Accurate polynomial chaos expansion for variability analysis using optimal design of experiments

Prasad, Aditi Krishna; Ahadi, Majid; Thakur, Bhavani Singh; Roy, Sourajeet

doi:10.1109/nemo.2015.7415055

Cited by 9 publications

(7 citation statements)

References 7 publications

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“…Polynomial regression [22,23] is a type of regression analyze in the nth degree polynomial modeling of the relationship between independent and dependent variables. Polynomial regression is a special case of MLR in which the polynomial equation of data blends in with curvilinear interplay of the dependent and independent variables [24].…”

Section: • Polynomial Regressionmentioning

confidence: 99%

A Review on Linear Regression Comprehensive in Machine Learning

Maulud

Abdulazeez

2020

JASTT

574

145

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Perhaps one of the most common and comprehensive statistical and machine learning algorithms are linear regression. Linear regression is used to find a linear relationship between one or more predictors. The linear regression has two types: simple regression and multiple regression (MLR). This paper discusses various works by different researchers on linear regression and polynomial regression and compares their performance using the best approach to optimize prediction and precision. Almost all of the articles analyzed in this review is focused on datasets; in order to determine a model's efficiency, it must be correlated with the actual values obtained for the explanatory variables.

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Section: • Polynomial Regressionmentioning

confidence: 99%

A Review on Linear Regression Comprehensive in Machine Learning

Maulud

Abdulazeez

2020

JASTT

574

145

View full text Add to dashboard Cite

show abstract

“…This hyperbolic truncation scheme for two input random variables (M = 2) is illustrated in Figs. 1(a) and 1(b), where the circles represent all terms of the polynomial basis of degree less than or equal to l = 5, included in the set (2) for k = 1 (blue circles) and k = 0.5 (pink circles). From Fig.…”

Section: From Classical Truncation Scheme To Sparse Chaos Representationmentioning

confidence: 99%

“…We intend now to discuss the efficiency of the sparse PC at two different frequencies: we have chosen 202 MHz as a representative example of the smooth behavior of |H 1 |, where Q 2 202 MHz = 99.80%, and 2.23 GHz as an illustrative example of the irregular behavior, where Q 2 2.23 GHz = 96.62%. Fig.…”

Section: Sparse Pc Metamodelmentioning

confidence: 99%

“…To address the problem of uncertainty quantification (UQ) of high-speed information and communication systems, several approaches based on the so-called polynomial chaos (PC) technique have been successfully developed [1][2][3]. This technique represents the random response of a model in terms of a linear combination of orthonormal polynomial basis involving the input random variables.…”

Section: Introductionmentioning

confidence: 99%

“…This technique represents the random response of a model in terms of a linear combination of orthonormal polynomial basis involving the input random variables. Intrusive [3][4][5] or non-intrusive [2,6,7] approaches exist for the computation of the basis coefficients, thus reproducing an analytic representation called metamodel (or surrogate model) of the system response. The metamodel can be profitably used to estimate statistical quantities of the system output, like moments and probability density functions (PDF).…”

Section: Introductionmentioning

confidence: 99%

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Identfication of Main Factors of Uncertainty in a Microstrip Line Network

Larbi¹,

Stievano²,

Canavero³

et al. 2018

PIER

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This paper deals with uncertainty propagation applied to the analysis of crosstalk in printed circuit board microstrip traces. Complex interconnection networks generally are affected by many uncertain parameters and their point-to-point transfer functions are computationally expensive, thus making Monte-Carlo analyses rather inefficient. To overcome this situation, a metamodel is highly desirable. This paper presents a sparse and accelerated polynomial chaos approach, which proves to be well adapted for high-dimensional uncertainty quantification and well suited for the sensitivity analysis of crosstalk effects. We highlight the significant advantage of the advocated approach for the design of microstrip line networks of complex topology. In fact, we demonstrate how a small number of system simulations can help to quantify the statistics of the output variability and identify a reduced set of high-impact parameters.

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Accurate Identification of Harmonic Distortion for Micro-Grids Using Artificial Intelligence-Based Predictive Models

Abed,

El-Sehiemy,

Bentouati

et al. 2024

IEEE Access

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This paper proposes an accurate harmonic identification strategy for microgrids and distributed power systems. The harmonic identification strategy is one of the complex tasks in microgrids due to the need of high computational burden in terms of memory and computational time. The complexity of the considered problem is resulted from solving the transcendental nonlinear equations that characterize harmonics especially in real time is considered as a highly challenged problem. The proposed identification strategy aims at detecting individual and total harmonic distortion levels that is generated from several harmonic sources. In the current paper, the Machine Learning Regression Analysis (MLRA) including location-specific data and the Artificial Neural Networks (ANNs) are proposed to identify the harmonic distortion. To enhance the identification and prediction performance, the standard IEEE 34-bus test feeder with verified harmonic sources power system is emulated for various scenarios using Electric Transient Analysis Program (ETAP). An extracting procedure for individual and total harmonic components are employed . The higher reduction level of error with approximately maximum median of 3.7127e-15 % assures the accurate prediction of harmonic components. In addition, this work investigates the impact of several practical cases when the voltages of the renewable clean energy source arrays vary (e.g., solar cell, wind turbine, and EV), and a double-stage topology is needed to have the same amount of voltage at the input of the inverter before inversion.

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Accurate polynomial chaos expansion for variability analysis using optimal design of experiments

Cited by 9 publications

References 7 publications

A Review on Linear Regression Comprehensive in Machine Learning

A Review on Linear Regression Comprehensive in Machine Learning

Identfication of Main Factors of Uncertainty in a Microstrip Line Network

Accurate Identification of Harmonic Distortion for Micro-Grids Using Artificial Intelligence-Based Predictive Models

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