Crest Factor Optimization for Multisine Excitation Signals with Logarithmic Frequency Distribution Based on a Hybrid Stochastic-Deterministic Optimization Algorithm

Abstract

For diagnosis of batteries and fuel cells based on impedance spectroscopy, excitation signals are required, including low frequencies down to the mHz range. This leads to a long measurement time and compromises the stability condition for impedance spectroscopy. Multisine excitation signals with logarithmic frequency distribution can significantly reduce the measurement time but need optimization of the crest factor to realize a high signal-to-noise ratio at all excitation frequencies and maintain at the same time the linearity and stability conditions of impedance spectroscopy. Crest factor optimization is challenging, as the obtained results strongly depend on the initial phase values and many trials are necessary. It takes a very long time and can not be easily performed automatically up to now. In this paper, we propose a time-efficient hybrid stochastic-deterministic crest factor optimization method for multisine signals with logarithmic frequency distribution. A sigmoid transform on the multisine signal gradually transforms the multi-frequency signal into a binary-alike signal. The crest factor is significantly decreased, but the phases of the singular frequency signals remain sub-optimal. Further optimization based on the Gauss-Newton algorithm can determine the final phases, realizing a lower crest factor. The proposed method is less sensitive to initial phase values and provides more reasonable results in a reasonable time. The validation on a Samsung INR-18650-25R Lithium-ion battery cell shows that the crest factor of the optimized multisine signals has a median of 3.62 ± 0.7 within 6 min of run time, which is significantly better than the best previous work in the state-of-the-art of 3.85 ± 0.11 for the same run time.