Original scientific paper

https://doi.org/10.30765/er.3217

Engineering applications of nonhomogeneous Markov chains in machine learning

Neven Hadžić ; Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia *
Hrvoje Kozmar orcid.org/0000-0002-8490-3543 ; Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia
Nikola Vladimir orcid.org/0000-0001-9164-1361 ; Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia
Marija Koričan ; Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia
Viktor Ložar ; Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia

* Corresponding author.

Abstract

Machine Learning (ML) methods have been increasingly applied in engineering systems for predictive analytics and decision support. However, their implementation in real-time applications is often limited by computational complexity, memory requirements, and limited interpretability. This study proposes a novel probabilistic ML framework based on nonhomogeneous Markov chains, in which the system state space and transition probability matrix are continuously adapted as new observations become available. The proposed Markov Chain Machine Learning (MCML) methodology was developed by defining adaptive state transitions and evaluating the corresponding limiting probability distributions using both an analytical solution and a modal superposition method (MSM) to reduce computational requirements. The framework was implemented and validated using two physically different cases: purse seiner operational dynamics and high-altitude wind velocity prediction. The obtained results demonstrated excellent consistency between the analytical and MSM approaches, with the mean absolute errors of 0.00424 km/h for the sailing speed and 0.0001 m/s for the wind velocity predictions. The proposed methodology significantly reduces computational complexity while preserving prediction accuracy and probabilistic interpretability, thus providing an efficient framework for real-time engineering applications such as intelligent monitoring, predictive maintenance, and digital twins.

Keywords

machine learning; nonhomogeneous Markov chains; ship and wind speed forecasting; stochastic process; transition matrix; modal superposition method

Hrčak ID:

349632

URI

https://hrcak.srce.hr/349632

Publication date:

21.7.2026.

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