, J. Mikael, Expert aggregation for financial forecasting, J. Finan. Data Sci., 9 (2023), 1–21. https://doi.org/10.1016/j.jfds.2023.100108 doi: 10.1016/j.jfds.2023.100108
|
| [14] |
N. S. Gehlot, P. J. Alsina, A discrete model of induction motors for real-time control applications, IEEE Transact. Industr. Electron., 40 (1993), 317–325. https://doi.org/10.1109/41.232211 doi: 10.1109/41.232211
|
| [15] |
L. D. Paarmann and M. J. Korenberg, Estimation of the parameters of an ARMA signal model based on an orthogonal search, IEEE Transact. Automat. Control, 37 (1992), 347–352. https://doi.org/10.1109/9.119634 doi: 10.1109/9.119634
|
| [16] |
F. Ding, Y. Shi, T. Chen, Performance analysis of estimation algorithms of nonstationary ARMA processes, IEEE Transact. Signal Process., 54 (2006), 1041–1053. https://doi.org/10.1109/TSP.2005.862845 doi: 10.1109/TSP.2005.862845
|
| [17] |
S. U. Pillai, Theodore I. Shim, D. C. Youla, A new technique for ARMA-system identification and rational approximation, IEEE Transact. Signal Process., 41 (1993), 1281–1304. https://doi.org/10.1109/78.205730 doi: 10.1109/78.205730
|
| [18] |
S. Li, Y. Zhu, B. W. Dickinson, A comparison of two linear methods of estimating the parameters of ARMA models, IEEE Transact. Automat. Control, 34 (1989), 915–917. https://doi.org/10.1109/9.29444 doi: 10.1109/9.29444
|
| [19] |
J. K. Sabiti, A fast estimation method for ARMA processes, Automatica, 32 (1996), 235–239. https://doi.org/10.1016/0005-1098(96)85553-1 doi: 10.1016/0005-1098(96)85553-1
|
| [20] |
T. Wang, X. Li, J. Guo, Y. Zhao, Identification of ARMA models with binary-valued observations, Automatica, 149 (2023), 110832. https://doi.org/10.1016/j.automatica.2022.110832 doi: 10.1016/j.automatica.2022.110832
|
| [21] | B. R. Pramod, A. Regressive, S. C. Bose, System identification using ARMA modeling and neural networks, 115 (1993), 487–491. https://doi.org/10.1115/1.2901794 |
| [22] |
S. Lu, K. H. Chon, Nonlinear autoregressive and nonlinear autoregressive moving average model parameter estimation by minimizing hypersurface distance, IEEE Transact. Signal Process., 51 (2003), 3020–3026. https://doi.org/10.1109/TSP.2003.818999 doi: 10.1109/TSP.2003.818999
|
| [23] |
D. Marelli, K. You, M. Fu, Identification of ARMA models using intermittent and quantized output observations, Automatica, 49 (2013), 360–369. https://doi.org/10.1016/j.automatica.2012.11.020 doi: 10.1016/j.automatica.2012.11.020
|
| [24] |
C. Yu, K. You, L. Xie, Quantized identification of ARMA systems with colored measurement noise, Automatica, 66 (2016), 101–108. https://doi.org/10.1016/j.automatica.2015.12.013 doi: 10.1016/j.automatica.2015.12.013
|
| [25] |
F. Ding, L. Xu, F. E. Alsaadi, T. Hayat, Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique, IET Control Theory Appl., 12 (2018), 892–899. https://doi.org/10.1049/iet-cta.2017.0821 doi: 10.1049/iet-cta.2017.0821
|
| [26] |
Y. Wang, W. Zhang, M. Fan, Q. Ge, B. Qiao, X. Zuo, Regression with adaptive lasso and correlation based penalty, Appl. Math. Model., 105 (2022), 179–196. https://doi.org/10.1016/j.apm.2021.12.016 doi: 10.1016/j.apm.2021.12.016
|
| [27] |
S. Basu, G. Michailidis, Regularized estimation in sparse high-dimensional time series models, Ann. Statist., 43 (2015), 1535–1567. https://doi.org/10.1214/15-AOS1315 doi: 10.1214/15-AOS1315
|
| [28] | S. S. Mannelli, P. Urbani, Analytical study of momentum-based acceleration methods in paradigmatic high-dimensional non-convex problems, Adv. Neural Inform. Process. Syst., 34 (2021), 187–199. https://hal.science/hal-04425461v1 |
| [29] |
G. E. P. Box, G. M. Jenkins, Some recent advances in forecasting and control, J. Royal Statist. Soc. Series C Appl. Statist., 17 (1968), 91–109. https://doi.org/10.2307/2985674 doi: 10.2307/2985674
|
| [30] |
Y. Shigeto, I. Suzuki, K. Hara, M. Shimbo, Y. Matsumoto, Ridge regression, hubness, and zero-shot learning, Mach. Learn. Knowl. Discovery Databases, 9284 (2015), 135–151. https://doi.org/10.1007/978-3-319-23528-8_9 doi: 10.1007/978-3-319-23528-8_9
|
| [31] |
