Energy harvesting (EH), which scavenges electric power from ambient, otherwise wasted, energy sources, has received considerable attention for the purpose of powering wireless sensor networks and low-power electronics. Among ambient energy sources, widely available vibration energy can be converted into electrical energy using piezoelectric materials that generate an electrical potential in response to applied mechanical stress. As a basis for designing a piezoelectric energy harvester, an analytical model should be developed to estimate electric power under a given vibration condition. Many analytical models under the assumption of the deterministic excitation cannot deal with random nature in vibration signals, although the randomness considerably affects variation in harvestable electrical energy. Thus, predictive capability of the analytical models is normally poor under random vibration signals. Such a poor power prediction is mainly caused by the variation of the dominant frequencies and their peak acceleration levels. This paper thus proposes the three-step framework of the stochastic piezoelectric energy harvesting analysis under non-stationary random vibrations. As a first step, the statistical time-frequency analysis using the Wigner-Ville spectrum was used to estimate a time-varying power spectral density (PSD) of an input random excitation. The second step is to employ an existing electromechanical model as a linear operator for calculating the output voltage response. The final step is to estimate a time-varying PSD of the output voltage response from the linear relationship. Then, the expected electric power was estimated from the autocorrelation function that is inverse Fourier transform of the time-varying PSD of the output voltage response. Therefore, the proposed framework can be used to predict the expected electric power under non-stationary random vibrations in a stochastic manner.
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