Student Research Project

Title: Spectral Analysis of Non-linear, Non-stationary Time Series Data Using Hilbert-Huang Transform and Spectrogram.

Abstract

This research project aims to explore and compare the effectiveness of Fourier Spectral Analysis (FSA), including Fourier Transform and Spectrogram, alongside Hilbert Huang Transform (HHT) and Hilbert Spectral Analysis (HSA) in analyzing non-linear and non-stationary time series signals. This research investigates the intricacies of FSA, HHT, and HSA with an in-depth discussion of their mathematical background, working, and limitations with examples.

The research applies these methods/frameworks to analyze both synthetic and natural signals and extracts valuable insights by comparing the performance of the two frameworks. This research also explores the limitations of traditional Fourier Spectral Analysis when dealing with non-stationary and non-linear signals and demonstrates the effectiveness of HHT in providing better time-frequency resolution.

The research includes practical applications to real-world sensor data from off-shore wind turbines such as accelerometers, showcasing the potential application of these methods in various scientific and engineering disciplines. This research also scrutinizes the limitations of HHT and examines recent advancements in the field aimed at addressing these challenges.

Key Words: Time Series, Fourier Spectral Analysis, Hilbert Huang Transform, Spectrogram, Empirical Mode Decomposition, Intrinsic Mode Functions.

Work summary and key goals

• To deeply understand the working, limitations and strengths of the Fourier Spectral analysis (FFT + Spectrogram) and able to write codes for FSA in Matlab and Python.
• To understand the working of the Hilbert Huang Transform and able to write codes for Hilbert Spectral Analysis (HSA) in Matlab and Python
• To apply these methods to artificial as well as natural time series signals to generate valuable insights.
• Performance comparisons of both the algorithms / Frameworks.
• Finding out about the limitations of HHT and recent research in HHT to overcome these shortcomings.
• Apply these methods to sensor data from offshore Wind Turbines (mainly accelerometer, temperature, pressure sensors) and generate insights.

Analysis of Artificially generated signal

FSA and HSA was applied to artificially generated signals. These artificial signals were generated by a combination sinusoids. The purpose was illustrate the application of FSA, HHT and HSA to these signals in order to illustrate the limitations of FSA.

Analysis of sensors data from offshore wind turbines

Data sets of natural signals were obtained from In-Situ-Wind project of SHM department of University of Siegen. The datasets were meant to be used for student research project only. They were obtained by the permission of Prof. Dr-Ing Peter Kreamer.

Contents of the repository

• Matlab codes for data analysis (live script mlx files)

• Jupyter notebooks for data analysis (python)

• Images of the data analysis results

• Latex source file of the report

• Research Papers and Books

• Notes - Presentations and scanned

• CSV files from Offshore-Wind Turbine data. These CSVs were extracted from two large Data Structures in Matlab files/tables. These CSVs contains the following sensor data:

• D1--- Data set 1, obtained on 24-01-2022

• D2--- Data set 2, obtained on 29-01-2022

• Acc---Acclerometer data

• DMS---Strain gauge data

• INC--- Inclination data

• Temp--- Temperature data

• EOC--- Environmental operating conditions data

Only relevant parts of the datasturcture were converted and extracted into CSVs. These files were later analysed by applying Hilbert Huang Transform and Spectrogram for a comparitive study.

Scope of future Work :

To build an inexpensive, modular, wireless sensor data acquisition, measurement and analysis system.

Measurement System Phase I

Project Description

• Goal: Implementation of a standalone wireless sensor data measurement system. Measurement system will do FSA and HHT + HSA and other time series analysis on raspberry Pi for processing real time sensor data (Updating graphs every 1-5 minutes).

• For first phase of the measurement system, a temperature-pressure sensor (Bosch BMP280) with a rpi PicoW board will be used for wirelessly transmitting data to a server (using MQTT/HTTP).

• Initial data logging system will be based on CSV files, later logging systems will move from CSV to SQL/Time Series DB (Postgre SQL / Influx DB)

• Backend logic for FSA, HSA and other Time-series data analysis functions will be implemented in Python/JavaScript.

• Initial data manipulation and visualization will be done using Python and Jupyter Notebooks

• GUI implementation will be done on rpi for interaction with the measurement system (HTML5 or React based) in the later prototypes 2,3 ....

• Experiments with system architechture will be done by trying and changing communication protocols- (MQTT, HTTP Restful APIs), sensor data logging system (CSV, PostgreSQL, InfluxDB), Data Visualization System (Jupyter notebooks, PowerBI, HTML/React based GUI)

Measurement System | Phase 1 | Prototype - 1 | System Architechture

Measurement System Phase II

• Implementation of the measurement system backend logic (With reduced functionalities) on inexpensive $10-20 computer like ESP32 / RP PicoW / RPzeroW2 in MicroPython/Arduino framework. (Edge Computing)
• Running the board on battery source and visualization of results via Mobile device using a Wifi Connection
• Implementation of the data visualization system using React (Native)
• Implementation of the whole system Measurement system using containerization with Docker.
• Assigning Static IP address to the MQTT/HTTP Server

Measurement System Phase III

• Building a custom PCB for sensor data acquisition, logging, computing algorithms, and visualization of sensor data using Mobile device with WiFi connection.
• Cyber Security -- Password protection, Hardware encryption, Sensor data encryption using ECC(Elliptic Curve Cryptography) / other suitable crytographic algorithms for IoT devices.
• Upload of telemetry data to the cloud account/remote server.

Hardware specifications for custom PCB:

Prtotype Hardware device I

• PCB with ESP32/RP2040 | (Wroom/Wrover module), ESP32 S/C/P series, PicoW board
• UART-USB bridge | (CP2102)
• Inbuilt accelerometer/IMU unit | (SPI/I2C)
• Inbuilt temperature, humidity, pressure sensor | (Bosch BME280, BMP280 series) | (I2C)
• Inbuilt LDR
• Inbuilt Flash/EPROM storage + removable memory card support | (SPI)
• Option for programming the chip (RP2040) via SWD and USB| (USB to UART bridge) | CP2102
• Native USB support, USB OTG, WiFi and BLE capabilities | ESP32 S series chips
• Power supply via USB and 3.3V cheap Li-ion battery.
• Charging circuit for Li-ion battery
• Programming via USB interface using MicroPython/Arduino framework/ Embedded C
• Future boards to have LoRaWAN communication capabilities by adding the module/SOC | Semtech Sx1276 series chips

Functional Software specifications and requirements

Algorithm and analysis

• In depth study of the variants of EMD/HHT
• In depth study of time and memory complexity of HHT and its variants
• Implementation of advance variants of HHT/EMD/HSA algorithms in a) Python b) C++
• First sandbox to be in Jupyter Notebooks --> Python Modules
• Developing Python libraries for implementation of HHT and its variants -- EEMD, MEMD, HHSA

Please refer to the following repository for updates and progress of the planned future work Measurement System