Can Random Excitation Truly Assess Energy Harvester Performance? A Literature Review

The research on energy harvesting has evolved significantly, moving from idealized sinusoidal tests to more realistic random and broadband vibration scenarios. The following literature review outlines key studies that use stochastic loading to evaluate the performance of vibration energy harvesters (VEHs), supporting the methodological approach of using power spectral density (PSD), frequency response functions (FRFs), and average power to characterize energy harvesting devices.

Key Research Directions in Stochastic Energy Harvesting

1. The Stochastic Nature of Ambient Vibrations

A comprehensive review of piezoelectric VEH highlights a fundamental challenge: ambient vibrations in real-world applications are often random and broadband, making the narrow frequency bandwidth of linear energy harvesters inadequate for practical use. This review is crucial for justifying why random excitation tests are more relevant than single-frequency sinusoidal tests for evaluating a harvester's performance under realistic conditions.

2. Theoretical Frameworks for Broadband Random Vibrations

Adhikari et al. (2009) provided an early theoretical foundation for piezoelectric energy harvesting from broadband random vibrations. By modeling ambient base excitation as stationary Gaussian white noise with a constant PSD, they derived the mean power output using the theory of random vibrations. This work establishes the legitimacy of using a given input PSD as a known input condition and calculating theoretical response and output power, a common approach in current research.

3. Experimental Comparisons of Harmonic, Random, and Sine-on-Random Vibration

A dedicated experimental study compared the performance of a piezoelectric energy harvesting system under harmonic, random, and sine-on-random (SOR) input vibrations. The research explicitly analyzed the implications of excitation characteristics on harvested power. This work is a direct precedent for using random vibration experiments as a standard tool for comparing harvester performance across different excitation types.

4. The Impact of Band-Limited Random Base Excitation

More recent research explores the effect of band-limited random base excitation on energy harvesters, bridging the gap between studies using wide-band random and pure harmonic excitation. This study specifically investigates how the bandwidth of the random vibration influences performance, with findings showing that harvesters like galloping devices are insensitive to random excitation characteristics, while vortex-induced vibration (VIV) harvesters in lock-in conditions are significantly affected. This aligns directly with the methodological approach of using input PSD and frequency range to define experimental conditions.

5. Nonlinear and Multistable Harvesters for Random Environments

Nonlinear and multistable designs are frequently proposed to overcome the narrow bandwidth problem. Studies confirm that introducing nonlinearity and multioscillator structures can broaden the operating bandwidth, enabling more efficient energy harvesting under random vibrations. Specific examples include bistable energy harvesters for random wave environments and parametric excitation for broadband energy harvesting. These works support the idea that a nonlinear system's response to random excitation cannot be fully captured by a linear FRF, making metrics like response spectra, RMS quantities, and average power more appropriate for evaluation.

6. Combining Stochastic Models with Experiment

A strong line of research combines numerical stochastic models with experimental validation. One study modeled a piezoelectric harvester driven by broadband vibrations using an underdamped Langevin equation, experimentally validating the power extraction for both linear and nonlinear electrical loads. Another study evaluated a novel piezoelectric harvester through frequency response, force response, and power under optimal load, with experimental results matching simulations. This combined approach validates the research pathway of using experimental input acceleration to drive a theoretical model and then comparing theoretical and experimental responses and power.

Methodological Support for Your Research

The reviewed literature provides a strong evidence base for the following points relevant to a paper using random excitation:

• Random excitation is a valid and necessary tool for evaluating practical energy harvesting performance.
• Real-world vibrations are stochastic and broadband, so harvesters must be designed and tested for such inputs.
• Nonlinear and multistable structures are particularly suited for random vibrations, and their performance should be evaluated using appropriate metrics like average power, RMS values, and response spectra, not just linear FRFs.
• Combining experimental data with numerical models (e.g., using experimental input acceleration to drive an ODE model) is a well-established and accepted research methodology.

Important Considerations for Your Paper

While the literature strongly supports the use of random excitation, it is important to note that not all studies employ the exact same post-processing pipeline of Welch's method, FRF estimation, coherence functions, and direct ODE comparison. A safer and more accurate approach in your paper is to describe your methodology as borrowing the core ideas from this body of research (input PSD, random response, output power evaluation) and then extending and combining them with a more detailed experimental data analysis pipeline (e.g., equivalent FRF, coherence).

Furthermore, if your device is nonlinear or multistable, it is scientifically critical to frame your FRF as an "equivalent frequency response under random excitation" rather than a strict linear transfer function, as the response level will be a function of the excitation amplitude.

Example Wording for Your Paper

"Ambient vibrations are generally broadband and stochastic rather than purely harmonic. Therefore, random excitation has been widely used to evaluate the practical performance of vibration energy harvesters, particularly in terms of response statistics, output voltage and harvested power. Previous studies have considered broadband random vibrations, band-limited random base excitation, and random environmental excitations to assess the energy harvesting capability of piezoelectric, electromagnetic and nonlinear multistable harvesters."

"For nonlinear or multistable harvesters, random excitation is particularly relevant because nonlinear dynamics can broaden the operating bandwidth and may enable more effective energy harvesting under random vibrations. Accordingly, the harvesting performance should be evaluated using response spectra, RMS quantities, output voltage and average power, while a frequency response estimated from random data should be interpreted as an equivalent response under the specified excitation level rather than a unique linear transfer function."