Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-16T07:05:30.560Z Has data issue: false hasContentIssue false

Estimation of Composite Laminate Ply Angles Using an Inverse Bayesian Approach Based on Surrogate Models

Published online by Cambridge University Press:  26 May 2022

M. Franz*
Affiliation:
Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
S. Pfingstl
Affiliation:
Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany Technical University of Munich, Germany
M. Zimmermann
Affiliation:
Technical University of Munich, Germany
S. Wartzack
Affiliation:
Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A digital twin (DT) relies on a detailed, virtual representation of a physical product. Since uncertainties and deviations can lead to significant changes in the functionality and quality of products, they should be considered in the DT. However, valuable product properties are often hidden and thus difficult to integrate into a DT. In this work, a Bayesian inverse approach based on surrogate models is applied to infer hidden composite laminate ply angles from strain measurements. The approach is able to find the true values even for ill-posed problems and shows good results up to 6 plies.

Type
Article
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
The Author(s), 2022.

References

Avendaño-Valencia, L. D., Chatzi, E. N. & Tcherniak, D. (2020). Gaussian process models for mitigation of operational variability in the structural health monitoring of wind turbines. Mechanical Systems and Signal Processing, 142, 106686. 10.1016/j.ymssp.2020.106686CrossRefGoogle Scholar
Barkanov, E., Skukis, E. & Petitjean, B. (2009). Characterisation of viscoelastic layers in sandwich panels via an inverse technique. Journal of Sound and Vibration, 327(3-5), 402412. 10.1016/j.jsv.2009.07.011Google Scholar
Blaheta, R., Béreš, M., Domesová, S. & Pan, P. (2018). A comparison of deterministic and Bayesian inverse with application in micromechanics. Applications of Mathematics, 63(6), 665686. 10.21136/AM.2018.0195-18Google Scholar
Cappelli, L., Montemurro, M., Dau, F. & Guillaumat, L. (2019a). Multiscale Identification of Material Properties for Anisotropic Media: A General Inverse Approach (Bd. 204). Springer Berlin Heidelberg. 10.1007/978-3-030-11969-0_10Google Scholar
Cappelli, L., Montemurro, M., Dau, F. & Guillaumat, L. (2018). Characterisation of composite elastic properties by means of a multi-scale two-level inverse approach. Composite Structures, 204(6), 767777. 10.1016/j.compstruct.2018.08.007CrossRefGoogle Scholar
Cappelli, L., Montemurro, M., Dau, F. & Guillaumat, L. (2019b). Multi-scale identification of the viscoelastic behaviour of composite materials through a non-destructive test. Mechanics of Materials, 137(1), 103137. 10.1016/j.mechmat.2019.103137CrossRefGoogle Scholar
Castillo, A. R. & Kalidindi, S. R. (2020). Bayesian estimation of single ply anisotropic elastic constants from spherical indentations on multi-laminate polymer-matrix fiber-reinforced composite samples. Meccanica, 44(1), 120. 10.1007/s11012-020-01154-wGoogle Scholar
Daghia, F., Miranda, S. de, Ubertini, F. & Viola, E. (2007). Estimation of elastic constants of thick laminated plates within a Bayesian framework. Composite Structures, 80(3), 461473. 10.1016/j.compstruct.2006.06.030CrossRefGoogle Scholar
Euler, E., Sol, H. & Dascotte, E. (2006). Identification of the material properties of composite beams: inverse method approach. In A, C.. Brebbia (Hrsg.), High performance structures and materials III (S. 225–237). WIT Press. 10.2495/HPSM06023Google Scholar
Franz, M., Schleich, B. & Wartzack, S. (2021). Tolerance management during the design of composite structures considering variations in design parameters. The International Journal of Advanced Manufacturing Technology, 204(5), 359. 10.1007/s00170-020-06555-5Google Scholar
Gentile, R. & Galasso, C. (2020). Gaussian process regression for seismic fragility assessment of building portfolios. Structural Safety, 87, 101980. 10.1016/j.strusafe.2020.101980CrossRefGoogle Scholar
Glaessgen, E. & Stargel, D. (2012). The Digital Twin Paradigm for Future NASA and U.S. Air Force Vehicles. In 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. 10.2514/6.2012-1818Google Scholar
