# Two-phase Dual COPOD Method for Anomaly Detection in Industrial Control System

arXiv: https://arxiv.org/abs/2305.00982 · HTML: https://mlsanity.com/paper/2305.00982/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 30 Apr 2023.

## Builds on (most cited first, 14 of 14)

- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [A Multimodal Anomaly Detector for Robot-Assisted Feeding Using an LSTM-based Variational Autoencoder](https://mlsanity.com/paper/1711.00614/) (2017)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Anomaly Detection with Generative Adversarial Networks for Multivariate Time Series](https://mlsanity.com/paper/1809.04758/) (2018)
- [LSCP: Locally Selective Combination in Parallel Outlier Ensembles](https://mlsanity.com/paper/1812.01528/) (2018)
- [Detecting Cyberattacks in Industrial Control Systems Using Convolutional Neural Networks](https://mlsanity.com/paper/1806.08110/) (2018)
- [Anomaly Detection for a Water Treatment System Using Unsupervised Machine Learning](https://mlsanity.com/paper/1709.05342/) (2017)
- [Detecting Anomalous User Behavior Using an Extended Isolation Forest Algorithm: An Enterprise Case Study](https://mlsanity.com/paper/1609.06676/) (2016)
- [Anomaly Detection for Water Treatment System based on Neural Network with Automatic Architecture Optimization](https://mlsanity.com/paper/1807.07282/) (2018)
- [Secure State Estimation against Sensor Attacks in the Presence of Noise](https://mlsanity.com/paper/1510.02462/) (2015)
- [Unsupervised Ensemble Methods for Anomaly Detection in PLC-based Process Control](https://mlsanity.com/paper/2302.02097/) (2023)

## Abstract (arXiv)

Critical infrastructures like water treatment facilities and power plants depend on industrial control systems (ICS) for monitoring and control, making them vulnerable to cyber attacks and system malfunctions. Traditional ICS anomaly detection methods lack transparency and interpretability, which make it difficult for practitioners to understand and trust the results. This paper proposes a two-phase dual Copula-based Outlier Detection (COPOD) method that addresses these challenges. The first phase removes unwanted outliers using an empirical cumulative distribution algorithm, and the second phase develops two parallel COPOD models based on the output data of phase 1. The method is based on empirical distribution functions, parameter-free, and provides interpretability by quantifying each feature's contribution to an anomaly. The method is also computationally and memory-efficient, suitable for low- and high-dimensional datasets. Experimental results demonstrate superior performance in terms of F1-score and recall on three open-source ICS datasets, enabling real-time ICS anomaly detection.