Tilt-angle stabilization of electrostatically actuated micromechanical mirrors beyond the pull-in point

Recently proposed optical subsystems utilizing microelectromechanical system (MEMS) components are being developed for use in optical crossconnects, add-drop multiplexers, and spectral equalizers. Common elements to these subsystems are electrostatically actuated micromechanical mirrors that steer optical beams to implement the subsystem functions. In the past, feedback control methods were used to obtain precise mirror orientations to minimize loss through optical switch fabrics or to stabilize attenuation through spectral equalizers. However, the mirror tilt angle range is limited because of inherent instability beyond a critical tilt angle (pull-in angle), and the usual feedback schemes do not counteract this effect. This work presents a feedback control method to enable operation of electrostatic micromirrors beyond the pull-in angle, yielding advantages including greater scalability of switch arrays and increased dynamic range of optical attenuators. Both static and dynamic tilting behaviors of electrostatic micromirrors under the feedback control are studied. In addition, a practical implementation of the feedback control system by using linear voltage control law is developed. A voltage slightly larger than the pull-in voltage is first applied when the mirror is at small angle positions, and the voltage is then linearly reduced as the mirror approaches the desired position. Experimental measurements, showing that tilt angles beyond the pull-in point can be achieved, are in good agreement with theoretical analysis.     

Investigation of the internal stress effects on static and dynamic characteristics of an electrostatically actuated beam for MEMS and NEMS application

Internal stress is often encountered in fixed–fixed beam based devices with micron or sub-micron length scales during device fabrication or operation. In this paper, we have investigated the effects of internal stress on static and dynamic characteristics of an electrostatically actuated cylindrical beam. The beam has been modelled using Euler–Bernoulli theory including the nonlinearities due to beam stretching and electrostatic forcing. The analysis has been carried out by solving the governing differential equations using a Galerkin based multi-modal reduced order modelling technique. A standard collocation based numerical scheme has also been used to confirm the results of the reduced order method. Our study shows that internal stress significantly influences the static and dynamic characteristics of the beam. We also find that, when compressive internal stress is high, it is important to include higher modes in the reduced order model. A design technique to achieve high resonant frequency stability under temperature variation, for electrostatically actuated beam oscillators, has also been proposed as a result of this investigation.     

Simple and accurate analytical solution to the post-buckling response of an electrostatically actuated MEMS curled cantilever

In this work, we propose to investigate the micro-electromechanical post-buckling response of an electrostatically-actuated curled cantilever microbeam. The analytical/numerical model is based on a nonlinear differential governing equation, derived via assuming a continuous Euler–Bernoulli beam model, combined with a multi-modes Galerkin decomposition of the beam deflection. The pull-in voltages which govern the stability of the micro-curled beam actuator are also obtained analytically. These approximate solutions show excellent agreements compared to solutions obtained by other computationally expensive numerical methods as well some previously reported experimental data, for a wide range of the microbeam length. The derived expressions of these analytical approximate solutions are easy to implement, quick to solve, and could be conveniently used by MEMS designers for quick estimations of the effects of the various micro-actuator parameters on its structural stability.     

Applications of the cluster variation method to empirical phase diagram calculations

The treatment of short- and long-range order is an important problem in the modelling of solid solutions, and therefore in the modelling of order-disorder phase transitions. This can be correctly handled by the cluster variation method (CVM). The basis of this method are briefly recalled. The methods of resolution of the CVM are outlined with their advantages and disadvantages. The input parameters of the CVM are the cluster interactions which can be obtained either by ab-initio calculations of total energies (or energies of mixing) or by fitting thermodynamic experimental data. This last method, called the mixed CVM-CALPHAD, has been used in the past to calculate binary and ternary systems. Some examples are given, and the various strategies employed are described. A review of the systems, binaries and ternaries, for which the mixed CVM-CALPHAD has been used to compute the phase diagram is proposed.     

A genetic approach to the identification of linear dynamical systems with static nonlinearities

This paper investigates the use of genetic algorithms in the identification of linear systems with static nonlinearitites. Linear systems with static nonlinearities at the input known as the Hammerstein model, and linear systems with static nonlinearities at the output known as the Wiener model are considered in this paper. The parameters of the Hammerstein and the Wiener models are estimated using genetic algorithms from the input-output data by minimizing the error between the true model output and the identified model output. Using genetic algorithms, the Hammerstein and the Wiener models with known nonlinearity structure and unknown parameters can be identified. Moreover, systems with non-minimum phase characteristics can be identified. Extensive simulations have been used to study the convergence properties of the proposed scheme. Simulation examples are included to demonstrate the effectiveness and robustness of the proposed identification scheme.     

