ProbMon: Probabilistic Condition Monitoring

Bayesian change-point detection and degradation modeling for predictive maintenance of LEDs and semiconductors.

ProbMon implements probabilistic condition monitoring using two core Bayesian methods:

1. Bayesian Online Change-Point Detection (BOCD) — detects regime changes in sensor signals in real time
2. Bayesian Degradation Modeling — estimates Remaining Useful Life (RUL) with full uncertainty quantification

Architecture

                  Sensor Data
                      |
         +------------+------------+
         |                         |
    BOCD Detector           Degradation Model
    (changepoint.py)        (degradation.py)
         |                         |
    Change-point             RUL Distribution
    probabilities            (mean, std, samples)
         |                         |
         +------------+------------+
                      |
              Visualization & Report
              (plots.py, dashboard.py)

BOCD Algorithm

The change-point detector implements the Adams & MacKay (2007) algorithm from scratch:

• Maintains a posterior distribution over run lengths (time since last change-point)
• Uses a constant hazard function as the prior on change-point occurrence
• Employs a Normal-Inverse-Gamma conjugate model for the observation likelihood
• Updates run length probabilities online with O(t) complexity per step
• Detects change-points where P(run_length = 0) exceeds a configurable threshold

Degradation Model

The RUL estimator uses conjugate Bayesian inference:

• Linear degradation model: y(t) = a + b*t + noise
• Sequential Normal-Normal updates on the degradation rate b
• Monte Carlo projection to failure threshold for RUL distribution
• Full posterior uncertainty propagated to predictions

Project Structure

probmon/
├── probmon/
│   ├── __init__.py
│   ├── sensors.py         # Synthetic sensor data (temperature, vibration, current)
│   ├── changepoint.py     # BOCD implementation (Adams & MacKay 2007)
│   ├── degradation.py     # Bayesian degradation model (RUL estimation)
│   ├── plots.py           # Visualization (heatmaps, fan charts, dashboards)
│   └── dashboard.py       # Text summary report
├── demo.py                # Entry point
├── requirements.txt
├── LICENSE
└── README.md

Quick Start

# Install dependencies
pip install -r requirements.txt

# Run full demo (all sensors)
python demo.py

# Run specific sensor
python demo.py --sensor temp --points 500

# Custom output directory
python demo.py --output-dir results/

Command-line Options

Flag	Description	Default
--sensor	Sensor type: temp, vibration, current, all	all
--points	Number of data points	500
--output-dir	Output directory for plots and report	output
--seed	Random seed for reproducibility	42

Output

The demo generates:

• BOCD plots: Signal with detected/ground-truth change-points + run-length heatmap
• RUL plots: Observed data + predicted trajectory with uncertainty fan + failure threshold
• Posterior evolution: How the degradation rate estimate converges over time
• Multi-sensor dashboard: All sensors at a glance
• Text report: Precision, recall, F1, detection latency, RUL estimates

Sensors

Sensor	Physical Model	Degradation Pattern
Temperature	LED thermal sensor (~65C baseline)	Gradual rise + pre-failure spikes
Vibration	Bearing RMS vibration	Increasing amplitude + harmonic defects
Current	Semiconductor leakage	Step changes + exponential runaway

References

• Adams, R. P., & MacKay, D. J. C. (2007). Bayesian Online Changepoint Detection. arXiv:0710.3742.
• Murphy, K. P. (2007). Conjugate Bayesian analysis of the Gaussian distribution. Technical report, UBC.

Requirements

• Python 3.9+
• numpy >= 1.24
• scipy >= 1.11
• matplotlib >= 3.7
• seaborn >= 0.13

No C compiler or external Bayesian libraries needed. Pure Python/NumPy/SciPy implementation.

License

MIT License - see LICENSE.

Author

Eric Gil — BSc Computer Science, Universitat de Lleida