Harvesting wind energy to detect weak signals using mechanical stochastic resonance

Wind is free and ubiquitous and can be harnessed in multiple ways. We demonstrate mechanical stochastic resonance in a tabletop experiment in which wind energy is harvested to amplify weak periodic signals detected via the movement of an inverted pendulum. Unlike earlier mechanical stochastic resonance experiments, where noise was added via electrically driven vibrations, our broad-spectrum noise source is a single flapping flag. The regime of the experiment is readily accessible, with wind speeds $\sim 20$ m/s and signal frequencies $\sim 1$ Hz. We readily obtain signal-to-noise ratios on the order of 10 dB.

Figure 1

Schematic of the mechanical stochastic resonance apparatus. At lower right, a wind-blown flapping flag delivers noise to the main axle via a slipless pulley. At lower left, a rotary motor delivers a subthreshold sinusoidal signal to the main axle indirectly via a tensioned slipping belt. At upper left, a bistable inverted pendulum rotates back and forth between two stops.

Figure 2

Apparatus photograph. At right, the jet fan blows downward on the horizontal flag. At left, the inverted (blue) pendulum tops the tower. At center, a string passing through the acrylic tube couples the motion of the flag to the rotation of the pendulum. At bottom left, a rotary motor provides the drive signal.

Figure 3

Angle $\theta$ vs time $t$ for a typical time series with wind speed $v_w=19$ m/s. Continuous unfiltered (black) data exhibit both interwell and intrawell motion. Discrete filtered (red) data record only interwell motion.

Figure 4

Power spectral density or spectrum $S$ vs frequency $f$ with wind speed $v_w=23$ m/s. The (red) average spectrum overlays the (gray) spectra from individual time series. Averaging reduces noise variation and makes more distinct the signal peak at drive frequency $f_D=1.0$ Hz. Inset: spectrum $S({\text{rad}}^2/\text{Hz})$ vs frequency $f\left(\text{Hz}\right)$ for noise only.

Figure 5

Signal-to-noise ratio $R$ vs wind speed $v_w$ for the filtered time series. A smoothing spline connects uncertainty boxes. Stochastic resonance occurs near wind speed $v_w=23$ m/s where the noise cooperates with the weak signal to maximize the signal-to-noise ratio. Insets: at top, ratio $R$ (dB) vs noise variance ${\sigma }^2\left({\text{N}}^2\right)$; at bottom, filtered angle ${\theta }_F$ vs time $t$ (s) near resonance.