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A probabilistic approach for approximation of optical and opto-electronic properties of an opto-semiconductor wafer under consideration of measuring inaccuracy and model uncertainty

Stroka Stefan M., Heumann Christian, Suhrke Fabian, Meindl Kathrin

Opto-Electronics Review

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2023

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Vol. 31, No. 2

art. no. e145863

EN

This paper presents a probabilistic machine learning approach to approximate wavelength values for unmeasured positions on an opto-semiconductor wafer after epitaxy. Insufficient information about optical and opto-electronic properties may lead to undetected specification violations and, consequently, to yield loss or may cause product quality issues. Collection of information is restricted because physical measuring points are expensive and in practice samples are only drawn from 120 specific positions. The purpose of the study is to reduce the risk of uncertainties caused by sampling and measuring inaccuracy and provide reliable approximations. Therefore, a Gaussian process regression is proposed which can determine a point estimation considering measuring inaccuracy and further quantify estimation uncertainty. For evaluation, the proposed method is compared with radial basis function interpolation using wavelength measurement data of 6-inch InGaN wafers. Approximations of these models are evaluated with the root mean square error. Gaussian process regression with radial basis function kernel reaches a root mean square error of 0.814 nm averaged over all wafers. A slight improvement to 0.798 nm could be achieved by using a more complex kernel combination. However, this also leads to a seven times higher computational time. The method further provides probabilistic intervals based on means and dispersions for approximated positions.

2

Prediction of blast-induced ground vibration using GPR and blast-design parameters optimization based on novel grey-wolf optimization algorithm

Lawal A. I., Olajuyi S. I., Kwon S., Aladejare A. E., Edo T. M.

Acta Geophysica

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2021

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Vol. 69, no. 4

1313--1324

EN

Blasting is an intrinsic component of mining cycle of operation. However, it is usually associated with negative environmental efects such as blast-induced ground vibration (BIGV) which require accurate prediction and control. Therefore, in this study, Gaussian process regression (GPR) has been proposed for prediction of BIGV in terms of peak particle velocity (PPV), while grey-wolf optimization (GWO) algorithm has been used to optimize the blast-design parameters for the control of BIGV in Obajana limestone quarry, Nigeria. The blast-design parameters such as burden (B), spacing (S), hole depth (Hd), stemming length (T), and number of holes (nh) were obtained from the quarry. The distance from the blasting point to the measuring point (D) and the charge per delay (W) were measured and determined, respectively. The PPV was also measured for the number of blasting operations witnessed. These seven parameters were used as inputs to the proposed GPR model, while the PPV was the targeted output. The performance of the proposed model was evaluated using some statistical indices. The output of the GPR model was compared with ANN model and three empirical models, and the GPR model proved to be more accurate with the coefcient of determination (R2 ) of approximately 1 and variance accounted for VAF of about 100%, respectively. In addition, the GWO was also developed to select the optimum blasting parameters using the ANN model for the generation of objective function. The output of the GWO revealed that if the number of holes (nh) can be reduced by 45% and W by 8%, the PPV will be reduced by about 94%. Hence, the proposed models are both suitable for prediction of PPV and optimization of blast-design parameters.

3

Kernel function based regression approaches for estimating the oxygen transfer performance of plunging hollow jet aerator

Kumar M., Tiwari N. K., Ranjan S.

Journal of Achievements in Materials and Manufacturing Engineering

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2019

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Vol. 95, nr 2

74--84

EN

Purpose: To evaluate the capability of various kernels employed with support vector regression (SVR) and Gaussian process regression (GPR) techniques in estimating the volumetric oxygen transfer coefficient of plunging hollow jets. Design/methodology/approach: In this study, a data set of 81 observations is acquired from laboratory experiments of hollow jets plunging on the surface of water in the tank. The jet variables: jet velocity, jet thickness, jet length, and water depth are varied accordingly and the values of volumetric oxygen transfer coefficient is computed. An empirical relationship expressing the oxygenation performance of plunging hollow jet aerator in terms of jet variables is formulated using multiple nonlinear regression. The performance of this nonlinear relationship is compared with various kernel function based SVR and GPR models. Models developed with the training data set (51 observations) are checked on testing data set (24 observations) for performance comparison. Sensitivity analysis is carried out to examine the influence of jet variables in effecting the oxygen transfer capabilities of plunging hollow jet aerator. Findings: The overall comparison of kernels yielded good estimation performance of Radial Basis Function kernel (RBF) and Pearson VII Function kernel (PUK) using the SVR technique which is followed by nonlinear regression, and other kernel function based regression models. Research limitations/implications: The results of the study pertaining to the performance of kernels are based on the current experimental conditions and the estimation potential of the regression models may fluctuate beyond the selection of current data range due to datadependant learning of the soft computing models. Practical implications: Volumetric oxygen transfer coefficient of plunging hollow jets can be predicted precisely using SVR model by employing RBF as kernel function as compared to empirical correlation and other kernel function based regression models. Originality/value: The comparative analysis of kernel functions is conducted in this study. In previous studies, the predictive modelling approaches are implemented in simulating the aeration properties of cylindrical solid jets only, while this paper simulates the volumetric oxygen transfer coefficient of diverging hollow jets with the jet variables by utilizing polynomial, normalized polynomial, PUK, and RBF kernels in SVR and GPR.

4

One-match-ahead forecasting in two-team sports with stacked Bayesian regressions

Lam M. W. Y.

Journal of Artificial Intelligence and Soft Computing Research

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2018

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Vol. 8, No. 3

159--172

EN

There is a growing interest in applying machine learning algorithms to real-world examples by explicitly deriving models based on probabilistic reasoning. Sports analytics, being favoured mostly by the statistics community and less discussed in the machine learning community, becomes our focus in this paper. Specifically, we model two-team sports for the sake of one-match-ahead forecasting. We present a pioneering modeling approach based on stacked Bayesian regressions, in a way that winning probability can be calculated analytically. Benefiting from regression flexibility and high standard of performance, Sparse Spectrum Gaussian Process Regression (SSGPR) – an improved algorithm for the standard Gaussian Process Regression (GPR), was used to solve Bayesian regression tasks, resulting in a novel predictive model called TLGProb. For evaluation, TLGProb was applied to a popular sports event – National Basketball Association (NBA). Finally, 85.28% of the matches in NBA 2014/2015 regular season were correctly predicted by TLGProb, surpassing the existing predictive models for NBA.

5

Bayesian regression approaches on example of concrete fatigue failure prediction

Słoński M.

Computer Assisted Mechanics and Engineering Sciences

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2006

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Vol. 13, No. 4

655-668

EN

The focus of this paper is the application of two nonlinear regression models in the context of Bayesian inference to the problem of failure prediction of concrete specimen under repeated loads based on experimental data. These two models are compared with an empirical formulae. Results on testing data show that both models give better point predictions than empirical formulae. Moreover, Bayesian regression approach makes it possible to calculate prediction intervals (error bars) describing the reliability of the models predictions.