A Study on the Parameter Estimation of Harmonic Equivalent Model Using the RANSAC and Recursive Least Square Algorithms

Park, Jong-Il; Park, Chang-Hyun

doi:10.5370/kiee.2020.70.2.269

Cited by 2 publications

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“…The ultra-precision measurement of displacement is the foundation for the rapid development of modern ultra-precision machining, integrated circuits, precision scientific instruments and other fields. The ultra-high line density grating and grating interferometer are key components for precise displacement measurement and control [1][2][3][4][5]. Increasing the grating line density can effectively reduce the raw signal of displacement measurement and improve the displacement measurement resolution [2].…”

Section: Introductionmentioning

confidence: 99%

“…In cases (1) and ( 2), the traditional method of discriminating coarse errors is not applicable to the Heydemann correction process of grating interferometer non-linear errors where the rejection of outliers has some influence on the fitting effect. In recent years, also with the rapid development of integrated circuits, machine learning with different optimization strategies to achieve fast traversal and analysis of each sample point has become increasingly popular, and the random sample consensus (RANSAC) is a machine learning optimization method that analyses the availability of the grating interferometer acquisition signal elements by iterative traversal, guided by the optimality of the ellipse fitting results [5,[29][30][31].…”

Section: Introductionmentioning

confidence: 99%

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Study of interferometric signal correction methods in ultra-precision displacement measurement

Xie,

Jin,

Lei

et al. 2023

Meas. Sci. Technol.

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The measurement of critical dimensions in the field of integrated circuits has moved from 7 nm to 5 nm. The existing chromium atomic lithography grating has a pitch period of 4700 l mm−1 and uniformity of picometer, and the interferometric signal period based on the above grating is as small as 106.4 nm, which brings new problems and challenges to the accurate processing of the signal. This paper investigates the error characteristics of ultra-high precision grating interferometric signals, establishes a Heydemann correction mathematical model for high inscribed line density grating interferometric signals, corrects the grating interferometer signals based on the random sample consensus (RANSAC), and verifies the effectiveness of the algorithm through simulation. By comparing the repeatability and linearity of the original algorithm and the self-traceable grating interferometric displacement measurement data processed by RANSAC, the conclusion that the standard deviation of the self-traceable grating interferometer repeat measurement after RANSAC is 1.60 nm in a 10 000 nm travel is obtained, and the purpose of improving the stability and uniformity of the signal solution with the algorithm of this paper is achieved, which is important for the study of laser interferometer and grating interferometer The results show that the stability and uniformity of the signal solution can be improved by the algorithm of this paper, which is of great significance for the study of the displacement solution of laser and grating interferometers.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Study of interferometric signal correction methods in ultra-precision displacement measurement

Xie,

Jin,

Lei

et al. 2023

Meas. Sci. Technol.

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Harmonic Contribution Assessment Based on the Random Sample Consensus and Recursive Least Square Methods

Park

2022

Energies

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This paper deals with a method of quantifying the harmonic contribution of each harmonic source to system voltage distortion. Assessing the harmonic contribution of individual harmonic sources is essential for mitigating and managing system harmonic levels. Harmonic contributions can be evaluated using the principle of voltage superposition with equivalent voltage models for harmonic sources. In general, the parameters of equivalent voltage models are estimated numerically because it is difficult to measure them directly. In this paper, we present an effective method for estimating equivalent model parameters based on the random sample consensus (RANSAC) and recursive least square (RLS) with a variable forgetting factor. The procedure for quantifying harmonic contributions using equivalent models is also introduced. Additionally, we propose a network diagram of harmonic contributions that makes it easy to understand the harmonic distortion contributions of all harmonic sources.

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A Study on the Parameter Estimation of Harmonic Equivalent Model Using the RANSAC and Recursive Least Square Algorithms

Cited by 2 publications

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Study of interferometric signal correction methods in ultra-precision displacement measurement

Study of interferometric signal correction methods in ultra-precision displacement measurement

Harmonic Contribution Assessment Based on the Random Sample Consensus and Recursive Least Square Methods

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