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Robustness evaluation in virtual product development

Manufacturing tolerances, material scatter, random load or other stochastic effects cause scattering properties of components or structures that are usually of spatial distribution. To ensure your product quality, to avoid recalls or to fulfill safety requirements, you can consider these random effects by using appropriate statistical models and methods already in the design phase.

SoS® assists you to extend and to simplify your statistical analysis of field data. Thus, you can locate areas with a high probability of failure or variation („hot spots“) and identify the causes of the scatter.



Visualization of statistical quantities on FEM meshes may simplify the evaluation of robustness significantly. Visualization helps in particular if the critical regions are a priori not known or if their positions vary randomly (e.g. in crash simulation, metal forming simulation, etc.). Further, visualization helps to increase the acceptance of statistical results in CAE and production departments.

Statistics on Structures® supports a robustness analysis in these ways:

  • Analyze random  properties of structures
  • Identify consequences of manufacturing tolerances and random loads
  • Inspect statistics directly on the structure
  • Easily detect hot spots and potential failure locations
  • Improve robustness and product quality
  • Understand  the cause of scatter
  • Decompose response scatter using random field parametric
  • Generate  random designs by using the random field parametric
  • Eliminate random noise in consecutive analysis


New Features in SoS® 7

  • Free-form shape optimization
  • SoS for ANSYS: Apply mesh morphing inside ANSYS Mechanical
  • Standalone SoS ROM Viewer for 3D variation analysis
  • Direct visualization of changes in geometry and their invoked changes in structural performance (stresses, strains etc.)
  • New algorithm for estimating F-CoP[Total] and sensitivity indices in FMOP
  • New backend (beta option) for approximation model with FMOP

Improvements in SoS® 7

  • Support for components (node sets, element sets)
  • Interactive variation analysis in 3D for random fields and FMOP (using sliders)
  • Improved graphics (GUI and engine)
  • Free-form variation models for synthetic localized variations
  • Better stabilization algorithms for geometric imperfections
  • Photographic analysis: Autoscale images of different resolution
  • New export formats usable by ANSYS WB External Data
  • Add support for quadratic tetrahedra in Abaqus INP format
  • Add ability to query FEM mesh connectivity from script and in FMOPSolver lib API

Data-based Reduced Order Model (ROM)

ROMs are very important in system simulation and are expected to become a key technology for digital twins. In typical applications a detailed product simulation needs to be linked to sensor data in order to predict product parameters (e.g. life of turbine blades) accurately enough to be capable of optimizing the maintenance and operation. To fulfill the reaction time requirements from digital twin, the detailed simulation models need to be reduced. The classical approach of ROMs uses a matrix condensation which is called “physics-based” ROMs, because the formula still contains the physics of how input variation affects response. However, these reductions are often restricted to linear systems. The alternative for non-linear systems are data-based ROMs. They use functional models to approximate response surfaces considering the effect of input variations on the response variation based on the given sample set. For field data as input or response, SoS provides the Field Metamodel of Optimal Prognosis (FMOP) which can be used to approximate signals, FEM solutions or geometric deviations.

Software on demand & academic licenses

SoS is also available as software on demand in Germany, Austria and Switzerland. This service provides fast and economical access to the latest software version for a customized billing of use. For further information, please contact our support.

Use SoS in your research and teaching. We provide special conditions for universities!


SoS is sold worldwide. A list of our distributors can be found here.

Information material

Your contact person

Dr. Sebastian Wolff

Fon: +43 (0) 1997 1207-11
Fax: +43 (0) 1997 1207-20