GramCharlier

01 / Overview

Probabilistic models from statistical moments

GramCharlier is a standalone software tool for uncertainty quantification and probabilistic modelling of inputs to mathematical models of physical systems. It provides an efficient, easy-to-use way to estimate the probability distribution of a quantity of interest from measurements.

The software has three stages. In pre-processing, users enter the first four central statistical moments manually or load measurements from a CSV file, then set semi-probabilistic details for estimating design quantiles. Processing automatically constructs a Gram–Charlier probabilistic model parameterized by those moments. In post-processing, users can calibrate moments and semi-probabilistic parameters, plot results, evaluate PDF/CDF values for new CSV data, and generate statistical samples.

02 / Workflow

Pre-processing, processing & post-processing

03 / Theory

Scientific background

The theoretical methods implemented in GramCharlier are described in:

• L. Novák, “On distribution-based global sensitivity analysis by polynomial chaos expansion,” Computers & Structures, volume 267, 2022. ISSN: 0045-7949.

Further details, theoretical innovations and applications are described in:

• L. Novák and D. Novák, “Semi-Probabilistic Assessment of Concrete Bridge Using Polynomial Chaos and Gram-Charlier Expansions,” in Engineering Mechanics 2022 Proceedings, vol. 27/28, pp. 289–292, 2022. ISBN: 978-80-214-5896-3.

04 / Applications

Prestressed concrete girders

The first GramCharlier application came from long-term research on precast prestressed concrete roof girders failing in shear, carried out for the Austrian company Franz Oberndorfer GmbH & Co KG. The study covered several girder types with different geometries and reinforcement. Its main objective was to optimize structural members with respect to structural reliability.

05 / Contact

Software enquiries