Multi-resolution force estimation algorithm for a 3D-printed piezoresistive solid with quasi-linear approximation of strain-softening behavior

We present the framework for a force-estimation algorithm for a piezoresistive viscoelastic solid, 3D-printed from a conductive polymer composite (CPC) to be used as a low-cost but easily implementable force sensor. A key challenge with CPCs is their hysteretic response in a loading-unloading cycle, which varies with loading speed. Because model parameters differ in loading and unloading stages, reliable stage recognition is essential for accurate force estimation. To address this, we developed a causal, sample-by-sample stage recognition algorithm—suitable for real-time implementation—using a wavelet filter bank. The specimen was characterized using data from the first five cycles of ten-cycle compression tests at different loading speeds, and model parameters were extracted via mixed-effects regression. The algorithm’s performance was validated through force estimation for the remaining five cycles, resulting in an average root mean squared error of ~37.8 N or ~9.28% of measured peak force. These results demonstrate the algorithm’s robustness and suggest that it can be implemented effectively in practical situations.