Gogu, C., Haftka, R., Le Riche, R., Molimard, J. & Vautrin, A. (2010). Introduction to the Bayesian Approach Applied to Elastic Constants Identification. AIAA Journal, 48(5), 893903. 10.2514/1.40922Google Scholar
Grieves, M. & Vickers, J. (2017). Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems. In Kahlen, F.-J., Flumerfelt, S. & Alves, A. (Hrsg.), Transdisciplinary Perspectives on Complex Systems (Bd. 89, S. 85–113). Springer International Publishing. 10.1007/978-3-319-38756-7_4Google Scholar
Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97109. 10.1093/biomet/57.1.97CrossRefGoogle Scholar
Kong, D., Chen, Y. & Li, N. (2018). Gaussian process regression for tool wear prediction. Mechanical Systems and Signal Processing, 104, 556574. 10.1016/j.ymssp.2017.11.021Google Scholar
Pedersen, P. & Frederiksen, P.S. (1992). Identification of orthotropic material moduli by a combined experimental/numerical method. Measurement, 10(3), 113118. 10.1016/0263-2241(92)90003-MCrossRefGoogle Scholar
Polini, W. & Corrado, A. (2020). Digital twin of composite assembly manufacturing process. International Journal of Production Research, 1, 115. 10.1080/00207543.2020.1714091Google Scholar
Rahmani, B., Mortazavi, F., Villemure, I. & Levesque, M. (2013). A new approach to inverse identification of mechanical properties of composite materials: Regularized model updating. Composite Structures, 105(4), 116125. 10.1016/j.compstruct.2013.04.025CrossRefGoogle Scholar
Rasmussen, C. E. & Williams, C. K. I. (2008). Gaussian processes for machine learning (3. Aufl.). Adaptive computation and machine learning. MIT Press.Google Scholar
Reddy, J. N. (2004). Mechanics of laminated composite plates and shells: Theory and analysis (2nd ed.). CRC Press.Google Scholar
Sayer, F., Antoniou, A., Goutianos, S., Gebauer, I., Branner, K. & Balzani, C. (2020). ReliaBlade Project: A Material's Perspective towards the Digitalization of Wind Turbine Rotor Blades. IOP Conference Series: Materials Science and Engineering, 942, 12006. 10.1088/1757-899X/942/1/012006CrossRefGoogle Scholar
Schleich, B., Anwer, N., Mathieu, L. & Wartzack, S. (2017). Shaping the digital twin for design and production engineering. CIRP Annals, 66(1), 141144. 10.1016/j.cirp.2017.04.040Google Scholar
Stark, R., Anderl, R., Thoben, K.-D. & Wartzack, S. (2020). WiGeP-Positionspapier: „Digitaler Zwilling“. Zeitschrift für wirtschaftlichen Fabrikbetrieb, 115(s1), 4750. 10.3139/104.112311CrossRefGoogle Scholar
Steuben, J., Michopoulos, J., Iliopoulos, A. & Turner, C. (2015). Inverse characterization of composite materials via surrogate modeling. Composite Structures, 132(2), 694708. 10.1016/j.compstruct.2015.05.029Google Scholar
Tarantola, A. (2005). Inverse problem theory and methods for model parameter estimation. SIAM - Soc. for Industrial and Applied Math.CrossRefGoogle Scholar
Trauer, J., Schweigert-Recksiek, S., Engel, C., Spreitzer, K. & Zimmermann, M. (2020). WHAT IS A DIGITAL TWIN? – DEFINITIONS AND INSIGHTS FROM AN INDUSTRIAL CASE STUDY IN TECHNICAL PRODUCT DEVELOPMENT. Proceedings of the Design Society: DESIGN Conference, 1, 757766. 10.1017/dsd.2020.15Google Scholar
Trauer, J., Pfingstl, S., Finsterer, M. & Zimmermann, M. (2021). Improving Production Efficiency with a Digital Twin Based on Anomaly Detection. Sustainability, 13(18), 10155. 10.3390/su131810155CrossRefGoogle Scholar
Wesolowski, M. & Barkanov, E. (2014). Improving an inverse technique for characterisation of laminated plates. In Pietraszkiewicz, W. & Górski, J. (Hrsg.), Shell structures: Theory and applications : proceedings of the 10th SSTA Conference, Gdańsk, Poland, 16–18 October 2013 (Bd. 27, S. 157–160). CRC Press/Taylor & Francis Group. 10.1201/b15684-37Google Scholar
Zambal, S., Eitzinger, C., Clarke, M., Klintworth, J. & Mechin, P.-Y. (2018). A digital twin for composite parts manufacturing : Effects of defects analysis based on manufacturing data. In I. I. C. o. I. Informatics (Hrsg.), Proceedings IEEE 16th International Conference on Industrial Informatics (INDIN): Faculty of Engineering of the University of Porto, Porto, Portugal, 18–20 July 2018 (S. 803–808). IEEE. 10.1109/INDIN.2018.8472014CrossRefGoogle Scholar
Zebdi, O., Boukhili, R. & Trochu, F. (2009). An Inverse Approach Based on Laminate Theory to Calculate the Mechanical Properties of Braided Composites. Journal of Reinforced Plastics and Composites, 28(23), 29112930. 10.1177/0731684408094063Google Scholar