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

Nanoelectronic COupled problems solutions - nanoCOPS: modelling, multirate, model order reduction, uncertainty quantification, fast fault simulation

The FP7 project nanoCOPS derives new methods for simulation during development of designs of integrated products. It covers advanced simulation techniques for electromagnetics with feedback couplings to electronic circuits, heat and stress. It is inspired by interest from semiconductor industry and by a simulation tool vendor in electronic design automation. The project is on-going and the paper presents the outcomes achieved after the first half of the project duration

Model order reduction for nonlinear IC models. CASA-Report 07-41

Abstract Due to refined modelling of semiconductor devices and increasing packing densities, reduced order modelling of large nonlinear systems is of great importance in the design of integrated circuits (ICs). Despite the linear case, methodologies for nonlinear problems are only beginning to develop. The most practical approaches rely either on linearisation, making techniques from linear model order reduction applicable, or on proper orthogonal decomposition (POD), preserving the nonlinear characteristic. In this paper we focus on POD. We demonstrate the missing point estimation and propose a new adaption of POD to reduce both dimension of the problem under consideration and cost for evaluating the full nonlinear system

Trajectory piecewise linear approach for nonlinear differential-algebraic equations in circuit simulation

In this paper we extend the Trajectory Piecewise Linear (TPWL) model order reduction (MOR) method for nonlinear differential algebraic equations (DAE). The TPWL method is based on combining several linear reduced models at different time points, which are created along a typical trajectory, to approximate the full nonlinear model.We discuss how to select the linearization tuples for linearization and the choice of linear MOR method. Then we study how to combine the local linearized reduced systems to create a global TPWL model. Finally, we show a numerical result.</p

A retrospective analysis of the combined use of PERC rule and Wells score to exclude pulmonary embolism in the Emergency Department

BACKGROUND: The pulmonary embolism rule-out criteria (PERC) rule is an eight-factor decision rule to support the decision not to order a diagnostic test when the gestalt-based clinical suspicion on pulmonary embolism (PE) is low. METHODS: In a retrospective cohort study, we determined the accuracy of a negative PERC (0) in patients with a low Wells score (<2) to rule-out PE, and compared this to the accuracy of the default algorithm used in our hospital (a low Wells score in combination with a negative D-dimer). RESULTS: During the study period, 377 patients with a Wells score <2 were included. CT pulmonary angiography (CTPA) was performed in 86 patients, and V/Q scintigraphy in one patient. PE was diagnosed in 18 patients. 78 patients (21%) had a negative PERC score. When further diagnostic studies would have been omitted in these patients, two (subsegmental) PEs would have been missed, resulting in a sensitivity of 89% (64%-98%) and a negative likelihood ratio (LR-) of 0.52 (0.14-1.97). The default algorithm missed one (subsegmental) PE, resulting in a sensitivity of 95% (71%-99%) and an LR- of 0.25 (0.04-1.73). CONCLUSIONS: The combination of a Wells score <2 and a PERC rule of 0 had a suboptimal sensitivity for excluding PE in our sample of patients presenting in the ED. Further studies are warranted to test this algorithm in larger populations

Modified extended BDF time-integration methods, applied to circuit equations Modified Extended BDF Time-Integration Methods, Applied to Circuit Equations

Abstract. Electric circuits designers are frequently interested in the transient behaviour of the designed circuit. A common method for time integration of the Differential Algebraic circuit Equations (DAE) is the Backward Differentiation Formula (BDF) method. In 1983, J. Cash proposed the Modified Extended BDF (MEBDF) method, which combines better stability properties and higher order of convergence than BDF, but requires more computations per step. We prove reduction of convergence order for MEBDF when applied to DAE&apos;s with higher DAE-index. However, because in practice, in circuit analysis, the DAE-index does not exceed 2, the reduction is quite moderate and it equals the BDF-order in that case. One gains better, or even unconditional, stability. One also obtains consistent solutions

Robust DC and efficient time-domain fast fault simulation Citation for published version (APA): Robust DC and efficient time-domain fast fault simulation Robust DC and efficient time-domain fast fault simulation

Abstract Purpose -Imperfactions in manufacturing processes may cause unwanted connections (faults) that are added to the nominal, &quot;golden&quot;, design of an electronic circuit. By fault simulation one simulates all situations. Normally this leads to a large list of simulations in which for each defect a steady-state (DC) solution is determined followed by a transient simulation. We improve the robustness and the effciency of these simulations. Design/methodology/approach -Determining the DC solution can be very hard. For this we present an adaptive time domain source stepping procedure that can deal with controlled sources. The method can easily be combined with existing pseudo-transient procedures. The method is robust and efficient. In the subsequent transient simulation the solution of a fault is compared to a golden, fault-free, solution. A strategy is developed to efficiently simulate the faulty solutions until their moment of detection. Finding -We fully exploit the hierarchical structure the circuit in the simulation process to bypass parts of the circuit that appear to be unaffected by the fault. Accurate prediction and efficient solution procedures lead to fast fault simulation. Originality/value -Our fast fault simulation helps to store a database with detectable deviations for each fault. If such a detectable output &quot;matches&quot; a result of a product that has been returned because of malfunctioning it helps to identify the subcircuit that may contain the real fault. One aims to detect as much as possible candidate faults. Because of the many options the simulations must be very efficient