Stochastic analysis of circuits, cables, and interconnects

The recent years have seen an ever-growing interest in techniques for studying stochastic systems, i.e., systems affected by parameters that are random in nature. Relevant examples in electrical engineering are for instance a circuit made up by components whose value is only known within a certain manufacturing tolerance, or a cable harness illuminated by an electromagnetic field that impinges from an unknown direction. In this scenario, the outputs of interest must be regarded as stochastic, rather than deterministic quantities. Polynomial chaos became a popular tool to investigate this class of problems. It approximates stochastic quantities by series of suitable orthogonal polynomials in the random parameters. Over the years, several techniques were developed to calculate the polynomial chaos expansion coefficients and to address some issues regarding, for example, nonlinearity in the equations or high-dimensional problems. Another tool that is used in this context is Taylor models. This is an algebraic technique that calculates a Taylor approximation of a given variable with guaranteed-conservative error bounds, thus being suitable for a worst-case type of analysis.

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ERC Sector:

  • PE7_3 Simulation engineering and modelling

Keywords:

  • Statistical analysis
  • Stochastic systems
  • Polynomial chaos
  • Uncertainty quantification

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