STOCHASTIC DIFFERENTIATED MODELS FOR PREDICTING MAINTENANCE IN INDUSTRIAL MACHINES

Background: Manufacturing and process plants commonly subject industrial equipment to highly fluctuating operating conditions, leading to gradual deterioration and unexpected breakdowns. Such failures increase downtime and operational expenses. Traditional preventive maintenance strategies are based on predetermined inspection intervals; thus, they cannot capture the fundamental stochastic quality of equipment wear and degradation.Objectives: This study aims to establish a predictive maintenance model that considers the random nature of degradation. In particular, it aims to model the wear and tear of machinery based on stochastic calculus, approximate the failure-time distributions, update real-time states of degradation, and generate maintenance policies that are cost-effective and less prone to downtime. Methods: Stochastic Differential Equations (SDEs) are used to explain a degradation process as a time-dependent stochastic process. Drift terms in the model, model the systematic wear, and model the random shocks caused by changes in load, in the environment, and operational stresses. Ito’s lemma is used to define the failure time probability distribution. Stochastic filtering techniques, such as Kalman filters and particle filters, are used to provide real-time state estimates by incorporating sensor data to refresh the degradation levels. Finally, the methods of optimal stopping and stochastic control are combined to identify cost-efficient maintenance programs.Results: A numerical simulation case study shows that the SDE-based predictive maintenance strategy will save the equipment downtime and maintenance expenses. The model-based approach is more efficient and reliable in making maintenance decisions than periodic and reactive maintenance policies because the approach is more dynamic to real-time degradation signals. Conclusion: The findings underscore the effectiveness of stochastic modeling in representing real-world machinery degradation and operational uncertainty. The proposed framework supports the adoption of data-driven predictive maintenance strategies in modern industrial systems by leveraging SDEs, stochastic filtering, and optimal control, ultimately improving reliability and reducing operational expenditure