Autor/innen
F. Niklas Schietzold, Institute for Structural Analysis, Technische Universität Dresden, 01062 Dresden, Germany; Felix Harazin, Institute for Structural Analysis, Technische Universität Dresden, 01062 Dresden, Germany; Yoshi Diepelt, Institute of Mechanics and Shell Structures & Institute of Numerical Mathematics, Technische Universität Dresden, 01062 Dresden, Germany; Wolfgang Graf, Institute for Structural Analysis, Technische Universität Dresden, 01062 Dresden, Germany; Michael Kaliske, Institute for Structural Analysis, Technische Universität Dresden, 01062 Dresden, Germany
Über dieses Buch
In order to realistically characterize data uncertainty in engineering – and consequently to reliably assess safety – it is required to thoroughly investigate spatial and temporal dependencies of uncertainty, e.g. in material characteristics, geometrical or environmental parameters. Recognizing the fact that probability-based approaches are inappropriate for databases with a severe lack of knowledge, purely epistemic uncertainty concepts for modeling dependent quantities are required. Several approaches to convex dependency modeling of interval quantities, as well as proposals for spatially dependent interval/fuzzy uncertainty modeling, exist. This contribution continues these researches by investigation of an existing fuzzy field concept. Based on discussion of limitations in the existing concept, novel developments in modeling and uncertainty quantification of fuzzy fields are presented. The developments are based on extending an existing interval dependency method, where multidimensional parallelepipeds characterize the underlying interval dependency. Therefore, a dependency model is formulated by extension from interval to fuzzy fields. The proposed (auto-)interaction concept is in analogy to the (auto-)correlation concept of random fields. It is demonstrated how an eigenvalue decomposition of the auto-interaction structure with reduced orthogonal basis variables can be implemented to reduce the high-dimensional α-level optimization problem in uncertainty quantification. Finally, the novel methods are validated by uncertainty quantification examples in benchmark functions to demonstrate the safety assessment capabilities.
Veröffentlicht
21.08.2026
Copyright (c) 2026 Matthias Faes, Michael Beer, Julian Behrend, Marco Broccardo, Guohai Chen, Hanshu Chen, Jieyu Chen, Fang Cong, Henrik Ebel, Peter Eberhard, Andrea Franchini, Zhuojia Fu, Yanzhao Gu, Michael Hanss, Hui Huang, Md Maidul Islam, Jafar Jafari-Asl, Balsa Jovanovic, Tom Könecke, Olga Kosheleva, Vladik Kreinovich, Hao-Ming Li, Pei-Pei Li, Qinghe Li, Ruikun Li, Stefano Marelli, Rafi L. Muhanna, Robert L. Mullen, Chiara Nardin, Lukáš Novák, Shenghao Piao, Mario Rosenfelder, Styfen Schär, Jan Schneider, Wei Shi, Panagiotis Spyridis, Bruno Sudret, Ruben Van Coile, Bo-Yu Wang, Dixiong Yang, Xuan-Yi Zhang, Zi-Xin Zhang, Bo-Qi Zhao, Yan-Gang Zhao, Zhibao Zheng, Baihong Zhong, Zhaowei Zhou, Marcos A. Valdebenito, Chao Dang, Lan-Xin Li, Marius Bittner, Parth Tambat, Marco Behrendt, Zhao Liu, Ping Zhu, Zlatan Dimitrov, Petar O. Hristov, Meng-Ze Lyu, Yang-Yi Liu, Jian-Bing Chen, Qitian Lu, Miroslav Vořechovský, Ekaterina Auer, Lorenz Gillner, Julien Alexandre dit Sandretto, Binod K. Yadav, Ghifari Adam Faza, Hans Hallez, David Moens, Reza Naeimaei, Steffen Schön, Elisabeth Ötsch, Hans Neuner, Zhanhua Liang, Jingwen Song, Michael Desch, Mehdi Modares, Valentin Nikolov, Paulo Lucas Figueiredo, José Torres Farinha, Hugo Raposo, António J. Marques Cardoso, Alice do Carmo Duarte Rodrigues, Paula Gonçalves, Peihan Chen, Xinyu Zhu, Pengfei Wei, Kaiwen Li, Mansoureh Shahabi, Y. F. Cui, Johannes O. Royset, Salvatore Russotto, Mario Di Paola, Antonina Pirrotta, Til Lux, Johannes Sundheim, Tania Feiri, Udo Wiens, Marcus Ricker, F. Niklas Schietzold, Felix Harazin, Yoshi Diepelt, Wolfgang Graf, Michael Kaliske, Rongyao Song, Changcong Zhou, Xuanyi Zhao, Weiping Zhang, Juntao Hu, Yu Chen, Edoardo Patelli, Tingting Sun, Jianbing Chen, Bouwe Verkens, L. Bogaerts, Patrick Van Rymenant, Maximilian Schweizer, Marc Fina, Werner Wagner, Steffen Freitag, George Stefanou, Dimitros Savvas, Panagiotis Gavalas, Luigi Schiano, Razhan S. Ahmed, Oleksandr Al-Shboul, David Ringeloth, Vladislav Gudžulić, Stefanie Schoen, Jelena Bijeljić, Ernst Niederleithinger, Iurie Curoşu, Gerrit E. Neu, Jia-Hui Fu, Yi Luo, De-Cheng Feng, Xiao-Qiu Ai, Luyi Li, Hao Wang, Tairan Wang, Sifeng Bi, Emily Zeller (Kapitelautor/in)
Zitationsvorschlag
Fuzzy fields based on the parallelepiped dependency model. (2026). In
REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World (pp. 255-270). TUDObooks.
https://doi.org/10.17877/tudobooks-11.181
