PSI - Issue 64

Ina Reichert et al. / Procedia Structural Integrity 64 (2024) 145–152 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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5. Discussion The results show a dependency of the cost function value from the distances of the sensor positions which is associated with the total number of sources and receivers. The presumption that less distance between the sensors and therefore having a higher number of sensors leads to a lower cost function value is proved to be true. This results in a better approximation of the model parameter values, as the minimization of the cost function value leads to optimal experimental designs. Nevertheless, as Fig. 5 shows, the cost function value increases close to linear for the sensor distances between 1 m and 5 m to 6 m, but for greater sensor distances it flattens. Hence, it can be concluded that for the second part, larger sensor distances (= less number of sensors) lead to only slightly worse values in the cost function value. Overall, the suggestion of a sensor distance for the experiments is possible with the calculation of the cost function value. On the other hand, considering the noise levels, their influence on the cost function value is rather small. As assumed, higher noise levels lead to higher values in the cost function value. The behavior of the curves with different noise levels for the same fault combination is nearly parallel. 6. Conclusion Especially, in the second part of Fig. 5 lies the opportunity to save time, costs and computing resources without losing much quality in the model parameter estimation when larger sensor distances can be chosen with only a small increase in the cost function value. In addition, one needs to decide on the quality of the model parameter estimation to choose a reasonable amount of sensors or sensor distance. Here, especially artifacts play a big role. Nevertheless, the value of the cost function does not provide information about the occurrence of artifacts, which might lead to a false positive identification of defects. For future works, the consideration of a confusion matrix to study both false positive and false negative defect identification regions is recommended to quantify the accuracy of the identified model parameters. The influence of the noise level is rather low and the findings suggest that it is not necessary to include noise considerations to optimize the sensor setup. For future work, more fault combinations need to be calculated and the aim is to find an optimization strategy for the sensor setup such that all representative fault sizes and positions can be identified by the FWI approach with a reasonable sensor distance considering economic and computational issues. These optimized designs are to be validated by exhaustive search results. Acknowledgements This research was supported in part through computational resources provided on the VEGAS cluster at the Digital Bauhaus Lab in Bauhaus-Universität Weimar, Germany. References M. Alalade, L. Nguyen-Tuan, F. Wuttke, and T. Lahmer. Damage identification in gravity dams using dynamic coupled hydro-mechanical xfem . International Journal of Mechanics and Materials in Design , 14(1):157 – 175, 2018. A. Bardow. Optimal experimental design of ill-posed problems: The meter approach. Computers & Chemical Engineering , 32(1-2):115 – 124, 2008. J.-P. Berenger. A perfectly matched layer for the absorption of electromagnetic waves. Journal of computational physics , 114(2):185 – 200, 1994. D. K ö hn . Time domain 2D elastic full waveform tomography . PhD thesis, Christian-Albrechts Universit ä t Kiel, 2011. T. Lahmer. Optimal experimental design for nonlinear ill-posed problems applied to gravity dams. Inverse Problems , 27(12):125005, 2011. R. Schenkendorf, A. Kremling, and M. Mangold. Optimal experimental design with the sigma point method. IET systems biology , 3(1):10 – 23, 2009. A. Tarantola. Inversion of seismic reflection data in the acoustic approximation. Geophysics , 49(8):1259 – 1266, 1984. D. Uci ń ski. Measurement Optimization for Parameter Estimation in Distributed Systems . Technical University of Zielona G ó ra Press, Zielona G ó ra, 1999.