UQ software based on
Gram-Charlier Expansion

Standalone software tool for uncertainty quantification and probabilistic modeling of inputs of mathematical models of physical systems. GramCharlier represents efficient and easy-to-use tool for estimation of the probability distribution of quantity of interest based on measurements. The software can be virtually divided to three parts: pre-processing, processing and post-processing.

In pre-processing part, users define the first four central statistical moments. This task can be done manually or users can load measuremets in .csv file. Very last step of pre-processing is settings of semi-probabilistic details used for estimation of design quantiles.

Processing is fully-automatic and it contains several crucial steps deeply described in papers reference in a theory section. The main task of processing is construction of the probabilistic model in form of Gram-Charlier expansion parametrized by given statistical moments.

During post-processing user can manually calibrate statistical moments and semi-probabilisticstic parameters and plot results. Moreover, it is also possible to use the Gram-Charlier expansion for evalution of PDF/CDF for new data in .csv file or statistical sampling.

The software GramCharlier was developed with financial support of Technology Agency of the Czech Republic under project No. TM04000012.

Theoretical background

Theoretical methods implemented into GramCharlier were described in the following scientific journal paper:

NOVÁK, L. On distribution-based global sensitivity analysis by polynomial chaos expansion. COMPUTERS & STRUCTURES, 2022, 267, ISSN: 0045-7949.

Additional details of GramCharlier, theoretical inovations and applications were described in following selected papers:

L. Novák, D. Novák, Semi-Probabilistic Assessment of Concrete Bridge Using Polynomial Chaos and Gram-Charlier Expansions, In ENGINEERING MECHANICS 2022 PROCEEDINGS, VOL 27/28 289-292, 2022, ISBN: 978-80-214-5896-3.

Applications of GramCharlier

Prestressed concrete girders:

The very first application of GramCharlier software was during long term research of precast prestressed concete roof girders failing in shear for austrian company Franz Oberndorfer GmbH & Co KG. There were several types of girders with different geometry and reinforcement. The main task was an optimization of structural members with respect to reliability of structures.

If you are interested in software GramCharlier and its possibilities for your applications/research, please contact main developer Lukas Novak:

Lukas Novak
novak.l@fce.vutbr.cz
Institute of structural mechanics
Faculty of civil engineering
Brno University of Technology
Czech republic

Software for estimation of probability distributions

Accuracy of probabilistic analysis and uncertainty quantification is governed by accuracy of assumed probability distributions of input random variables. GramCharlier software creates the most suitable probabilistic model of quanity of interest based on experimental results.

Uncertainty quantification
of engineering problems

is a scientific field of great importance focused on analysis of uncertainties in mathemtical models. It is important especially in engineering field in order to optimize the design of structures and reflect given safety requirements.