The Method of Generalized Influence Functions – Adjoint Sensitivity Analysis for the Effective and Efficient Numerical Design of Structures with special Application for Reliability and Uncertainty Modelling
Abstract of the planned project content, taking into account the results from the first project phase
The general goal of the project is carried forward for the second research period which is to serve with sensitivity information and all the systematic insight which may be derived from that. Therefore the resarch is focused on the development of a complete set of methodologic tools and their underlying theory to (i) determine, (ii) visualize and (iii) process sensitivity information of first and second order. The theoretical basis is to efficiently determine sensitivities by the generalized influence function method.
As the research of the fist research period was exclusively focused on first order sensitivity analysis, the emphasis of the second period lies consequently on second order adjoint sensitivity analysis. Therefore it is necessary to further establish the theory on a consistent, continuum mechanical basis and on a discrete formulation based on the finite element method for practical usage as well.
Furthermore, first and second sensitivity information shall be used to support applications for uncertainty quantification as well as many other application fields, e.g. robust design, structural optimization or the evaluation of parameter variations in all stages (from early to final) of design and production. This includes additive manufacturing as a prominent example of actual importance, in which the goal is to utilize systematic parameter variations justified by sensitity information to improve the design and its robustness. In view of constrained and very large scale structural optimization problems a special goal of the project is also to further develop effective design update approaches based on singular value decomposition of sensitivities.
In total, the goal of the project is to serve with data and methodologies to further push digital and innovative technologies for digital design and production.
Essential project goals and objectives
- Extending the method of generalized influence functions to second order, adjoint sensitivity analysis
- Determination, visualization and processing of second order adjoint fields and sensitivity maps
- Enhance existing sensitivity analysis with automatic differentiation tools
- Usage of sensitivities within various methods in view of practical relevant engineering applications
- Usage of sensitivities within applications of engineering relevance (e.g. systematic parameter variations in the digital design process)
Prof. Bletzinger
Prof. Dr.-Ing. Kai-Uwe Bletzinger
TU München
Ingenieurfakultät Bau Geo Umwelt
Lehrstuhl für Statik
Fußeder, Martin; Wüchner, Roland; Bletzinger, Kai-Uwe: The Method of Generalized Influence Functions – Adjoint Sensitivity Analysis for the Numerical Design of Structures Under Uncertainty. 14th Virtual Congress WCCM & ECCOMAS 2020, 2021
Fußeder, Martin; Wüchner, Roland; Bletzinger, Kai-Uwe. (2021). Sensitivitätsanalyse mit verallgemeinerten Einflussfunktionen zur Tragwerksbewertung bei Modellparametervariationen/Sensitivity analysis with generalized influence functions for the treatment of model parameter variations in structural analysis. Bauingenieur. 96. 191-200. 10.37544/0005-6650-2021-06-33.