• Simulate expected performance with confidence intervals of antenna radiation patterns and scattering parameters
  • Uncertainty due to any parameter, such as manufacturing tolerances and alignment or excitation errors
  • Accelerated Monte Carlo, Stochastic Collocation and Polynomial Chaos Expansion algorithms to quantify uncertainties
  • Sobol indices, to identify parameters contributing most to the total uncertainty
  • Sensitivity analysis


  • Seamless integration with TICRA Tools products
  • Insights to do more robust antenna designs
  • Fewer design iterations and better antenna prototypes
  • Avoid overdesign and achieve tighter margins
  • Better correlation of measurements and simulations
  • More general and powerful than sensitivity analysis in competing tools

Uncertainty quantification

With the Uncertainty Quantification (UQ) product, the antenna designer may augment the usual antenna design process with uncertainties on design parameters and get data on the expected antenna performance and confidence intervals. Using advanced statistical methods, UQ works together with TICRA Tools antenna analysis products, where uncertainty due to any variable specifying the antenna may be included. The outcome of a UQ analysis is the expected performance and confidence intervals, for instance for the antenna radiation pattern, as well as probability distributions for key parameters, such as peak directivity.

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Uncertainty due to any parameter

The UQ product may be used to estimate the uncertainty due to any parameter describing the antenna. Parameters may include geometrical dimensions, positions of elements of the antenna, surface distortions, material parameters, array excitation coefficients, and many more. Both Real Variables and Bulk Variables in TICRA Tools may be used with UQ, and the uncertainty due to any one or any group of parameters may be analysed.

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Easy integration with other TICRA software products

UQ is integrated in the TICRA Tools software framework. This means that you may quantify uncertainties for any antenna system modelled with one or more of the TICRA Tools antenna products, GRASP, ESTEAM, CHAMP 3D, QUPES, and/or POS. Assessment of uncertainties with UQ is based on dedicated EM analysis methods available in each of the antenna products, making UQ analysis feasible for both simple and advanced antenna systems in TICRA Tools.

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Design parameters contributing most to uncertainty

In UQ, the so-called Sobol indices provide data on the partial contribution from each design variable to the uncertainty, which allows the antenna designer to identify the most critical design parameters. For any UQ output, Sobol indices due to each uncertainty parameter are computed. Sobol indices are obtained when using the Polynomial Chaos Expansion algorithm.

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Accurate uncertainty estimates in a reasonable time

Assessment of the effect of uncertainties is conventionally done in one of two ways: Assuming the extreme uncertainty and performing one or a few additional simulations, or by brute-force Monte Carlo simulations. The former approach is fast but yields conservative results, while the latter is typically slow. TICRA's UQ, on the other hand, employs a higher-order approach and thus provides accurate uncertainty estimates in a reasonable time, allowing the antenna designer to avoid overdesigning and achieve tighter margins.

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Your project may be complex, but we keep things simple. If you have any questions about our software or services, or you need expert consultancy, we are here to help.

Jakob Rosenkrantz de Lasson


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