Material parameter extraction in THz-TDS using a converging beam transfer function

We demonstrate a parameter extraction algorithm based on a theoretical transfer function, which takes into account a converging THz beam. Using this, we successfully extract material parameters from data obtained for a quartz sample with a THz time domain spectrometer. © 2010 IEEE.

Convective heat dissipation with lattice-frame materials

This paper presents experimental results on heat transfer and pressure drop for a compact heat sink made of fully triangulated, lightweight (porosity∼0.938), aluminum lattice-frame materials (LFMs). Due to the inherent structural anisotropy of the LFMs, two mutually perpendicular orientations were selected for the measurements. Constant heat flux was applied to the heat sink under steady state conditions, and dissipated by forced air convection. The experimental data were compared with those predicted from an analytical model based on fin analogy. The experimental results revealed that pressure drop is strongly dependent upon the orientation of the structure, due mainly to the flow blockage effect. For heat transfer measurements, typical local temperature distributions on the substrate under constant heat flux conditions were captured with infrared camera. The thermal behavior of LFMs was found to follow closely that of cylinder banks, with early transition Reynolds number (based on strut diameter) equal to about 300. The Nusselt number prediction from the fin-analogy correlates well with experimental measurements, except at low Reynolds numbers where a slightly underestimation is observed. Comparisons with empty channels and commonly used heat exchanger media show that the present LFM heat sink can remove heat approximately seven times more efficient than an empty channel and as efficient as a bank of cylinders at the same porosity level. The aluminum LFMs are extremely stiff and strong, making them ideal candidates for multifunctional structures requiring both heat dissipation and mechanical load carrying capabilities. © 2003 Elsevier Ltd. All rights reserved.

Direct parameter extraction in capacitively transduced micromechanical resonators using the anti-resonance

This paper presents a method for the fast and direct extraction of model parameters for capacitive MEMS resonators from their measured transmission response such as quality factor, resonant frequency, and motional resistance. We show that these parameters may be extracted without having to first de-embed the resonator motional current from the feedthrough. The series and parallel resonances from the measured electrical transmission are used to determine the MEMS resonator circuit parameters. The theoretical basis for the method is elucidated by using both the Nyquist and susceptance frequency response plots, and applicable in the limit where CF > CmQ; commonly the case when characterizing MEMS resonators at RF. The method is then applied to the measured electrical transmission for capacitively transduced MEMS resonators, and compared against parameters obtained using a Lorentzian fit to the measured response. Close agreement between the two methods is reported herein. © 2010 IEEE.

Binary excitation of a high-Q bulk acoustic microresonator by actuation polarity inversion

We present a technique for independently exciting two resonant modes of vibration in a single-crystal silicon bulk mode microresonator using the same electrode configuration through control of the polarity of the DC actuation voltage. Applications of this technique may include built-in temperature compensation by the simultaneous selective excitation of two closely spaced modes that may have different temperature coefficients of resonant frequency. The technique is simple and requires minimum circuit overhead for implementation. The technique is implemented on square plate resonators with quality factors as high as 3.06 × 106. Copyright © 2008 by ASME.

Direct parameter extraction in feedthrough-embedded capacitive MEMS resonators

This paper presents a method for fast and accurate determination of parameters relevant to the characterization of capacitive MEMS resonators like quality factor (Q), resonant frequency (fn), and equivalent circuit parameters such as the motional capacitance (Cm). In the presence of a parasitic feedthrough capacitor (CF) appearing across the input and output ports, the transmission characteristic is marked by two resonances: series (S) and parallel (P). Close approximations of these circuit parameters are obtained without having to first de-embed the resonator motional current typically buried in feedthrough by using the series and parallel resonances. While previous methods with the same objective are well known, we show that these are limited to the condition where CF ≪ CmQ. In contrast, this work focuses on moderate capacitive feedthrough levels where CF > CmQ, which are more common in MEMS resonators. The method is applied to data obtained from the measured electrical transmission of fabricated SOI MEMS resonators. Parameter values deduced via direct extraction are then compared against those obtained by a full extraction procedure where de-embedding is first performed and followed by a Lorentzian fit to the data based on the classical transfer function associated with a generic LRC series resonant circuit. © 2011 Elsevier B.V. All rights reserved.

Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Approximate Bayesian computation (ABC) is a popular technique for analysing data for complex models where the likelihood function is intractable. It involves using simulation from the model to approximate the likelihood, with this approximate likelihood then being used to construct an approximate posterior. In this paper, we consider methods that estimate the parameters by maximizing the approximate likelihood used in ABC. We give a theoretical analysis of the asymptotic properties of the resulting estimator. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how sequential Monte Carlo methods provide a natural method for implementing our likelihood-based ABC procedures.

An overview of sequential Monte Carlo methods for parameter estimation in general state-space models

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, are numerical techniques based on Importance Sampling for solving the optimal state estimation problem. The task of calibrating the state-space model is an important problem frequently faced by practitioners and the observed data may be used to estimate the parameters of the model. The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed for this task accompanied with a discussion of their advantages and limitations.

Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation

Sequential Monte Carlo (SMC) methods are popular computational tools for Bayesian inference in non-linear non-Gaussian state-space models. For this class of models, we propose SMC algorithms to compute the score vector and observed information matrix recursively in time. We propose two different SMC implementations, one with computational complexity $\mathcal{O}(N)$ and the other with complexity $\mathcal{O}(N^{2})$ where $N$ is the number of importance sampling draws. Although cheaper, the performance of the $\mathcal{O}(N)$ method degrades quickly in time as it inherently relies on the SMC approximation of a sequence of probability distributions whose dimension is increasing linearly with time. In particular, even under strong \textit{mixing} assumptions, the variance of the estimates computed with the $\mathcal{O}(N)$ method increases at least quadratically in time. The $\mathcal{O}(N^{2})$ is a non-standard SMC implementation that does not suffer from this rapid degrade. We then show how both methods can be used to perform batch and recursive parameter estimation.