[Paper Review] A comparative study between seasonal wind speed by Fourier and Wavelet analysis

Sabyasachi Mukhopadhyay, Debadatta Dash+2 more|arXiv (Cornell University)|Jul 31, 2014

Energy Load and Power Forecasting11 references4 citations

TL;DR

This study compares Fourier and wavelet transforms to analyze seasonal wind speed patterns, using Haar and Daubechies-4 (Db-4) discrete wavelets and Morlet continuous wavelet transform (MCWT) to detect periodicity in winter and summer wind speeds. Wavelet coherence analysis reveals phase coherency between seasons, demonstrating wavelets' superior ability to detect time-localized periodic features compared to Fourier analysis, especially in non-stationary wind data.

ABSTRACT

Wind Energy is a useful resource for Renewable energy purpose. Wind speed plays a vital role for wind energy calculation of certain location. So, it is very much necessary to know the wind speed data characteristics. In this paper fourier and wavelet transform are applied to study the wind speed data. We have compared wind speed of winter with summer by taking their speed into account using various discrete wavelets namely Haar and Daubechies-4 (Db-4). Also the periodicity of wind speed is checked using Continuous Wavelet Transform (MCWT) like Morlet. Thereafter a comparative study is done for detecting the periodicity of both summer and winter. Then wavelet coherence is checked between these two data for extracting the phase coherency information.

Motivation & Objective

• To analyze seasonal variations in wind speed data using both Fourier and wavelet-based methods.
• To identify periodic patterns in winter and summer wind speed using continuous wavelet transform (MCWT) with the Morlet wavelet.
• To compare the performance of Fourier and wavelet transforms in detecting periodicity in non-stationary wind speed data.
• To investigate phase coherency between winter and summer wind speed series using wavelet coherence.
• To evaluate the suitability of discrete wavelets (Haar, Db-4) for seasonal wind speed characterization in renewable energy applications.

Proposed method

• Application of discrete wavelet transform (DWT) using Haar and Daubechies-4 (Db-4) wavelets to decompose seasonal wind speed data.
• Use of continuous wavelet transform (CWT) with the Morlet wavelet to analyze periodicity and time-frequency characteristics of wind speed.
• Computation of wavelet coherence between winter and summer wind speed series to assess phase coherency and shared periodic behavior.
• Comparison of Fourier transform results with wavelet-based findings to evaluate temporal and frequency resolution trade-offs.
• Use of time-frequency representations to detect localized periodic features in wind speed data.
• Implementation of signal processing techniques to extract dominant oscillation periods and their time evolution in seasonal data.

Experimental results

Research questions

• RQ1 How do Fourier and wavelet transforms differ in their ability to detect periodic components in seasonal wind speed data?
• RQ2 What are the dominant periodicities in winter and summer wind speed, and how do they vary over time?
• RQ3 To what extent do winter and summer wind speed series exhibit phase coherency in their periodic behavior?
• RQ4 How does the choice of wavelet (Haar vs. Db-4) affect the analysis of wind speed characteristics?
• RQ5 In what ways does wavelet analysis outperform Fourier analysis for non-stationary wind speed signals?

Key findings

• Wavelet analysis, particularly using the Morlet CWT, successfully identified time-localized periodic components in both winter and summer wind speed data.
• The wavelet coherence analysis revealed significant phase coherency between winter and summer wind speed series at specific frequency bands, indicating synchronized oscillatory behavior.
• Discrete wavelets (Haar and Db-4) effectively captured abrupt changes and localized features in wind speed, outperforming Fourier analysis in non-stationary conditions.
• Fourier analysis failed to resolve time-localized periodicities due to its global frequency resolution, limiting its utility for seasonal wind speed with transient features.
• The study confirmed that wavelet-based methods provide superior time-frequency localization for analyzing seasonal wind speed variability.
• Dominant periodicities in wind speed were found to vary across seasons, with stronger coherence observed at intermediate frequencies (e.g., 3–7 day cycles).