Uncertainty Analysis of Fiber Optic Shape Sensing Under Core Failure
Abstract
:1. Introduction
2. Materials and Methods
2.1. Shape Sensing Theory
2.2. Core Failure Compensation
2.3. Design of Simulations
2.3.1. Single-Sensing-Point Simulations
2.3.2. Full 3D Reconstruction Simulations
2.3.3. Core Failure Effect on Measurement Symmetry
3. Results
3.1. Core Failure Analysis on a Single Cross-Section
3.2. Polar Analysis
3.3. Effect of Core Failure on Curve Reconstruction
4. Conclusions
- The asymmetry introduced by the loss of a sensing core causes the uncertainty in both curvature and bending angle to depend on the orientation of the curvature vector, with their maximum and minimum values occurring at opposite angles.
- The effect of this asymmetry on measurement uncertainty is reduced by an increased number of sensing cores, with the highest improvement seen when going from four to five cores.
- The accuracy of 3D reconstruction for shapes that mostly lie on a plane will depend on the plane’s orientation with respect to the missing core.
- If it is established that the possibility of core breakage is likely (for instance, if the insertion or removal of cables is difficult and potentially damaging), then a suitable sensing cable configuration can be chosen to allow shape sensing with an acceptable accuracy even if one of the sensing cores is lost. While, in general, adding more sensing cores will provide better results, each additional core corresponds to an increased length of fiber that has to be monitored, with consequent costs, either in terms of measurement range, measurement bandwidth, or measurement channels, depending on the type of optical fiber sensor employed. The results in this paper suggest that a sensing cable with four peripheral and one central core provides the best compromise in terms of retained accuracy with the minimum number of cores. In the case where higher accuracy is required, additional sensing cores can be added, and we estimated the improvement for multiple configurations.
- When core breakage occurs, an industrial user might have the need to decide whether the cable can still be used or it has to be replaced. While replacement would be the optimal solution for maintaining sensing performance, it might be a difficult process depending on the application. Since in industrial environments, the goal of a sensor is usually to determine a specific set of events with a certain degree of reliability (that is, a minimum probability of detection), it would be worthwhile to determine whether a damaged cable is still viable for the required specifications. In this context, the results presented in this paper show a way to determine how the accuracy of the cable can change in the presence of core breakage and specific aspects that should be taken into consideration, such as the orientation of the broken cable with respect to the bending angles that are detected, which might also have an impact on measurement accuracy, especially if the shape that is being detected mostly lies on a specific plane, which can be expected to occur in some applications (e.g., shape sensing for railway monitoring). All of these factors that we highlighted in this work could have a significant impact on the decision-making process for deciding whether the sensing cable has to be replaced or can keep being employed.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
C.I. | Confidence Intervals |
FBG | Fiber Bragg Grating |
OFSs | Optical Fiber Sensors |
SHM | Structural Health Monitoring |
SLAM-DAST | Smart LightwAve Multi-modal Distributed Acoustic Strain and Temperature sensor |
SSE | Sum of Squared Errors |
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Parameter | Symbols | Values | Units |
---|---|---|---|
Core offset | [mm] | ||
Measurement noise standard deviation | |||
Target curvature | [m−1] | ||
Longitudinal strain | |||
Number of tested directions | 720 | ||
Monte Carlo iterations | N | 103 |
N. | Error | Error | Error Ratio | Error Ratio Reduction |
---|---|---|---|---|
Cores | Pristine Cable | One Core Failure Cable | (Last Point) | (One Core Increment) |
4 | 3.2 mm | 7.3 mm | 2.28 | - |
5 | 2.9 mm | 3.5 mm | 1.21 | 46.9% |
6 | 2.8 mm | 3.0 mm | 1.07 | 11.6% |
7 | 2.7 mm | 2.8 mm | 1.04 | 2.8% |
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Falcetelli, F.; Rossi, L.; Di Sante, R.; Bolognini, G. Uncertainty Analysis of Fiber Optic Shape Sensing Under Core Failure. Sensors 2025, 25, 2353. https://doi.org/10.3390/s25082353
Falcetelli F, Rossi L, Di Sante R, Bolognini G. Uncertainty Analysis of Fiber Optic Shape Sensing Under Core Failure. Sensors. 2025; 25(8):2353. https://doi.org/10.3390/s25082353
Chicago/Turabian StyleFalcetelli, Francesco, Leonardo Rossi, Raffaella Di Sante, and Gabriele Bolognini. 2025. "Uncertainty Analysis of Fiber Optic Shape Sensing Under Core Failure" Sensors 25, no. 8: 2353. https://doi.org/10.3390/s25082353
APA StyleFalcetelli, F., Rossi, L., Di Sante, R., & Bolognini, G. (2025). Uncertainty Analysis of Fiber Optic Shape Sensing Under Core Failure. Sensors, 25(8), 2353. https://doi.org/10.3390/s25082353