Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Influence of different light sources and photo-activation methods on degree of conversion and polymerization shrinkage of a nanocomposite resin

The purpose of this study was to evaluate the influence of different light sources and photo-activation methods on degree of conversion (DC%) and polymerization shrinkage (PS) of a nanocomposite resin (Filtek (TM) Supreme XT, 3M/ESPE). Two light-curing units (LCUs), one halogen-lamp (QTH) and one light-emitting-diode (LED), and two different photo-activation methods (continuous and gradual) were investigated in this study. The specimens were divided in four groups: group 1-power density (PD) of 570 mW/cm(2) for 20 s (QTH); group 2-PD 0 at 570 mW/cm(2) for 10 s + 10 s at 570 mW/cm(2) (QTH); group 3-PD 860 mW/cm(2) for 20 s (LED), and group 4-PD 125 mW/cm(2) for 10 s + 10 s at 860 mW/cm(2) (LED). A testing machine EMIC with rectangular steel bases (6 x 1 x 2 mm) was used to record the polymerization shrinkage forces (MPa) for a period that started with the photo-activation and ended after two minutes of measurement. For each group, ten repetitions (n = 40) were performed. For DC% measurements, five specimens (n = 20) for each group were made in a metallic mold (2 mm thickness and 4 mm diameter, ISO 4049) and them pulverized, pressed with bromide potassium (KBr) and analyzed with FT-IR spectroscopy. The data of PS were analyzed by Analysis of Variance (ANOVA) with Welch`s correction and Tamhane`s test. The PS means (MPa) were: 0.60 (G1); 0.47 (G2); 0.52 (G3) and 0.45 (G4), showing significant differences between two photo-activation methods, regardless of the light source used. The continuous method provided the highest values for PS. The data of DC% were analyzed by Analysis of Variance (ANOVA) and shows significant differences for QTH LCUs, regardless of the photo-activation method used. The QTH provided the lowest values for DC%. The gradual method provides lower polymerization contraction, either with halogen lamp or LED. Degree of conversion (%) for continuous or gradual photo-activation method was influenced by the LCUs. Thus, the presented results suggest that gradual method photo-activation with LED LCU would suffice to ensure adequate degree of conversion and minimum polymerization shrinkage.

Influence of chromium concentration on the optical-electronic properties of ruby microstructures

Films of amorphous aluminium nitride (AlN) were prepared by conventional radio frequency sputtering of an Al + Cr target in a plasma of pure nitrogen. The Cr-to-Al relative area determines the Cr content, which remained in the similar to 0-3.5 at% concentration range in this study. Film deposition was followed by thermal annealing of the samples up to 1050 degrees C in an atmosphere of oxygen and by spectroscopic characterization through energy dispersive x-ray spectrometry, photoluminescence and optical transmission measurements. According to the experimental results, the optical-electronic properties of the Cr-containing AlN films are highly influenced by both the Cr concentration and the temperature of the thermal treatments. In fact, thermal annealing at 1050 degrees C induces the development of structures that, because of their typical size and distinctive spectral characteristics, were designated by ruby microstructures (RbMSs). These RbMSs are surrounded by a N-rich environment in which Cr(3+) ions exhibit luminescent features not present in other Cr(3+)-containing systems such as ruby, emerald or alexandrite. The light emissions shown by the RbMSs and surroundings were investigated according to the Cr concentration and temperature of measurement, allowing the identification of several Cr(3+)-related luminescent lines. The main characteristics of these luminescent lines and corresponding excitation-recombination processes are presented and discussed in view of a detailed spectroscopic analysis.