Sensitivity analysis of linear dynamical systems in uncertainty quantification

We consider linear dynamical systems including random parameters for uncertainty quantification. A sensitivity analysis of the stochastic model is applied to the input-output behaviour of the systems. Thus the parameters that contribute most to the variance are detected. Both intrusive and non-intrusive methods based on the polynomial chaos yield the required sensitivity coefficients. We use this approach to analyse a test example from electrical engineering

Robust and Efficient Uncertainty Quantification and Validation of RFIC Isolation

Modern communication and identification products impose demanding constraints on reliability of components. Due to this statistical constraints more and more enter optimization formulations of electronic products. Yield constraints often require efficient sampling techniques to obtain uncertainty quantification also at the tails of the distributions. These sampling techniques should outperform standard Monte Carlo techniques, since these latter ones are normally not efficient enough to deal with tail probabilities. One such a technique, Importance Sampling, has successfully been applied to optimize Static Random Access Memories (SRAMs) while guaranteeing very small failure probabilities, even going beyond 6-sigma variations of parameters involved. Apart from this, emerging uncertainty quantifications techniques offer expansions of the solution that serve as a response surface facility when doing statistics and optimization. To efficiently derive the coefficients in the expansions one either has to solve a large number of problems or a huge combined problem. Here parameterized Model Order Reduction (MOR) techniques can be used to reduce the work load. To also reduce the amount of parameters we identify those that only affect the variance in a minor way. These parameters can simply be set to a fixed value. The remaining parameters can be viewed as dominant. Preservation of the variation also allows to make statements about the approximation accuracy obtained by the parameter-reduced problem. This is illustrated on an RLC circuit. Additionally, the MOR technique used should not affect the variance significantly. Finally we consider a methodology for reliable RFIC isolation using floor-plan modeling and isolation grounding. Simulations show good comparison with measurements

Efficient calculation of uncertainty quantification

We consider Uncertainty Quanti¿cation (UQ) by expanding the solution in so-called generalized Polynomial Chaos expansions. In these expansions the solution is decomposed into a series with orthogonal polynomials in which the parameter dependency becomes an argument of the orthogonal polynomial basis functions. The time and space dependency remains in the coef¿cients. In UQ two main approaches are in use: Stochastic Collocation (SC) and Stochastic Galerkin (SG). Practice shows that in many cases SC is more ef¿cient for similar accuracy as obtained by SG. In SC the coef¿cients in the expansion are approximated by quadrature and thus lead to a large series of deterministic simulations for several parameters. We consider strategies to ef¿ciently perform this series of deterministic simulations within SC

Sensitivity analysis and model order reduction for random linear dynamical systems

Abstract We consider linear dynamical systems defined by differential algebraic equations. The associated input-output behaviour is given by a transfer function in the frequency domain. Physical parameters of the dynamical system are replaced by random variables to quantify uncertainties. We analyse the sensitivity of the transfer function with respect to the random variables. Total sensitivity coefficients are computed by a nonintrusive and by an intrusive method based on the expansions in series of the polynomial chaos. In addition, a reduction of the state space is applied in the intrusive method. Due to the sensitivities, we perform a model order reduction within the random space by changing unessential random variables back to constants. The error of this reduction is analysed. We present numerical simulations of a test example modelling a linear electric network

ICESTARS : integrated circuit/EM simulation and design technologies for advanced radio systems-on-chip

ICESTARS solved a series of critical issues in the currently available infrastructure for the design and simulation of new and highly-complex Radio Frequency (RF) front ends operating beyond 10 and up to 100 GHz. Future RF designs demand an increasing blend of analog and digital functionalities. The super and extremely high frequency (SHF, 3-30GHz, and EHF, 30-300GHz) ranges will be used to accomplish future demands for higher capacity channels. With todays frequency bands of approximately 1 to 3 GHz it is impossible to realize extremely high data transfer rates. Only a new generation of CAD and EDA tools will ensure the realization of complex nanoscale designs. It necessitates both new modeling approaches and new mathematical solution procedures for differential equations with largely differing time scales, analysis of coupled systems of DAEs (circuit equations) and PDEs (Maxwell equations for electromagnetic couplings) plus numerical simulations with mixed analog and digital signals. In ICESTARS new techniques and mathematical models working in highly integrated environments were developed to resolve this dilemma. The ICESTARS research area covered the three domains of RF design: (1) time-domain techniques, (2) frequency-domain techniques, and (3) EM analysis and coupled EM circuit analysis. The ICESTARS consortium comprised two industrial partners (NXP Semiconductors, Infineon Technologies AG), two SMEs (Magwel, AWR-APLAC) and five universities (Upper Austria, Cologne, Oulu, Wuppertal, Aalto), involving mathematicians, electronic engineers, and software engineers

Stochastic Galerkin methods and model order reduction for linear dynamical systems

Linear dynamical systems are considered in form of ordinary differential equations or differential algebraic equations. We change their physical parameters into random variables to represent uncertainties. A stochastic Galerkin method yields a larger linear dynamic al system satisfied by an approximation of the random processes. If the original systems own a high dimensionality, then a model order reduction is required to decrease the complexity. We investigate two approaches: the system of the stochastic Galerkin scheme is reduced and, vice versa, the original systems are reduced followed by an application of the stochastic Galerkin method. The properties are analyzed in case of reductions based on moment matching with the Arnoldi algorithm. We present numerical computations for two test examples

Stochastic Galerkin methods and model order reduction for linear dynamical systems

Linear dynamical systems are considered in the form of ordinary differential equations or differential algebraic equations. We change their physical parameters into random variables to represent uncertainties. A stochastic Galerkin method yields a larger linear dynamical system satisfied by an approximation of the random processes. If the original systems own a high dimensionality, then a model order reduction is required to decrease the complexity. We investigate two approaches: the system of the stochastic Galerkin scheme is reduced and, vice versa, the original systems are reduced followed by an application of the stochastic Galerkin method. The properties are analyzed in case of reductions based on moment matching with the Arnoldi algorithm. We present numerical computations for two test examples. Keywords: stochastic modeling, polynomial chaos, stochastic Galerkin method, model order reduction, quadrature, dynamical systems, uncertainty quantificatio