CAE-PSO

A Convolutional Autoencoder trained using the PSO (Particle Swarm Optimization) algorithm for extracting latent monotonic factors from multivariate time series.

Here we provide information about:

1. Introduction
2. Installation
3. Basic usage
4. Citation
5. License

1. Introduction

cae-pso is a Python package designed for unsupervised feature extraction from complex multivariate time series. By integrating a Convolutional Autoencoder (CAE) with Particle Swarm Optimization (PSO), this model is optimized to construct latent monotonic factors. This approach is highly effective for applications such as generating robust health indicators for predictive maintenance, condition monitoring, and degradation tracking (e.g., bearing health assessment) in wind energy and aerospace systems.

The package implements the hybrid training methodology proposed in the following research:

A hybrid Convolutional Autoencoder training algorithm for unsupervised bearing health indicator construction Engineering Applications of Artificial Intelligence, Volume 139, 2025. Read the full paper on ScienceDirect

In this work, the model is applied to extract the monotonic factor describing the degradation in bearings, i.e., Health Indicators (HIs). Leveraging PSO for training the CAE architecture enables maximising the global monotonicity of the extracted factor.

2. Installation

You can install the latest release of the package directly from PyPI.

pip install cae-pso

3. Basic usage

⚠️ Important Note on Multiprocessing: Because the train method uses Python's multiprocessing library to distribute the PSO population workload, you must wrap your execution code inside an if __name__ == '__main__': block. Failing to do so will cause recursive spawning of subprocesses and crash your program.

Below is a quick-start example demonstrating how to initialize the CAE model, prepare your data with the expected dimensional shapes, run the PSO training, and extract the monotonic health indicator (HI).

import numpy as np
from cae_pso import CAE

if __name__ == '__main__':
    # 1. Prepare your multivariate time series data
    # The model expects a list of arrays for training (e.g., multiple run-to-failure trajectories).
    # Each array MUST have the shape: (1, total_time_steps, n_features, 1)
    total_time_steps = 1000
    n_features = 4
    time_window = 10

    # Creating a single dummy run-to-failure (RTF) trajectory
    rtf_trajectory = np.random.rand(1, total_time_steps, n_features, 1)
    train_data = [rtf_trajectory]  # Add more trajectories to this list as needed

    # 2. Initialize the model
    # Define the time window (sequence length) and the number of features
    cae = CAE(
        time_w=time_window,
        n_features=n_features,
        n_filters=16,  # Default: 16 filters
        activation='elu'  # Default: Exponential Linear Unit
    )

    # The Keras model can be accessed using cae.model
    print(cae.model.summary())

    # 3. Train the model using PSO
    # The train method utilizes multiprocessing and logs the generation stats
    history = cae.train(
        data=train_data,
        n_gen=10,  # Number of generations
        pop_size=10,  # Particle swarm population size
        log_filepath='./logs/'  # The directory to save the training logs
    )

    # Access training history if needed
    # print("Best Fitness:", history.maxs[-1])

    # 4. Extract the Health Indicator (HI)
    # Pass a single trajectory to get_hi() to extract the smoothened, monotonic trend
    # Output will be a 1D array representing the health indicator over time
    health_indicator = cae.get_hi(rtf_trajectory)

    print(f"Extracted HI shape: {health_indicator.shape}")

4. Citation

If you use this package in your research or work, please cite the original paper:

@article{Milani2025,
  title = {A hybrid Convolutional Autoencoder training algorithm for unsupervised bearing health indicator construction},
  volume = {139},
  ISSN = {0952-1976},
  url = {http://dx.doi.org/10.1016/j.engappai.2024.109477},
  DOI = {10.1016/j.engappai.2024.109477},
  journal = {Engineering Applications of Artificial Intelligence},
  publisher = {Elsevier BV},
  author = {Milani,  Ali Eftekhari and Zappalá,  Donatella and Watson,  Simon J.},
  year = {2025},
  month = Jan,
  pages = {109477}
}

5. License

This project is licensed under the Apache License 2.0 - see the LICENSE file for details.

Copyright notice:

Technische Universiteit Delft hereby disclaims all copyright interest in the program "CAE-PSO" written by the Author(s). Henri Werij, Faculty of Aerospace Engineering, Technische Universiteit Delft.

© 2026, Ali Eftekhari Milani