Two shape-sensing algorithms, the calibration matrix (CM) method and the inverse Finite Element Method (iFEM), were compared on their ability to accurately reconstruct displacements, strains, and loads and on their computational efficiency. CM reconstructs deformation through a linear combination of known load cases using the sensor data measured for each of these known load cases and the sensor data measured for the actual load case. iFEM reconstructs deformation by minimizing a least-squares error functional based on the difference between the measured and numerical values for displacement and/or strain. In this study, CM is covered in detail to determine the applicability and practicality of the method. The CM results for several benchmark problems from the literature were compared to the iFEM results. In addition, a representative aerospace structure consisting of a twisted and tapered blade with a NACA 6412 cross-sectional profile was evaluated using quadratic hexahedral solid elements with reduced integration. Both methods assumed linear elastic material conditions and used discrete displacement sensors, strain sensors, or a combination of both to reconstruct the full displacement and strain fields. In our study, surface-mounted and distributed sensors throughout the volume of the structure were considered. This comparative study was performed to support the growing demand for load monitoring, specifically for applications where the sensor data is obtained from discrete and irregularly distributed points on the structure. In this study, the CM method was shown to achieve greater accuracy than iFEM. Averaged over all the load cases examined, the CM algorithm achieved average displacement and strain errors of less than 0.01%, whereas the iFEM algorithm had an average displacement error of 21% and an average strain error of 99%. In addition, CM also achieved equal or better computational efficiency than iFEM after initial set-up, with similar first solution times and faster repeat solution times by a factor of approximately 100, for hundreds to thousands of sensors.

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Structural health monitoring (SHM) is a growing field of research, as it has the potential to simultaneously improve the reliability of structures and reduce their maintenance cost. SHM requires accurate stress and strain information, preferably for the entire structure. Unfortunately, it is often infeasible to instrument every part of the structure, making it necessary to estimate the stress and strain fields based on data from a limited number of sensors. One promising technique for making this estimate is the inverse finite element method (iFEM), which can be applied to any combination of geometry and loading conditions. In addition, it can also process several different types of sensor data. In this study, benchmark problems based on the MacNeal and Harder linear elastic problem set for FEM algorithms were extended to test the accuracy of iFEM algorithms. As the benchmarks use linear elastic materials, small displacements and strains, the iFEM implementation was also limited to these conditions. Accurate iFEM estimates can be obtained for the benchmark problems for which accurate FEM solutions can be obtained with solid elements, specifically 3-dimensional 20 node hexahedral elements with reduced integration (C3D20R), based on either displacement sensors, strain sensors, or both combined, and provided that a sufficient number of sensors is used. The iFEM algorithms generally produce more accurate estimates of displacements than of strains. The addition of Tikhonov regularization does not result in a significant increase in accuracy for either the displacement or strain distribution estimates and can even deteriorate the results in certain cases.

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Heating the thermoset tape to a higher temperature than is used in the conventional automated tape laying process can affect the cure cycle, void content, interlaminar shear strength and residual stresses of the final product. In this study, the effects of different heating strategies on the degree of cure in thermoset tapes were modelled. This was done for two tape laying speeds and by heating different combinations of the incoming tape, the previously laid tape and the mould. The model predicts the thermochemical profile of two different materials and is validated by experimental data from thermocouples and a pyrometer. @en

Shape sensing utilizing an inverse finite element method (iFEM) was considered for obtaining the displacement fields of two cantilever beams. Traditional iFEM techniques make use of only a single type of sensor, which can lead to errors in the strain and/or displacement distributions. This study has reduced these errors by combining data from multiple sensor types. A new iFEM algorithm was developed in order to minimize the error on computed strain profiles. The new iFEM algorithm incorporates Tikhonov smoothing in addition to compensating for the lack of sensors in areas of the structure where no sensors are present. The new iFEM algorithm was demonstrated for cantilever plates under various load cases. The preliminary results showed that the new iFEM algorithm is able to determine the structural deformations of two cantilever plates with greater accuracy than a traditional iFEM implementation that was found in the literature, using fewer sensors. @en

Computing global strain distributions in complex aerospace and wind energy structures in quasi-real time is an important challenge for the aerospace and wind energy industry. Shape sensing is being considered as a potential means for obtaining global strain fields of complex structures. This is achieved through the use of inverse finite element methods (iFEM). Traditional shape sensing techniques use a variety of sensors in isolation. These isolated approaches lead to a number of drawbacks, including significant errors in the strain and/or displacement distributions that they determine. This study focuses on reducing these errors by combining data from various sensor types. In order to achieve this objective, a new iFEM approach was developed to improve how shape sensing determines a structure’s deformation from distributed sensors. The method utilizes a procedure that minimizes a quadratic error functional, based on the difference between the theoretical and the measured strains and displacements. The analytical iFEM equations are discretized for use in a numerical model, which is used to analyze simulated sensor data. The simulated data is obtained from a FEM analysis of a structure loaded in bending, torsion and shear, in addition to experiencing combined loads. As with previous inverse methods, the error functional weights were employed to manage missing measurements and Tikhonov regularization was applied to guarantee smoothness of the numerical solution. In this study, it has been shown that the new iFEM methodology can determine the structural deformations to within 1% of the FEM results for each of the load cases. In addition, the methodology is capable of achieving the same accuracy as single sensor type iFEM methods with a smaller total number of sensors. The single sensor type iFEM methods that were considered made use of only strain data or only displacement data. Finally, an experimental setup consisting of a simple cantilever plate structure was constructed in order to experimentally verify the newly developed iFEM algorithm. The experimental strain and displacement data were obtained utilizing a Rayleigh backscattering fiber optic distributed sensing system and MEMS sensors, respectively. Both of these sensor types were mounted on the structure and subjected to the load cases that were simulated in the FEM analysis.@en

Computing global strain distributions in complex aerospace and wind energy structures in quasi-real time is an important challenge for the aerospace and wind energy industry. Shape sensing is being considered as a potential means for obtaining global strain fields of complex structures. This is achieved through the use of inverse finite element methods (iFEM). Traditional shape sensing techniques use a variety of sensors in isolation. These isolated approaches lead to a number of drawbacks, including significant errors in the strain and/or displacement distributions that they determine. This study focuses on reducing these errors by combining data from various sensor types. In order to achieve this objective, a new iFEM approach was developed to improve how shape sensing determines a structure’s deformation from distributed sensors. The method utilizes a procedure that minimizes a quadratic error functional, based on the difference between the theoretical and the measured strains and displacements. The analytical iFEM equations are discretized for use in a numerical model, which is used to analyze simulated sensor data. The simulated data is obtained from a FEM analysis of a structure loaded in bending, torsion and shear, in addition to experiencing combined loads. As with previous inverse methods, the error functional weights were employed to manage missing measurements and Tikhonov regularization was applied to guarantee smoothness of the numerical solution. In this study, it has been shown that the new iFEM methodology can determine the structural deformations to within 1% of the FEM results for each of the load cases. In addition, the methodology is capable of achieving the same accuracy as single sensor type iFEM methods with a smaller total number of sensors. The single sensor type iFEM methods that were considered made use of only strain data or only displacement data. Finally, an experimental setup consisting of a simple cantilever plate structure was constructed in order to experimentally verify the newly developed iFEM algorithm. The experimental strain and displacement data were obtained utilizing a Rayleigh backscattering fiber optic distributed sensing system and MEMS sensors, respectively. Both of these sensor types were mounted on the structure and subjected to the load cases that were simulated in the FEM analysis.@en