CVDA for CSTR Process Fault Detection

MATLAB implementation CVDA for process incipient fault detection, including T^2, SPE (Q), and D statistics with KDE limits.

## Overview

This repository provides a MATLAB implementation for Statistical Process Monitoring (SPM) using both traditional **Canonical Variate Analysis (CVA)** and **Canonical Variate Dissimilarity Analysis (CVDA)**. It is particularly designed for incipient fault detection in industrial processes.

The code computes the dynamic control limits using **Gaussian Kernel Density Estimation (KDE)** and automatically evaluates the performance metrics: **Fault Detection Rate (FDR)** and **False Alarm Rate (FAR)**.

## Features

* Computes three key monitoring statistics:

* **$T^2$** (Traditional CVA State Statistic)

* **$Q$ or SPE** (Squared Prediction Error)

* **$D$ or $T_D$** (CVDA Dissimilarity Index for incipient faults)

* Calculates non-parametric control limits via KDE (Confidence level customizable, e.g., 99%).

* Automatically isolates the fault injection time and displays FDR/FAR directly on the plotted results.

* Handles pure data-driven training and monitoring using `.csv` datasets.

## How to Use

Simply run the `CVDA_main.m` script. It will load the normal training data and faulty test data, then execute the main monitoring function:

```matlab

% Example usage

alpha = 0.99; % 99% confidence limit

n = 25; % Retained states

p = 15; % Past observation window

f = 15; % Future observation window

cvda_fun(alpha, n, p, f, X_train, X_test);

This code is inspired by and implements the methodology described in:

[1] Pilario, K.E.S. and Cao, Y. "Canonical Variate Dissimilarity Analysis for Process Incipient Fault Detection," IEEE Transactions on Industrial Informatics, 2018. DOI: 10.1109/TII.2018.2810822.

[2] Yi Cao (2026). A Benchmark Case for Statistical Process Monitoring - Cranfield Multiphase Flow Facility (https://ww2.mathworks.cn/matlabcentral/fileexchange/50938-a-benchmark-case-for-statistical-process-monitoring-cranfield-multiphase-flow-facility), MATLAB Central File Exchange.

[3] Karl Ezra Pilario (2026). Feedback-controlled CSTR Process for Fault Simulation (https://ww2.mathworks.cn/matlabcentral/fileexchange/66189-feedback-controlled-cstr-process-for-fault-simulation), MATLAB Central File Exchange.

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