Soft piezoresistive strain sensors are one of the most common sensing solutions for wearable and soft robotic applications due to their flexibility and compliance. However, their resistance response is nonlinear and hysteretic, and a sensor can be pushed past its calibrated workspace or misbehave inside it, carrying that error into a decision or control loop. Probabilistic regressors track confidence but ignore those limits. A predictive mean can look unremarkable even when the reading comes from a sensor outside its admissible range or already failing internally, so a confident-looking estimate is not the same as a trustworthy one. This paper proposes a reliability framework pairing a physics-informed probabilistic inverse model, built on physics-guided input features, with a risk factor fusing uncertainty with strain and strain-rate limits into a three-state monitor. Tests on a Nitinol wire and a silver-coated polyamide thread with a Gaussian Process raised fit scores to 0.90-0.95 (RMSE 0.26%-0.15%) and a 96% empirical coverage against the 95% target. The monitor caught 95% of out-of-range and 100% of abnormal conditions while staying reliable under nominal operation. A sensor that reports confidence alongside its estimate lets a system withhold action instead, since it needs no labeled failure examples, which are hard to collect for soft materials.
Figures & tables
Fig. 1 : Reliability monitoring methodology using the risk factor. (a) The GP network’s uncertainty is high before training. (b) After training, GP uncertainty estimation within the training distribution x(t) decreases. For non-nominal data, risk increases either by exceeding physical constraints or by being outside the training distribution.
Fig. 2 : Piezoresistive strain sensing material used for experimental validation. Superelastic Nitinol wire, including (a) the sensing element, (b) characteristic hysteresis behavior, and (c) geometric deformation.
Dynamic
Static
Signal type
Sinusoidal
Step
Strain amplitude
A∈{1,...,6} %
A∈{1,...,6} %
Frequency
f∈{0.1k∣k=1,...,10} Hz
f=0 Hz
Duration
Ttot=f20s
Ttot=120s
TABLE I : Experimental dataset used for model training and validation. Static and dynamic loading conditions defined by strain amplitude and excitation frequency.
Fig. 3 : Definition of the operating workspace from the experimental dataset. (a) Maximum strain rate associated with each experimental condition. (b) Fit score across all loading conditions. (c) Resulting workspace partition into nominal, out-of-range, degraded, and rejected regions according to the selected physical constraints.
Gaussian process
Region
fit score
RMSE (%)
PICP-95
+ R~(t)
Nominal
0.90±0.06
0.26±0.33
0.98±0.02
Out-of-range
0.82±0.07
0.61±0.44
-
+ R~(t) , R~˙(t)
Nominal
0.93±0.03
0.16±0.08
0.98±0.02
Out-of-range
0.86±0.06
0.46±0.26
-
+ R~(t) , z(t)
Nominal
0.91±0.10
0.27±0.54
0.98±0.02
Out-of-range
0.83±0.12
0.63±0.67
-
TABLE II : Predictive performance of the GP for different physics-guided input features. Mean and standard deviation of the fit score, RMSE, and PICP-95 obtained from Leave-One-Condition-Out Cross-Validation (LOCOCV) in the nominal region and evaluated on out-of-range conditions.
Risk factor
Region
Reliable (%)
Warning (%)
Fault (%)
DR (%)
pu
Nominal
100±0
0±0
0±0
0
Out-of-range
89±21
2±3
9±19
40
Abnormal
69±21
0±0
31±21
100
pk
Nominal
100±0
0±0
0±0
0
Out-of-range
60±29
25±16
15±15
92
Abnormal
69±21
30±21
0±0
100
TABLE III : Reliability monitoring performance of the proposed risk factor. State occupancy and Detection Rate (DR) for nominal, out-of-range, and abnormal conditions using epistemic risk, physical risk, and their combination.
Fig. 4 : Representative strain estimation and reliability monitoring results. The measured relative resistance, probabilistic risk factor, reliability state, predicted strain, and ground-truth strain are shown for (a) nominal dynamic operation, (b) nominal static operation, (c) out-of-range operation, (d) abnormal signal spikes, (e) sensor fatigue, and (f) sensor breakage. The proposed framework maintains low risk within the calibrated operating region while detecting out-of-range operation and abnormal sensor behavior through the warning and fault states.
Carmen Ballester received her bachelor’s degree in Robotic Engineering from the University of Alicante in 2021, where she initiated her research career in 2019. She continued her academic pursuit, completing a Master’s in Robotics and Automation at Carlos III University of Madrid, where she became a member of the RoboticsLab in 2021. Currently a dedicated Ph.D. student in Electrical, Electronic, and Automation Engineering, Carmen specializes in wearable actuators and sensors within actuated exoskeletons for rehabilitation applications. Her expertise encompasses nonlinear control, soft robotics, smart materials, and rehabilitation robotics.
Table 8
Víctor Muñoz earned an Industrial Technology Engineering degree from the University of Málaga in 2021. He augmented his education with study programs in South Korea and completed his Master’s in Robotics and Automation at Carlos III University of Madrid in 2023. Starting his research career in 2021, he initially focused on mechanical ventilators at the University of Málaga. In 2022, he joined the RoboticsLab research group at Carlos III University, where he is currently a Ph.D. student specializing in Machine Learning applications in robotics.
Table 9
Dorin Copaci is an Assistant Professor in the Department of Systems Engineering and Automation at Carlos III University of Madrid, Spain. Since 2010, he has been a research member of RoboticsLab at the university. He completed his bachelor’s degree in Automatic Control and Systems Engineering at Politehnica University of Bucharest, Romania, in 2010. In 2012, he obtained his master’s degree in Robotics and Automation from Carlos III University in Spain, and he earned his Ph.D. degree in Electrical, Electronic, and Automatic Engineering in 2017. His research primarily focuses on the design and control of Shape Memory Alloy (SMA) actuators for rehabilitation devices.
Table 10
Dolores Blanco received the B.S. degree in physics from the University Complutense of Madrid, Spain, in 1992, and the Ph.D. degree in mechatronics from the University Carlos III of Madrid (UC3M), in 2002. In 1996, she joined the Department of Systems Engineering and Automation, UC3M, as a Fellowship Student, where she has been an Associate Professor since 2009. She is currently a member of the Robotics Laboratory Group, UC3M. Her current research interest includes emerging actuator technologies and design for rehabilitation robotics.