Dielectric analysis (DEA) is a well-known technology for monitoring chemical processes e.g., the curing of adhesives. DEA compares the changes in phase and amplitude of a sinusoid applied to a specimen with its response signal. Multi-sine excitation signals give spectroscopic insight in fast chemical processes over bandwidths from 101 Hz to 107 Hz. The crest factor (CF) determines the information density of a multi-sine signal. Minimizing the CF yields higher information density and is the goal of the presented work.
Four algorithms and a combination of two of them will be presented. The first one optimizes the phase angle of each signal thus reducing the CF. The second one optimizes the signal by calculating random phase angles and amplitudes. The combined algorithm alternates between the first and second optimization algorithm. Additionally, a simulated annealing approach and a genetic algorithm optimizing the CF were implemented. Optimizations were conducted for identical multi-sine configurations for each algorithm.
The results are compared with the performance of the algorithms Ojarand presented in his papers from 2017 [1] and 2014 [2]. First, multi-sine signals comprising the same configuration as used by Ojarand are optimized by the introduced algorithms. To overcome the limitations of the algorithms proposed by literature, the developed algorithms are applied to multi-sine signals comprising 50+ frequencies. The developed algorithms generally have better performance for optimization of multi-sine signals with wide bandwidth and non-flat amplitude spectra. The results are better in terms of resulting crest factor as well as computation time.
