This study proposes a delay-aware predictive maintenance control framework for multiequipment systems operating under dynamic and uncertain industrial environments. The proposed framework integrates a multilayer neural reliability prediction model, an approximate Bayesian reliability updating mechanism, and a rolling-horizon maintenance optimization model to support maintenance decision-making under delayed and asynchronous industrial information. Unlike conventional predictive maintenance approaches that rely primarily on instantaneous observations or static reliability estimation, the proposed framework explicitly models time-varying communication delays, degradation evolution, imperfect maintenance effects, and dynamic state propagation within a closed-loop maintenance control architecture. The proposed methodology first estimates machine failure probabilities using a multilayer neural network trained on heterogeneous operational and degradation-related variables. The predicted reliability is subsequently refined through approximate Bayesian filtering by integrating historical posterior information and delayed observations. Based on the updated reliability trajectories, a rolling-horizon genetic algorithm determines preventive maintenance schedules while considering maintenance capacity, workforce availability, and operational constraints. The optimization objective minimizes the total expected maintenance cost, including preventive maintenance, corrective maintenance, downtime, and reliability penalty costs. Experimental results demonstrate that the proposed framework provides competitive probability prediction performance while achieving superior maintenance cost reduction and improvements in reliability under delayed operating conditions.
Citation: Chih-Chiang Fang, Jianbin Wang. Delay-aware predictive maintenance control for multi-equipment systems using approximate Bayesian neural reliability networks[J]. Electronic Research Archive, 2026, 34(9): 6734-6771. doi: 10.3934/era.2026294
This study proposes a delay-aware predictive maintenance control framework for multiequipment systems operating under dynamic and uncertain industrial environments. The proposed framework integrates a multilayer neural reliability prediction model, an approximate Bayesian reliability updating mechanism, and a rolling-horizon maintenance optimization model to support maintenance decision-making under delayed and asynchronous industrial information. Unlike conventional predictive maintenance approaches that rely primarily on instantaneous observations or static reliability estimation, the proposed framework explicitly models time-varying communication delays, degradation evolution, imperfect maintenance effects, and dynamic state propagation within a closed-loop maintenance control architecture. The proposed methodology first estimates machine failure probabilities using a multilayer neural network trained on heterogeneous operational and degradation-related variables. The predicted reliability is subsequently refined through approximate Bayesian filtering by integrating historical posterior information and delayed observations. Based on the updated reliability trajectories, a rolling-horizon genetic algorithm determines preventive maintenance schedules while considering maintenance capacity, workforce availability, and operational constraints. The optimization objective minimizes the total expected maintenance cost, including preventive maintenance, corrective maintenance, downtime, and reliability penalty costs. Experimental results demonstrate that the proposed framework provides competitive probability prediction performance while achieving superior maintenance cost reduction and improvements in reliability under delayed operating conditions.
