A Critical Comparison of Shape Sensing Algorithms: The Calibration Matrix Method versus iFEM

Area of Science:

• Structural Health Monitoring
• Computational Mechanics
• Aerospace Engineering

Background:

• Accurate reconstruction of structural displacements and strains is crucial for load monitoring, especially with discrete and irregularly distributed sensor data.
• Existing shape-sensing algorithms like the calibration matrix (CM) method and the inverse Finite Element Method (iFEM) have different approaches to deformation reconstruction.

Purpose of the Study:

• To compare the accuracy and computational efficiency of the CM method and iFEM for shape sensing.
• To evaluate the applicability and practicality of the CM method for reconstructing full displacement and strain fields from sensor data.

Main Methods:

• The calibration matrix (CM) method reconstructs deformation using a linear combination of known load cases and measured sensor data.
• The inverse Finite Element Method (iFEM) reconstructs deformation by minimizing the least-squares error between measured and numerical values.
• Both methods were applied to benchmark problems and a representative aerospace structure (twisted, tapered blade) using quadratic hexahedral solid elements.

Main Results:

• The CM method demonstrated significantly higher accuracy, achieving average displacement and strain errors of less than 0.01%.
• In contrast, the iFEM algorithm resulted in average displacement and strain errors of 21% and 99%, respectively.
• CM exhibited comparable or superior computational efficiency, with repeat solution times approximately 100 times faster than iFEM for large sensor counts.

Conclusions:

• The CM method is a highly accurate and computationally efficient algorithm for shape sensing, particularly suitable for load monitoring applications with discrete sensor data.
• CM's superior performance in accuracy and speed makes it a practical and advantageous choice over iFEM for complex structural analysis.