Reliability Study of Power Harvesting System from Sea Waves with Piezoelectric Patches

Conversion of sea waves mechanical energies into the electrical form of energy by means of piezoelectric materials is considered as one of the most recent methods for powering low-power electronic devices at sea. In this paper, power harvesting from sea waves by consideration of JONSWAP wave theory is investigated and the uncertainties of sea waves are studied for the first time. For this purpose, a vertical beam fixed to the seabed which the piezoelectric patches are attached to it, is considered as energy harvester and is modeled and simulated by MATLAB software. The generated power is computed by calculating the beam vibration response and the effect of piezoelectric patches on the generated power is studied by statistical analysis. Furthermore, reliability of the energy harvesting system is investigated as the possibility of failure based on violation criteria. It is resulted that the probability of failure increases by increasing the power.

💡 Research Summary

This paper investigates a wave‑energy harvesting system that converts the mechanical energy of sea waves into electrical power using piezoelectric patches attached to a vertical cantilever beam fixed to the seabed. Unlike most previous studies that rely on the linear Airy wave theory, the authors adopt the JONSWAP irregular wave spectrum, which captures the stochastic nature of real ocean conditions. The beam dynamics are modeled with the Euler‑Bernoulli beam equation, while the horizontal wave‑induced force is described by the Morison equation. By applying mode‑shape expansion and variable separation, the continuous system is reduced to a finite set of modal coordinates. The resulting mass, stiffness and damping matrices are assembled into a state‑space representation and integrated in time using a fourth‑order Runge‑Kutta scheme implemented in MATLAB.

The mechanical response (transverse displacement) of the beam is used to compute the electrical response of the piezoelectric patches through linear electromechanical coupling equations. Voltage and charge histories are obtained, and the average harvested power is evaluated as the time‑average of the instantaneous power (V·I).

To assess the impact of manufacturing tolerances, the length (nominal 0.1 m) and thickness (nominal 0.001 m) of the patches are each assigned a uniform distribution with ±5 % bounds. A Monte‑Carlo simulation with tens of thousands of realizations is performed, yielding root‑mean‑square (RMS) power statistics (upper, lower and mean values) for various wave and beam parameters. The parametric study shows that increasing significant wave height, beam width, or beam length (sea depth) leads to higher harvested power, while the power is far more sensitive to the patch length than to its thickness. Moreover, as the harvested power grows, the spread of the power distribution widens, indicating amplified uncertainty.

Reliability is examined through a limit‑state function g = R − S, where R represents the system’s strength and S the stochastic load. The authors define failure as the condition where the average harvested power exceeds half of the maximum power observed in a simulation run, which translates into an excessive voltage level. Assuming normal distributions for R and S, the safety index β = (μ_R − μ_S)/√(σ_R² + σ_S²) is computed, and the probability of failure P_f = Φ(−β) is obtained from the standard normal cumulative distribution function. Results reveal a clear trend: higher harvested power corresponds to lower safety index and higher failure probability. This demonstrates a trade‑off between power output and system reliability that must be considered in design.

In summary, the study makes several contributions: (1) it introduces a realistic JONSWAP‑based stochastic wave loading model for wave‑energy harvesters; (2) it quantifies the influence of geometric uncertainties of piezoelectric patches on harvested power; (3) it integrates a probabilistic reliability assessment that links power performance to failure risk; and (4) it provides a MATLAB‑based simulation framework that can be extended for optimization and risk‑aware design of marine piezoelectric energy harvesters. The findings are valuable for researchers and engineers aiming to develop low‑power, ocean‑deployed sensors and devices that rely on ambient wave energy.