| [1] |
J. Li, Z. Zhang, X. Wang, W. Yan, Intelligent decision-making model in preventive maintenance of asphalt pavement based on PSO-GRU neural network, Adv. Eng. Inform., 51 (2022), 101525. https://doi.org/10.1016/j.aei.2022.101525 doi: 10.1016/j.aei.2022.101525
|
| [2] |
A. Nasser, H. Al-Khazraji, A hybrid of convolutional neural network and long short-term memory network approach to predictive maintenance, Int. J. Electr. Comput. Eng., 12 (2022), 721–730. https://doi.org/10.11591/ijece.v12i1.pp721-730 doi: 10.11591/ijece.v12i1.pp721-730
|
| [3] |
T. Zonta, C. A. Da Costa, F. A. Zeiser, G. de Oliveira Ramos, R. Kunst, R. da Rosa Righi, A predictive maintenance model for optimizing production schedule using deep neural networks, J. Manuf. Syst., 62 (2022), 450–462. https://doi.org/10.1016/j.jmsy.2021.12.013 doi: 10.1016/j.jmsy.2021.12.013
|
| [4] |
L. Xia, Y. Liang, J. Leng, P. Zheng, Maintenance planning recommendation of complex industrial equipment based on knowledge graph and graph neural network, Reliab. Eng. Syst. Saf., 232 (2023), 109068. https://doi.org/10.1016/j.ress.2022.109068 doi: 10.1016/j.ress.2022.109068
|
| [5] |
S. Apeiranthitis, P. Zacharia, A. Chatzopoulos, M. Papoutsidakis, Predictive maintenance of machinery with rotating parts using convolutional neural networks, Electronics, 13 (2024), 460. https://doi.org/10.3390/electronics13020460 doi: 10.3390/electronics13020460
|
| [6] |
S. Potharaju, R. K. Tirandasu, S. N. Tambe, D. B. Jadhav, D. A. Kumar, S. S. Amiripalli, A two-step machine learning approach for predictive maintenance and anomaly detection in environmental sensor systems, MethodsX, 14 (2025), 103181. https://doi.org/10.1016/j.mex.2025.103181 doi: 10.1016/j.mex.2025.103181
|
| [7] | Y. Zhang, Y. Ding, J. Su, L. Yang, Quality‐based tool remaining useful life prediction under time‐varying processing parameters by windowed sparse‐attention transformer, Qual. Reliab. Eng. Int., 2026 (2026). https://doi.org/10.1002/qre.70326 |
| [8] |
S. M. Seyedrezaei, S. Mirhashemi, H. Hematian, Integrated maintenance policy optimization in buffered serial production lines using neural networks, Int. J. Syst. Assur. Eng. Manag., 17 (2026), 2101–2115. https://doi.org/10.1007/s13198-025-03052-4 doi: 10.1007/s13198-025-03052-4
|
| [9] |
X. Liu, P. Zhang, H. Shi, Predictive maintenance of petrochemical equipment based on LSTM neural network and vibration signal analysis, Aust. J. Mech. Eng., 2026 (2026), 1–13. https://doi.org/10.1080/14484846.2025.2598194 doi: 10.1080/14484846.2025.2598194
|
| [10] |
W. Liu, G. Dong, M. Zou, Satellite road extraction method based on RFDNet neural network, Electron. Res. Arch., 31 (2023), 4362–4377. https://doi.org/10.3934/era.2023223 doi: 10.3934/era.2023223
|
| [11] |
H. C. Wu, Y. C. Tu, P. H. Chen, M. H. Tseng, An interpretable hierarchical semantic convolutional neural network to diagnose melanoma in skin lesions, Electron. Res. Arch., 31 (2023), 1822–1839. https://doi.org/10.3934/era.2023094 doi: 10.3934/era.2023094
|
| [12] |
J. Guo, Y. Shi, S. Wang, Synchronization analysis of delayed quaternion-valued memristor-based neural networks by a direct analytical approach, Electron. Res. Arch., 32 (2024), 3377–3395. https://doi.org/10.3934/era.2024156 doi: 10.3934/era.2024156
|
| [13] |
