Distributed Control Timing Uncertainty Modeling With Polynomial Chaos

The patent replaces traditional deterministic simulation methods with a stochastic simulation approach using polynomial chaos expansion. This substitution transforms the simulation from a purely computational deterministic model to one that incorporates probabilistic mathematical frameworks, enabling accurate representation of uncertain timing effects while maintaining computational efficiency through the structured mathematical approach.

The patent changes the fundamental parameters of the simulation by introducing stochastic parameters to represent uncertain timing effects. Instead of using fixed deterministic values for timing parameters, the invention employs random variables and probability distributions to model jitter and dead time, fundamentally altering how timing uncertainties are represented and processed in the simulation.

The patent applies preliminary action by pre-defining polynomial chaos basis functions and their statistical properties before running the main simulation. This preparatory step establishes the mathematical framework in advance, allowing the stochastic simulation to proceed efficiently by reusing pre-computed basis functions and avoiding redundant calculations during the actual uncertainty quantification process.

The patent implements partial action by selectively applying polynomial chaos expansion only to the specific timing parameters that exhibit uncertainty (jitter and dead time), rather than transforming the entire simulation model. This targeted approach incorporates stochastic effects where needed while keeping the rest of the deterministic model intact, thereby reducing the overall computational burden compared to a fully stochastic transformation.