On the sensitivity of linear discriminant analysis to sampling variation and analytical errors

The influence of analytical inaccuracy and imprecision on the linear discriminant function is considered. Analytical shifts occurring between the analysis of samples from each of two groups give spuriously low error rates if the function is evaluated on the training set, notably at high dimensions. Inaccuracy arising after the establishment of a discriminant function may change considerably the individual group error rates whereas the overall error rate is moderately affected. Imprecision decreases the group separation by an amount comparable to that in the univariate situation. In conclusion, evaluation of the error rates of a discriminant function on an independent test set is important to obtain realistic estimates of the performance and is preferable to using unbiased statistical methods or the split-sample principle based solely upon the training set.     

A unified approach to the stability of generalized static neural networks with linear fractional uncertainties and delays

In this paper, the robust global asymptotic stability (RGAS) of generalized static neural networks (SNNs) with linear fractional uncertainties and a constant or time-varying delay is concerned within a novel input-output framework. The activation functions in the model are assumed to satisfy a more general condition than the usually used Lipschitz-type ones. First, by four steps of technical transformations, the original generalized SNN model is equivalently converted into the interconnection of two subsystems, where the forward one is a linear time-invariant system with a constant delay while the feedback one bears the norm-bounded property. Then, based on the scaled small gain theorem, delay-dependent sufficient conditions for the RGAS of generalized SNNs are derived via combining a complete Lyapunov functional and the celebrated discretization scheme. All the results are given in terms of linear matrix inequalities so that the RGAS problem of generalized SNNs is projected into the feasibility of convex optimization problems that can be readily solved by effective numerical algorithms. The effectiveness and superiority of our results over the existing ones are demonstrated by two numerical examples.     

Application of the Hough transform to correct for linear variation of background illumination in images

The Hough transform has been formulated to detect areas of linear brightness variation within an image. The formulation leads to significant computational advantage involving a restricted parameter search space. Two applications are included to demonstrate the efficacy of this technique.     

On the variation of the tropospheric ozone over Indian region in relation to the meteorological parameters

Using monthly mean satellite measurements of TOMS/SBUV tropospheric ozone residual (TOR) data and meteorological parameters (tropopause height (TPH), 200 hPa geopotential height (GPH) and outgoing longwave radiation (OLR)) during 1979–2001, seasonal variability of TOR data and their association with meteorological parameters are outlined over the Indian region. Prominent higher values of TOR (44–48 DU, which is higher than the globally averaged 31.5 DU) are observed over the northern parts of the country during the summer monsoon season (June–September). Similar to the TOR variation, meteorological parameters (tropopause height, 200 hPa geopotential height and outgoing longwave radiation) also show higher values during the summer monsoon season, suggesting an in phase relationship and strong association between them because of deep convection present during summer monsoon time. The monthly trends in TOR values are found to be positive over the region. TOR has significant positive correlations (5% level) with GPH, and negative correlations with OLR and TPH for the month of September. The oxidation chains initiated by CH₄ and CO show the enhanced photochemical production of ozone that would certainly become hazardous to the ecological system. Interestingly, greenhouse gases (GHG) emissions were found to have continuously increased over the Indian region during the period 1990–2000, indicating more anthropogenic production of ozone precursor gases causing higher level of tropospheric ozone during this period.     

Convex models and interval analysis method to predict the effect of uncertain-but-bounded parameters on the buckling of composite structures

A new, non-probabilistic, set-theoretical models, that is interval analysis method is developed in this study to predict the variability or uncertainty in buckling loads of composite structures resulting from the unavoidable scatter in structural parameters. By mathematically analyzing and proving, the width of the upper and lower bounds on the critical buckling loads calculated by the interval analysis method is sharper than those that are obtained by convex models method, moreover, the interval analysis method has less computational cost than convex models method. Comparison between convex models and interval analysis method is performanced through numerical examples. For the specific cases considered, the results of numerical examples indicate that uncertainties in structural parameters have significant effect on the critical buckling loads of composite structures.     

ANN model to predict the effects of composition and heat treatment parameters on transformation start temperature of microalloyed steels

The paper presents some results of the research connected with the development of new approach based on the artificial neural network (ANN) of predicting the transformation start temperature of the phase constituents occurring in five steels after continuous cooling. The independent variables in the model are chemical compositions (C, Mn, Nb, Mo, Ti, N, Cu, P, S, Si, Al, V), austenitizing temperature, initial austenite grain size and cooling rate over the temperature range of the occurrence of phase transformations. For purpose of constructing these models, 138 different experimental data were gathered from the literature. The data used in the ANN model are arranged in a format of fourteen input parameters that cover the chemical compositions, initial austenite grain size and cooling rate, and output parameter which is transformation start temperature. In this model, the training and testing results in the ANN have shown strong potential for prediction of effects of chemical compositions and heat treatments on phase transformation of microalloyed steels.     