X. Zhao, Z. Liang, A. K. Parlikad, M. Xie, Performance-oriented risk evaluation and maintenance for multi-asset systems: A Bayesian perspective, IISE Trans., 54 (2022), 251–270. https://doi.org/10.1080/24725854.2020.1869871 doi: 10.1080/24725854.2020.1869871
|
| [14] |
F. Anderson, R. Dawid, D. McMillan, D. García‐Cava, A Bayesian reliability analysis exploring the effect of scheduled maintenance on wind turbine time to failure, Wind Energy, 26 (2023), 879–899. https://doi.org/10.1002/we.2846 doi: 10.1002/we.2846
|
| [15] |
L. Zhuang, A. Xu, X. L. Wang, A prognostic driven predictive maintenance framework based on Bayesian deep learning, Reliab. Eng. Syst. Saf., 234 (2023), 109181. https://doi.org/10.1016/j.ress.2023.109181 doi: 10.1016/j.ress.2023.109181
|
| [16] |
W. Liu, Y. Shao, C. Li, C. Li, Z. Jiang, Development of a non-Gaussian copula Bayesian network for safety assessment of metro tunnel maintenance, Reliab. Eng. Syst. Saf., 238 (2023), 109423. https://doi.org/10.1016/j.ress.2023.109423 doi: 10.1016/j.ress.2023.109423
|
| [17] |
C. C. Fang, L. Ma, W. Kuo, Bayesian analysis enhances sales and warranty strategies for repairable industrial products by considering hybrid deterioration modes, IEEE Access, 13 (2025), 72169–72188. https://doi.org/10.1109/ACCESS.2025.3563938 doi: 10.1109/ACCESS.2025.3563938
|
| [18] |
A. Cheng, Y. Bi, An integrated data-driven framework for vehicle quality analysis based on maintenance record mining and Bayesian network, Int. J. Qual. Reliab. Manag., 42 (2025), 377–400. https://doi.org/10.1108/IJQRM-03-2023-0114 doi: 10.1108/IJQRM-03-2023-0114
|
| [19] |
M. Xiong, L. Chen, J. Ming, J. Shin, Accelerating the Bayesian inference of inverse problems by using data-driven compressive sensing method based on proper orthogonal decomposition, Electron. Res. Arch., 29 (2021), 3383–3403. https://doi.org/10.3934/era.2021044 doi: 10.3934/era.2021044
|
| [20] |
H. Roch, C. Shen, Learning informed prior distributions with normalizing flows for Bayesian analysis, Phys. Rev. C, 113 (2026), 034903. https://doi.org/10.1103/wms4-m4cb doi: 10.1103/wms4-m4cb
|
| [21] |
C. Ling, J. Lei, S. Zhang, D. W. Coit, Reliability modeling of systems under dependent competing failures using bilateral coupling variables, Reliab. Eng. Syst. Saf., 272 (2026), 112625. https://doi.org/10.1016/j.ress.2026.112625 doi: 10.1016/j.ress.2026.112625
|
| [22] |
Y. S. Huang, C. C. Fang, C. M. Lu, T. L. Tseng, Optimal warranty policy for consumer electronics with dependent competing failure processes, Reliab. Eng. Syst. Saf., 222 (2022), 108418. https://doi.org/10.1016/j.ress.2022.108418 doi: 10.1016/j.ress.2022.108418
|
| [23] |
C. Ling, L. Yang, M. Wang, E. Zio, Variational Bayesian inference-assisted approach for multi-objective reliability-based design optimization, Appl. Math. Model., 159 (2026), 117023. https://doi.org/10.1016/j.apm.2026.117023 doi: 10.1016/j.apm.2026.117023
|
| [24] |
P. Djukic, S. Valaee, Delay aware link scheduling for multi-hop TDMA wireless networks, IEEE/ACM Trans. Netw., 17 (2008), 870–883. https://doi.org/10.1109/TNET.2008.2005219 doi: 10.1109/TNET.2008.2005219
|
| [25] |
X. Wang, C. Yuen, X. Chen, N. U. Hassan, Y. Ouyang, Cost-aware demand scheduling for delay tolerant applications, J. Netw. Comput. Appl., 53 (2015), 173–182. https://doi.org/10.1016/j.jnca.2015.04.002 doi: 10.1016/j.jnca.2015.04.002
|
| [26] |
L. Qu, C. Assi, K. Shaban, Delay-aware scheduling and resource optimization with network function virtualization, IEEE Trans. Commun., 64 (2016), 3746–3758. https://doi.org/10.1109/TCOMM.2016.2580150 doi: 10.1109/TCOMM.2016.2580150
|
| [27] |
