TMsim : an algorithmic tool for the parametric and worst-case simulation of systems with uncertainties

This paper presents a general purpose, algebraic tool—named TMsim—for the combined parametric and worst-case analysis of systems with bounded uncertain parameters.The tool is based on the theory of Taylor models and represents uncertain variables on a bounded domain in terms of a Taylor polynomial plus an interval remainder accounting for truncation and round-off errors.This representation is propagated from inputs to outputs by means of a suitable redefinition of the involved calculations, in both scalar and matrix form. The polynomial provides a parametric approximation of the variable, while the remainder gives a conservative bound of the associated error. The combination between the bound of the polynomial and the interval remainder provides an estimation of the overall (worst-case) bound of the variable. After a preliminary theoretical background, the tool (freely available online) is introduced step by step along with the necessary theoretical notions. As a validation, it is applied to illustrative examples as well as to real-life problems of relevance in electrical engineering applications, specifically a quarter-car model and a continuous time linear equalizer

Statistical crosstalk analysis via probabilistic machine learning surrogates

This paper discusses the application of a probabilistic surrogate modeling technique, based on Gaussian process regression (GPR), to the uncertainty quantification (UQ) of crosstalk. Compared to traditional deterministic surrogate models, the GPR provides a stochastic process that carries an estimate of the model uncertainty. This allows assigning confidence bounds to the model prediction and, in an UQ scenario, to statistical estimates. The advocated method is illustrated through its application to a literature test case

Efficient Implementation of the Vector-Valued Kernel Ridge Regression for the Uncertainty Quantification of the Scattering Parameters of a 2-GHz Low-Noise Amplifier

This paper focuses on the application of an efficient implementation of the vector-valued kernel Ridge regression (KRR) to the uncertainty quantification (UQ) of the scattering parameters of a low-noise amplifier (LNA). Specifically, the performance of the proposed technique have been investigated for the statistical assessment of the mean value, variance and probability density function (PDF) of the S11 and S21 parameters of a 2-GHz LNA induced by 25 stochastic input parameters and compared with the corresponding reference results computed via a plain Monte Carlo (MC) simulation

A Perturbative Stochastic Galerkin Method for the Uncertainty Quantification of Linear Circuits

This paper presents an iterative and decoupled perturbative stochastic Galerkin (SG) method for the variability analysis of stochastic linear circuits with a large number of uncertain parameters. State-of-the-art implementations of polynomial chaos expansion and SG projection produce a large deterministic circuit that is fully coupled, thus becoming cumbersome to implement and inefficient to solve when the number of random parameters is large. In a perturbative approach, component variability is interpreted as a perturbation of its nominal value. The relaxation of the resulting equations and the application of a SG method lead to a decoupled system of equations, corresponding to a modified equivalent circuit in which each stochastic component is replaced by the nominal element equipped with a parallel current source accounting for the effect of variability. The solution of the perturbation problem is carried out in an iterative manner by suitably updating the equivalent current sources by means of Jacobi- or Gauss-Seidel strategies, until convergence is reached. A sparse implementation allows avoiding the refinement of negligible coefficients, yielding further efficiency improvement. Moreover, for time-invariant circuits, the iterations are effectively performed in post-processing after characterizing the circuit in time or frequency domain by means of a limited number of simulations. Several application examples are used to illustrate the proposed technique and highlight its performance and computational advantages

Quaterpyridine Ligands for Panchromatic Ru(II) Dye Sensitizers

A new general synthetic access to carboxylated quaterpyridines (qpy), of interest as ligands for panchromatic dyesensitized solar cell organometallic sensitizers, is presented. The strategic step is a Suzuki−Miyaura cross-coupling reaction, which has allowed the preparation of a number of representative unsubstituted and alkyl and (hetero)aromatic substituted qpys. To bypass the poor inherent stability of 2-pyridylboronic acid derivatives, we successfully applied N-methyliminodiacetic acid (MIDA) boronates as key reagents, obtaining the qpy ligands in good yields up to (quasi)gram quantities. The structural, spectroscopic (NMR and UV−vis), electrochemical, and electronic characteristics of the qpy have been experimentally and computationally (DFT) investigated. The easy access to the bis-thiocyanato Ru(II) complex of the parent species of the qpy series, through an efficient route which bypasses the use of Sephadex column chromatography, is shown. The bis-thiocyanato Ru(II) complex has been spectroscopically (NMR and UV−vis), electrochemically, and computationally investigated, relating its properties to those of previously reported Ru(II)−qpy complexes.“This document is the Accepted Manuscript version of a Published Work that appeared in final form in [The Journal of Organic Chemistry], copyright © American Chemical Society after peer review and technical editing by the publisher

Self-Validated Time-Domain Analysis of Linear Systems with Bounded Uncertain Parameters

This paper presents a novel approach to predict the bounds of the time-domain response of a linear system subject to multiple bounded uncertain input parameters. The method leverages the framework of Taylor models in conjunction with the numerical inversion of Laplace transform (NILT). Different formulations of the NILT are reviewed, and their advantages and limitations are discussed. An implementation relying on an inverse fast Fourier transform (IFFT) turns out to be the most efficient and accurate alternative. The feasibility of the technique is validated based on several diverse application examples, namely a control loop, a lossy transmission-line network and an active low-pass filter

From Powders to Dense Metal Parts: Characterization of a Commercial AlSiMg Alloy Processed through Direct Metal Laser Sintering

In this paper, a characterization of an AlSiMg alloy processed by direct metal laser sintering (DMLS) is presented, from the analysis of the starting powders, in terms of size, morphology and chemical composition, through to the evaluation of mechanical and microstructural properties of specimens built along different orientations parallel and perpendicular to the powder deposition plane. With respect to a similar aluminum alloy as-fabricated, a higher yield strength of about 40% due to the very fine microstructure, closely related to the mechanisms involved in this additive process is observe

How affine arithmetic helps beat uncertainties in electrical systems

The ever-increasing impact of uncertainties in electronic circuits and systems is requiring the development of robust design tools capable of taking this inherent variability into account. Due to the computational inefficiency of repeated design trials, there has been a growing demand for smart simulation tools that can inherently and effectively capture the results of parameter variations on the system responses. To improve product performance, improve yield and reduce design cost, it is particularly relevant for the designer to be able to estimate worst-case responses. Within this framework, the article addresses the worst-case simulation of lumped and distributed electrical circuits. The application of interval-based methods, like interval analysis, Taylor models and affine arithmetic, is discussed and compared. The article reviews in particular the application of the affine arithmetic to complex algebra and fundamental matrix operations for the numerical frequency-domain simulation. A comprehensive and unambiguous discussion appears in fact to be missing in the available literature. The affine arithmetic turns out to be accurate and more efficient than traditional solutions based on Monte Carlo analysis. A selection of relevant examples, ranging from linear lumped circuits to distributed transmission-line structures, is used to illustrate this technique