R. T. Nakatsu, Validation of machine learning Ridge regression models using Monte Carlo, bootstrap, and variations in cross-validation, J. Intell. Syst., 32 (2023), 20220224. https://doi.org/10.1515/jisys-2022-0224 doi: 10.1515/jisys-2022-0224
|
| [32] |
P. M. T. Broersen, S. de Waele, Finite sample properties of ARMA order selection, IEEE Transact. Instrument. Measurement, 53 (2004), 645–651. https://doi.org/10.1109/TIM.2004.827058 doi: 10.1109/TIM.2004.827058
|
| [33] |
B. Yüzbaşı, M. Arashi, S. Ejaz Ahmed, Shrinkage estimation strategies in generalised Ridge regression Models: Low/High-dimension regime, Int. Statist. Rev., 88 (2020), 229–251. https://doi.org/10.1111/insr.12351 doi: 10.1111/insr.12351
|
| [34] |
J. A. Cadzow, ARMA Time Series Modeling: An effective method, IEEE Transact. Aerospace Electron. Syst., AES-19 (1983), 49–58. https://doi.org/10.1109/TAES.1983.309419 doi: 10.1109/TAES.1983.309419
|
| [35] |
J. A. Cadzow, ARMA Modeling of Time Series, IEEE Transact. Pattern Anal. Mach. Intell., PAMI-4 (1982), 124–128. https://doi.org/10.1109/TPAMI.1982.4767216 doi: 10.1109/TPAMI.1982.4767216
|
| [36] |
A. Godichon-Baggioni, W. Lu, B. Portier, Recursive Ridge regression using second-order stochastic algorithms, Comput. Statist. Data Anal., 190 (2024), 107854. https://doi.org/10.1016/j.csda.2023.107854 doi: 10.1016/j.csda.2023.107854
|
| [37] |
P. Goulet Coulombe, Time-varying parameters as Ridge regressions, Int. J. Forecast., 41 (2025), 982–1002. https://doi.org/10.1016/j.ijforecast.2024.08.006 doi: 10.1016/j.ijforecast.2024.08.006
|
| [38] |
G. Maroni, L. Cannelli, D. Piga, Gradient-based bilevel optimization for multi-penalty Ridge regression through matrix differential calculus, European J. Control, 81 (2023), 101150. https://doi.org/10.1016/j.ejcon.2024.101150 doi: 10.1016/j.ejcon.2024.101150
|
| [39] |
W. Jamil, A. Bouchachia, Iterative ridge regression using the aggregating algorithm, Pattern Recogn. Letters, 158 (2022), 34–41. https://doi.org/10.1016/j.patrec.2022.04.021 doi: 10.1016/j.patrec.2022.04.021
|
| [40] |
H. Gao, R. Diao, Z. Huang, Y. Zhong, Y. Mao, W. Tang, Parameter identification of SVG using multilayer Coarse-to-fine grid searching and particle swarm optimization, IEEE Access, 10 (2022), 77137–77146. https://doi.org/10.1109/ACCESS.2022.3192538 doi: 10.1109/ACCESS.2022.3192538
|
| [41] |
S. W. Mahmood, G. T. Basheer, Z. Y. Algamal, Improving kernel Ridge regression for medical data classification based on meta-heuristic algorithms, Kuwait J. Sci., 52 (2025), 100408. https://doi.org/10.1016/j.kjs.2025.100408 doi: 10.1016/j.kjs.2025.100408
|
| [42] |
M. Mahadi, T. Ballal, M. Moinuddin, U. M. Al-Saggaf, A recursive least-squares with a time-varying regularization parameter, Appl. Sci., 12 (2022), 2077. https://doi.org/10.3390/APP12042077 doi: 10.3390/APP12042077
|
| [43] |
C. Illg, T. Kösters, S. Kiroriwal, O. Nelles, Adaptive system identification with regularized FIR Models, IFAC-PapersOnLine, 55 (2022), 1–6. https://doi.org/10.1016/J.IFACOL.2022.07.279 doi: 10.1016/J.IFACOL.2022.07.279
|
| [44] |
M. Neumann, R. J. Plemmons, Convergent nonnegative matrices and iterative methods for consistent linear systems, Numer. Math., 31 (1978), 265–279. https://doi.org/10.1007/BF01397879 doi: 10.1007/BF01397879
|
| [45] |
V. I. Hasanov, S. A. Hakkaev, Convergence analysis of some iterative methods for a nonlinear matrix equation, Comput. Math. Appl., 72 (2016), 1164–1176. https://doi.org/10.1016/j.camwa.2016.06.035 doi: 10.1016/j.camwa.2016.06.035
|
| [46] |
A. S. Householder, On the convergence of matrix iterations, JACM, 3 (1956), 314–324. https://doi.org/10.1145/320843.320851 doi: 10.1145/320843.320851
|
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Cong Toai Truong, Trung Dat Phan, Van Tu Duong, Huy Hung Nguyen, Tan Tien Nguyen. Model identification of ventilation air pump utilizing Ridge-momentum regression and Grid-based structure optimization[J]. Mathematical Biosciences and Engineering, 2025, 22(8): 2020-2038. doi: 10.3934/mbe.2025074
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