Comparison of Fourier, principal component and wavelet analyses for high speed flame measurements

The continuing advancement of high speed, combustion diagnostics calls for mathematical techniques that can extract key information from large datasets. This paper therefore describes a case study to compare the characterization of combustion dynamics behind a V-gutter flame holder using three mathematical methods: Fourier analysis, principal component analysis, (PCA), and wavelet analysis (WA). The comparison focuses on the analysis of the characteristic frequencies of flow-flame interactions, with a particular emphasis on the analysis of transient and unsteady combustion procedures, such as lean blow off. Experimental data obtained under a range of conditions were analyzed using all three methods, and several observations were made. When applied to the analysis of stable combustion processes, all three methods reported frequency characteristics that were similar both quantitatively and qualitatively. Under unstable and transient combustion conditions, the WA method is capable of revealing the dynamics of the frequency components in the measurements, while traditional Fourier and PCA methods encounter application restrictions. Lastly, these applications also demonstrated WA's suitability for practical combustion measurements beyond chemiluminescence, such as its applicability to discrete signals, insensitivity to the choice of wavelet basis, and insensitivity to the target signal extracted from the raw measurements.