Stochastic Macromodeling of Nonlinear Systems Via Polynomial Chaos Expansion and Transfer Function Trajectories

Stochastic macromodeling for hierarchical uncertainty quantification of nonlinear electronic systems

“…The goal of the stochastic macromodeling technique [18] is to express the time-domain variability of a nonlinear system which depends on a vector of normalized random variables ξ via the PC expansion [3]- [8] of the corresponding TFT model [19]- [21] implemented as a multi-channel Wiener system with a linear time-invariant block at the input and a nonlinear readout map. The resulting model is called PC-TFT model and can be expressed as [18]:…”

“…Thanks to the properties of the PC expansion, it is possible to prove that (1) can be rewritten as M +1 independent systems of ordinary differential equations (ODEs) [18]:…”

“…The PC-TFT technique [18] combines the modeling power of the TFT modeling approach with the accurate and efficient representation of the system variability given by the PC expansion resulting in a robust, flexible and powerful modeling technique. It is worth to notice that the stability of the PC-TFT model in (1), fundamental property for time-domain simulations, can be guaranteed.…”

“…The PC methodology has been extensively applied to the variability analysis of linear systems, such as lumped elements circuits [9], [10], multiconductor transmission lines [11]- [13] and generic linear multiport systems [14]. Also, the PC methodology has been proposed for the variability analysis of nonlinear electronic circuits [15]- [18]. Recently in [18], a method has been proposed for the variability analysis of complex nonlinear systems based on the calculation of the PC expansion of Transfer Function Trajectory (TFT) [19]- [21] models.…”

“…Also, the PC methodology has been proposed for the variability analysis of nonlinear electronic circuits [15]- [18]. Recently in [18], a method has been proposed for the variability analysis of complex nonlinear systems based on the calculation of the PC expansion of Transfer Function Trajectory (TFT) [19]- [21] models. This method can be applied to a broad range of nonlinear circuits thanks to the modeling power of the TFT and it offers the efficiency and accuracy of the PC approach in performing the variability analysis.…”