Addressing the ability of a land biosphere model to predict key biophysical vegetation characterisation parameters with Global Sensitivity Analysis

Sensitivity Analysis (SA) of the SimSphere Soil Vegetation Atmosphere Transfer (SVAT) model has been performed in this study using a cutting edge and robust Global Sensitivity Analysis (GSA) approach, based on the use of the Gaussian Emulation Machine for Sensitivity Analysis (GEM-SA) tool. The sensitivity of the following model outputs was evaluated: the ambient CO₂ concentration, the rate of CO₂ uptake by the plant, the ambient O₃ concentration, the flux of O₃ from the air to the plant/soil boundary and the flux of O₃ taken up by the plant alone. The most sensitive model inputs for the majority of outputs were: The Leaf Area Index (LAI), Fractional Vegetation Cover (Fr), Cuticle Resistance (CR) and Vegetation Height (VH). The influence of the external CO₂ on the leaf and O₃ concentration in the air as input parameters was also significant. Our study provides an important step forward in the global efforts towards SimSphere verification given the increasing interest in its use as an independent modelling or educational tool. Results of this study are also timely given the ongoing global efforts focused on deriving, at an operational level, spatio-temporal estimates of energy fluxes and soil moisture content using SimSphere synergistically with Earth Observation (EO) data.     

Artificial neural network to predict the effects of coating parameters on layer thickness of chromium carbonitride coating on pre-nitrided steels

Chromium carbonitride coatings were formed on plain carbon and alloy steels by pre-nitrocarburizing, followed by thermoreactive deposition and diffusion in a salt bath below 700 °C. In the present study, an artificial neural network-based model (ANNs) was developed to predict the layer thickness of pre-nitrided steels. Seventeen parameters affecting the layer thickness were considered as inputs, including the pre-nitriding time, salt bath compositions ratio, salt bath aging time, ferrochromium particle size, ferrochromium weight percent, salt bath temperature, coating time, and different chemical compositions of steels. The network was then trained to predict the layer thickness amounts as outputs. A 2-feed-forward back-propagation network was developed and trained using experimental data form literatures. Five steels were investigated. The effects of coating parameters on the layer thickness of steels were modeled by ANNs as well. The predicted values are in very good agreement with the measured ones indicating that the developed model is very accurate and has the great ability for predicting the layer thickness.     

Retraction Note to: ANN model to predict the effects of composition and heat treatment parameters on transformation start temperature of microalloyed steels

Neural Computing and Applications - The Editor-in-Chief has retracted this article because it significantly overlaps with a number of previously published articles.     

Algebraic approach to the interval linear static identification,tolerance, and control problems,or one more application of kaucher arithmetic

In this paper, theidentification problem, thetolerance problem, and thecontrol problem are treated for the interval linear equation Ax=b. These problems require computing an inner approximation of theunited solution set Σ_??(A, b)={x ∈ ? ⁿ | (?A ∈ A)(Ax ∈ b)}, of thetolerable solution set Σ_??(A, b)={x ∈ ? ⁿ | (?A ∈ A)(Ax ∈ b)}, and of thecontrollable solution set Σ_??(A, b)={x ∈ ? ⁿ | (?b ∈ b)(Ax ∈b)} respectively. Analgebraic approach to their solution is developed in which the initial problem is replaced by that of finding analgebraic solution of some auxiliary interval linear system in Kaucher extended interval arithmetic. The algebraic approach is proved almost always to give inclusion-maximal inner interval estimates of the solutionsets considered. We investigate basic properties of the algebraic solutions to the interval linear systems and propose a number of numerical methods to compute them. In particular, we present the simple and fastsubdifferential Newton method, prove its convergence and discuss numerical experiments.     

The joint model of the logistic model and linear random effect model — An application to predict orthostatic hypertension for subacute stroke patients

Stroke is a common acute neurologic and disabling disease. Orthostatic hypertension (OH) is one of the catastrophic cardiovascular conditions. If a stroke patient has OH, he/she has higher chance to fall or syncope during the following courses of treatment. This can result in possible bone fracture and the burden of medical cost therefore increases. How to early diagnose OH is clinically important. However, there is no obvious time-saving method for clinical evaluation except to check the postural blood pressure.This paper uses clinical data to identify potential clinical factors that are associated with OH. The data include repeatedly observed blood pressure, and the patient’s basic characteristics and clinical symptoms. A traditional logistic regression is not appropriate for such data. The paper modifies the two-stage model proposed by Tsiatis et al. (1995) and the joint model proposed by Wulfsohn and Tsiatis (1997) to take into account of a sequence of repeated measures to predict OH. The large sample properties of estimators of modified models are derived. Monte Carlo simulations are performed to evaluate the accuracy of these estimators. A case study is presented.