Polynomial Approximation Approach Research Articles

Probabilistic small-signal stability analysis of power systems based on Hermite polynomial approximation

This paper proposes a probabilistic small-signal stability analysis method based on the polynomial approximation approach. Since the correct determination of unknown coefficients has a direct effect on the accuracy of the polynomial approximation method, this paper presents a method for determining these coefficients, with high coverage on the probabilistic input domain of the problem. In this method, by increasing the number of random input variables, the proposed method can continue to maintain its efficiency. After determining the unknown coefficients, the load flow results and the system state matrix are determined for random changes of all loads based on the Hermite polynomial approximation. Then, the small-signal stability of the system is probabilistically evaluated based on stochastic analysis of the system eigenvalues. The consistency and validity of the proposed method are demonstrated based on the simulation studies in the MATLAB® software environment. In the simulation studies, the performance of the proposed method is examined by comparison with Point Estimation, Cumulant, Monte Carlo, and Chebyshev polynomial-based methods, for IEEE 14-bus and IEEE 39-bus test systems.Article highlightsProbabilistic small-signal stability analysis of power systemsModeling of governing equations of power system based on Hermite polynomial approximationForming the Collocation matrix based on a robust method

Predictive Analysis and Prognostic Approach of Diabetes Prediction with Machine Learning Techniques

Medical experts indulge in numerous strategies for efficient and predictive measures to model the health status of patients and formulate the patterns that are formed in test results. Most patients would dream of their betterments of their health conditions and thus preventing the progression of any disease. When diabetics is considered in the model, or highly intervening methodology would be required for pre-diabetic individuals. Hidden Markov models have been modified into variant models to derive predictions that accurately produce expected results by investigating patterns of clinical observations from a detailed sample of patient’s dataset. There are yet unanswered and concerning challenges to derive an absolute model for predicting diabetes. The datasets from which the patterns are derived from, still holds levels of in completeness, irregularity and obvious clinical interventions during the diagnosis. The Electronic Medical Records are not furnished with all requisite information in all conditions and scenarios. Due to these irregularities prediction has become highly challenging and there is increase in misclassification rate. Newton’s Divide Difference Method (NDDM) is a conventional model for filling the irregularity in electronic datasets through divided differences. The classical approach considers a polynomial approximation approach, thus leading to Runge Phenomenon. If the interval between data fields id higher, severity of finding the irregularities is even higher. By using this type of technique it helps in improving the accuracy thereby bringing in high level prediction without any error and misclassification. In this technique proposed, a novel approximation technique is implemented using the Euclidean distance parameter over the NDDM approximation to predict the outcomes or risk of Type 2 Diabetes Mellitus among patients. Real world entities in CPCSSN are considered for this study and proposed method is tested. The proposed method filled the irregularity in the data components of EMR with better approximations and the quality of prediction has improved significantly.

Dynamic Relative Gain Array Estimation using Local Polynomial Approximation Approach

This article presents a procedure that utilizes the local polynomial approximation approach in the estimation of the Dynamic Relative Gain Array (DRGA) matrix and its uncertainty bounds for weakly ...

Mass transfer during osmotic dehydration of green bean in salt solution: A polynomial approximation approach

In this study, moisture and solute variations inside cylindrical green bean samples during osmotic dehydration in salt solution were predicted using a modified lumped mathematical model. The polynomial approximation approach was used to obtain the average moisture and solute concentrations in the radial direction. Results of the proposed model were compared with the experimental data, obtained from osmotic dehydration of long cylindrical samples of green bean in different temperatures and concentrations of salt solution, as well as the exact solution of the original partial differential equation. Results show that the P. A. method's predictions followed the general trend of the experimental dehydration curves. Also dehydration curves show a good agreement between the P. A. and exact analytical method's predictions. The values of mean relative errors between the P. A. method's predictions and experimental data are between 14 and 24%. Also the related mean relative errors for exact analytical method are between 10 and 27.5%. Although the exact analytical solution provides better results, as expected, but considering the approximate nature of the P. A. method and in view of the fact that the deviations of P. A. and the exact analytical methods from the experimental data are comparable, the P. A. method could be used because of its simplicity.

