Comprehensive Toolbox for Signal Processing and Predictive Modeling

This repository contains the implementation of a Comprehensive Toolbox for Signal Processing and Predictive Modeling. The system leverages advanced numerical methods to process sensor data, predict machine failures, optimize operational parameters, and enhance overall machinery efficiency. This solution is ideal for reducing downtime, preventing costly repairs, and optimizing maintenance schedules.

Overview

The system is designed to monitor sensor data and use mathematical techniques to provide insights on machine health. The project focuses on:

• Signal Processing with DFT (Discrete Fourier Transform): Converts time-domain sensor data into the frequency domain to detect patterns and anomalies.
• Predictive Modeling with Newton's Divided Difference: Builds an interpolation model to predict future machine conditions and key performance indicators (KPIs).
• Optimization with Newton's Method: Identifies optimal machine parameters, such as temperature and pressure, to maintain efficiency and avoid breakdowns.
• Avoiding Overfitting using Runge's Phenomenon: Ensures the predictive model generalizes well and avoids overfitting when making predictions.

Features

1. Anomaly Detection:

   • Utilizes the DFT to process vibration, pressure, and acoustic emission data from industrial machines.
   • Identifies anomalies such as excessive vibration or mechanical failure indicators.

2. Predictive Maintenance:

   • Forecasts machine performance using Newton’s Divided Difference interpolation based on historical sensor data.
   • Predicts remaining useful life (RUL) of machine components, enabling proactive maintenance scheduling.

3. Operational Optimization:

   • Uses Newton’s method to optimize machine parameters like temperature and pressure for efficient operation.
   • Automatically adjusts operational thresholds to extend the machinery's lifespan and reduce energy consumption.

4. Robust and Generalizable Model:

   • Addresses Runge's Phenomenon to prevent overfitting.
   • Ensures predictive models are stable and reliable for unseen data, making the system scalable to various types of industrial machinery.

Project Structure

.
├── dft_analysis.m          # Function for DFT signal processing
├── predictive_model.m      # Newton’s Divided Difference interpolation
├── optimization.m          # Newton's method for operational optimization
├── runge_phenomenon.m      # Handling Runge's phenomenon in interpolation
└── README.md               # Project documentation

Getting Started

Prerequisites

• MATLAB or Octave installed
• Sensor data from industrial machines (vibration, temperature, pressure)

Installation

Clone the repository:

git clone https://github.com/saadbenchekroun/root-finding-interpolation-algorithms/

Usage

1. Signal Processing:

   • Use dft_analysis.m to transform sensor data from time to frequency domain and detect anomalies.

2. Predictive Maintenance Model:

   • Use predictive_model.m to predict future machine conditions using Newton's Divided Difference interpolation.

3. Optimization:

   • Use optimization.m to compute the optimal operational parameters (e.g., temperature and pressure).

4. Handling Runge's Phenomenon:

   • Apply runge_phenomenon.m to ensure stability and avoid overfitting in the predictive model.

Example

Here's an example of how to run the DFT analysis on a sensor data vector:

x = load('sensor_data.mat'); % Load your time-domain sensor data
X = dft_analysis(x);         % Apply DFT to the data

Results

• Increased Machine Uptime: Predicts failures early and schedules maintenance before issues occur.
• Optimized Maintenance Schedules: Minimizes unnecessary inspections and avoids unexpected failures.
• Energy Efficiency: Keeps machines running at their most efficient settings, reducing power consumption.

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

License

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

Contact

For any inquiries, please contact [email protected].