Hidden Markov Models in Predictive Maintenance

Hidden Markov Models (HMMs) provide a probabilistic framework to model systems with unobserved (hidden) states using observable signals, enabling predictive maintenance algorithms to infer machinery health and forecast fault progression. Equipment degradation is represented as transitions between discrete hidden states—such as normal operation, alert and failure—while emission probabilities link noisy or incomplete sensor data (for example vibration, temperature or acoustic measurements) to those states. Transition probabilities capture the likelihood of moving between health conditions over time. Training employs the Baum–Welch algorithm to estimate model parameters from historical data, and the Viterbi algorithm to decode the most probable sequence of health states for new observations. This approach supports both condition-based maintenance and prognostics, delivering early warnings that reduce downtime, enhance safety and optimise resource allocation. Recent advances embed deep learning for robust feature extraction, extend HMMs to semi-Markov formulations to incorporate state duration, and adopt multi-sensor fusion to improve accuracy and generalisability. Applications span paper-drying presses, rotating machinery and power-generation units, demonstrating HMMs’ ability to infer latent degradation patterns with minimal labelled fault data.

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Recent studies have showcased the versatility of HMMs in predictive maintenance across industrial sectors. A 2024 case study integrated vibration analysis with deep artificial neural networks and an HMM to anticipate the health of paper-drying presses. By imputing missing sensor data online and optimising feature observations, the model classified three hidden states—proper function, alert and failure—via the Viterbi algorithm, achieving high accuracy and generalisability across different equipment types. A 2023 investigation into sensor calibration monitoring applied HMM filters to support condition-based maintenance by distinguishing production equipment faults from sensor drift. Following unsupervised feature extraction and clustering, an HMM defined three health states for both production and measurement devices, enabling calibrations only when necessary and correcting sensor anomalies in real time. Earlier work in 2021 presented a maintenance prediction framework for pulp-industry drying presses. Multivariate sensor data were merged and optimised into observable states for an HMM, which identified latent health states without prior failure annotations. The approach proved robust over nearly four years of one-minute sampling, underscoring HMMs’ potential for long-term monitoring and proactive intervention planning in complex industrial systems.

Hidden Markov Models in Predictive Maintenance publication trend

The graph below shows the total number of articles in hidden markov models in predictive maintenance across all publications each year (not limited to Nature Index journals).

Technical terms

Hidden Markov Model (HMM): A statistical model representing a system with unobservable (hidden) states that evolve over time and generate observable outputs according to state-dependent probability distributions.

Hidden state: A discrete condition of the system (for example normal, alert, failure) that is not directly observed but inferred from sensor measurements.

Emission probability: The likelihood of observing a particular sensor reading or feature given a specific hidden state.

Transition probability: The probability of moving from one hidden state to another between consecutive time steps.

Viterbi algorithm: A dynamic programming method to find the most probable sequence of hidden states given a series of observations and an HMM.

Baum–Welch algorithm: An expectation-maximisation procedure used to estimate the parameters (transition and emission probabilities) of an HMM from observed data.

References

1. Prediction maintenance based on vibration analysis and deep learning — A case study of a drying press supported on a Hidden Markov Model. Applied Soft Computing (2024).
2. Online Monitoring of Sensor Calibration Status to Support Condition-Based Maintenance. Sensors (2023).
3. Maintenance Prediction through Sensing Using Hidden Markov Models—A Case Study. Applied Sciences (2021).
4. A Hidden Semi‐Markov Model with Duration‐Dependent State Transition Probabilities for Prognostics. Mathematical Problems in Engineering (2014).