FPGA Designs with Optimized Logarithmic Arithmetic

Using a general polynomial approximation approach, we present an arithmetic library generator for the logarithmic number system (LNS). The generator produces optimized LNS arithmetic libraries that improve significantly over previous LNS designs on area and latency. We also provide area cost estimation and bit-accurate simulation tools that facilitate comparison between LNS and floating-point designs.

Phase estimation in digital holographic interferometry using cubic-phase-function based method

The paper introduces a cubic-phase-function based method to estimate interference phase in digital holographic interferometry. The proposed method relies on piecewise polynomial approximation of phase by dividing an arbitrary row/column of the complex reconstructed interference field in many segments and modeling signal data in each segment as a cubic phase signal. The polynomial coefficients in each segment are determined using cubic phase function algorithm. The phase is subsequently evaluated from the polynomial constructed using the obtained polynomial coefficients. The piecewise polynomial approximation approach is extended for all rows/columns and the overall phase is thus determined. The method's applicability is demonstrated using simulation and experimental results.

POSITIONING ACCURACY ENHANCEMENT USING ERROR MODELING VIA A POLYNOMIAL APPROXIMATION APPROACH

Location information is critical for the development of value-added location-based services, such as fraud protection, location- aware network access, person/asset tracking etc. Herein, a method for the enhancement of localization systems in terms of achieved accuracy is proposed, which can be applied to new as well as existing systems regardless the underlying localization technique. The method is based on modeling the position measurement error introduced by the localization algorithm using a polynomial approximation approach. Measurements results demonstrate the applicability of the proposed technique in enhancing accuracy in a low cost and e-cient manner.

Adomian Decomposition Method Applied to Nonlinear Normal Modes of an Inertially Coupled Conservative System

In this work, the nonlinear normal modes (NNMs) of a conservative spring—mass—pendulum system with quadratic inertial nonlinearity are determined by applying the Adomian decomposition method. The technique is applied to the governing boundary value problem that determines the nonlinear normal modes of the two degrees-of-freedom system in configuration space. The NNMs of this system are non-similar and such that the modal curves do not pass through the origin in the configuration space. Both the low energy and the high energy cases are considered, and nonlinear normal modes near 1:2 and 1:1 internal resonances in the two linear modes of vibration of the system are developed. It is seen that the ADM polynomial approximation approach, where the model nonlinearities are approximated by polynomials in the neighborhood of center—center equilibrium, greatly reduces algebraic calculations, and improves the convergence speed and the accuracy of the results obtained. The method also captures the possible multiple nonlinear normal modes that exist near internal resonance conditions. The advantages and disadvantages in using the Adomian decomposition method to construct the nonlinear normal modes of the system are discussed.

Stochastic Response of a Random Mass Structure

This paper proposes a polynomial approximation approach for the estimation of the stochastic response of a random mass structure subjected to an evolutionary random excitation. A bounded, monopeak, and symmetrically distributed probability density function, called λ -PDF, together with the Gegenbauer polynomial approximation, is introduced to deal with stochastic dynamic response problems of the random mass structures. The λ -PDF model is used to describe the random parameters in the engineering random structures. And then the Gegenbauer polynomial approximation method is used to reduce the random structures into its deterministic equivalent one. The numerical example shows the effectiveness of the proposed method to explore dynamic phenomena in random structures.

SYSTEMATIC VARIATION NORMALIZATION IN MICROARRAY DATA TO GET GENE EXPRESSION COMPARISON UNBIASED

Normalization removes or minimizes the biases of systematic variation that exists in experimental data sets. This study presents a systematic variation normalization (SVN) procedure for removing systematic variation in two channel microarray gene expression data. Based on an analysis of how systematic variation contributes to variability in microarray data sets, our normalization procedure includes background subtraction determined from the distribution of pixel intensity values from each data acquisition channel and log conversion, linear or non-linear regression, restoration or transformation, and multiarray normalization. In the case when a non-linear regression is required, an empirical polynomial approximation approach is used. Either the high terminated points or their averaged values in the distributions of the pixel intensity values observed in control channels may be used for rescaling multiarray datasets. These pre-processing steps remove systematic variation in the data attributable to variability in microarray slides, assay-batches, the array process, or experimenters. Biologically meaningful comparisons of gene expression patterns between control and test channels or among multiple arrays are therefore unbiased using normalized but not unnormalized datasets.