H. Yuan, J. Bi, M. Zhou, A. C. Ammari, Time-aware multi-application task scheduling with guaranteed delay constraints in green data center, IEEE Trans. Autom. Sci. Eng., 15 (2017), 1138–1151. https://doi.org/10.1109/TASE.2017.2741965 doi: 10.1109/TASE.2017.2741965
|
| [28] |
S. Liu, T. Yang, Delay aware scheduling in UAV-enabled OFDMA mobile edge computing system, IET Commun., 14 (2020), 3203–3211. https://doi.org/10.1049/iet-com.2020.0274 doi: 10.1049/iet-com.2020.0274
|
| [29] |
W. K. Lai, Y. C. Wang, S. C. Wei, Delay-aware container scheduling in Kubernetes, IEEE Internet Things J., 10 (2023), 11813–11824. https://doi.org/10.1109/JIOT.2023.3244545 doi: 10.1109/JIOT.2023.3244545
|
| [30] |
J. Gao, L. Feng, F. Zhou, M. Dong, P. Yu, K. Ota, et al., Deterministic delay-aware task scheduling over in-network computing: A graph embedding-based DRL approach, IEEE Trans. Netw. Serv. Manag., 23 (2026), 3585–3601. https://doi.org/10.1109/TNSM.2026.3676106 doi: 10.1109/TNSM.2026.3676106
|
| [31] |
W. Michiels, V. Van Assche, S. I. Niculescu, Stabilization of time-delay systems with a controlled time-varying delay and applications, IEEE Trans. Autom. Control, 50 (2005), 493–504. https://doi.org/10.1109/TAC.2005.844714 doi: 10.1109/TAC.2005.844714
|
| [32] |
P. Park, J. W. Ko, Stability and robust stability for systems with a time-varying delay, Automatica, 43 (2007), 1855–1858. https://doi.org/10.1016/j.automatica.2007.02.018 doi: 10.1016/j.automatica.2007.02.018
|
| [33] |
J. H. Kim, Note on stability of linear systems with time-varying delay, Automatica, 47 (2011), 2118–2121. https://doi.org/10.1016/j.automatica.2011.05.006 doi: 10.1016/j.automatica.2011.05.006
|
| [34] |
H. B. Zeng, Z. L. Zhai, W. Wang, Hierarchical stability conditions of systems with time-varying delay, Appl. Math. Comput., 404 (2021), 126222. https://doi.org/10.1016/j.amc.2021.126222 doi: 10.1016/j.amc.2021.126222
|
| [35] |
L. Cao, Y. Pan, H. Liang, T. Huang, Observer-based dynamic event-triggered control for multiagent systems with time-varying delay, IEEE Trans. Cybern., 53 (2022), 3376–3387. https://doi.org/10.1109/TCYB.2022.3226873 doi: 10.1109/TCYB.2022.3226873
|
| [36] |
C. K. Zhang, W. H. Chen, C. Zhu, Y. He, M. Wu, Stability analysis of discrete-time systems with time-varying delay via a delay-dependent matrix-separation-based inequality, Automatica, 156 (2023), 111192. https://doi.org/10.1016/j.automatica.2023.111192 doi: 10.1016/j.automatica.2023.111192
|
| [37] |
Z. Zhang, K. Zhang, X. Xie, V. Stojanovic, ADP-based prescribed-time control for nonlinear time-varying delay systems with uncertain parameters, IEEE Trans. Autom. Sci. Eng., 22 (2024), 3086–3096. https://doi.org/10.1109/TASE.2024.3389020 doi: 10.1109/TASE.2024.3389020
|
| [38] |
M. S. Aslam, H. Bilal, A. V. Vasilakos, Self-triggered scheme design for Takagi–Sugeno fuzzy model based on mismatch premise variable with time-varying delay, IEEE Trans. Autom. Sci. Eng., 22 (2025), 15536–15548. https://doi.org/10.1109/TASE.2025.3570089 doi: 10.1109/TASE.2025.3570089
|
| [39] |
S. Zhu, K. Deng, H. Yan, M. Shen, X. Liu, S. Wen, Mean square exponential stability of dynamic memristor neutral stochastic cellular neural networks with time-varying delays, IEEE Trans. Cybern., 56 (2026), 2829–2840. https://doi.org/10.1109/TCYB.2026.3666768 doi: 10.1109/TCYB.2026.3666768
|
Figures(7) / Tables(4)
Chih-Chiang Fang, Jianbin Wang. Delay-aware predictive maintenance control for multi-equipment systems using approximate Bayesian neural reliability networks[J]. Electronic Research Archive, 2026, 34(9): 6734-6771. doi: 10.3934/era.2026294
DownLoad: