Sensorless Current Estimation in Piezoelectric Energy Harvesting Networks Using a Takagi–Sugeno Fuzzy System

This paper proposes a sensorless current estimation method for piezoelectric energy harvesting (PEH) systems using a first-order Takagi–Sugeno fuzzy system. Unlike invasive current sensing, the proposed estimator uses only non-invasive measurements: output voltage VO, its derivative V˙O, and load resistance RL. The fuzzy rules are initialized directly from the physical equivalent circuit parameters and trained via the ANFIS on a large-scale dataset (78 million samples). The proposed model achieves a mean coefficient of determination R2=0.9999 (95% CI: [0.99989, 0.99991]), root mean square error RMSE=3.12×10−8 A, mean absolute percentage error MAPE = 2.51% (95% CI: [1.98, 3.04]%), and fitness FIT = 98.98%—outperforming multiple linear regression (R2=0.9738 and MAPE = 116.25%) and a shallow neural network with 211 parameters (R2=0.9991 and MAPE = 13.85%) despite having only 170 trainable parameters. Unlike black-box neural networks, the fuzzy model provides interpretable rules whose consequent parameters map directly to physical quantities (effective capacitance Cp(eff) and leakage conductance 1/Rp(eff)). The low computational footprint (170 parameters, <5 μs inference, and ≈1.4 kB of memory) makes it suitable for real-time deployment on low-power microcontrollers. These results demonstrate the viability of the proposed approach under controlled laboratory conditions for the single, series, and parallel PEH configurations considered. This work establishes that physically informed fuzzy modeling is a viable, interpretable, and efficient alternative to deep learning for sensorless monitoring in low-power energy harvesting systems.