polynomial fitting
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2022 ◽  
Vol 152 ◽  
pp. 106952
Author(s):  
Zixin Zhao ◽  
Junxiang Li ◽  
Chen Fan ◽  
Yijun Du ◽  
Menghang Zhou ◽  
...  

Author(s):  
Zixin Zhao ◽  
Menghang Zhou ◽  
Yijun Du ◽  
Junxiang Li ◽  
Chen Fan ◽  
...  

Abstract Phase unwrapping plays an important role in optical phase measurements. In particular, phase unwrapping under heavy noise conditions remains an open issue. In this paper, a deep learning-based method is proposed to conduct the phase unwrapping task by combining Zernike polynomial fitting and a Swin-Transformer network. In this proposed method, phase unwrapping is regarded as a regression problem, and the Swin-Transformer network is used to map the relationship between the wrapped phase data and the Zernike polynomial coefficients. Because of the self-attention mechanism of the transformer network, the fitting coefficients can be estimated accurately even under extremely harsh noise conditions. Simulation and experimental results are presented to demonstrate the outperformance of the proposed method over the other two polynomial fitting-based methods. This is a promising phase unwrapping method in optical metrology, especially in electronic speckle pattern interferometry.


2022 ◽  
Vol 9 ◽  
Author(s):  
Ming Liu ◽  
Lei Tan ◽  
Shuliang Cao

Pump as Turbine (PAT) is a technically and economically effective technology to utilize small/mini/micro/pico hydropower, especially in rural areas. There are two main subjects that influence the selection and application of PAT. On the one hand, manufacturers of pumps will not provide their characteristics under the turbine mode, which requires performance prediction methods. On the other hand, PAT efficiency is always slightly lower than that of pump, which requires further geometry optimization. This literature review summarized published research studies related to performance prediction and geometry optimization, aimed at guiding for selection and optimization of PAT. Currently, there exist four categories of performance prediction methods, namely, using BEP (Best Efficiency Point), using specific speed, loss modeling, and polynomial fitting. The using BEP and loss modeling methods are based on theoretical analysis, while using specific speed and polynomial fitting methods require statistical fitting. The prediction errors of published methods are within ±10% mostly. For geometry optimization, investigations mainly focus on impeller diameter and blade geometry. The influence of impeller trimming, blade rounding, blade wrap angle, blade profile, blade number, blade trailing edge position, and guide vane number has been studied. Among published methods, the blade rounding and forward-curved impellers are the most effective and feasible techniques.


2022 ◽  
pp. 004051752110687
Author(s):  
Cankun Ming ◽  
Xinfu Chi ◽  
Zhijun Sun ◽  
Yize Sun

The working efficiency and stability of the double hook-based fishing net-weaving machine is mainly determined by the lower hook mechanism. In this work, a new kind of lower hook mechanism, which is driven by four servo motors, is presented, and the electronic cam curve of the lower hook mechanism is introduced. First, cubic B-spline interpolation is used to get the basic motion path of the lower hook plate, and then the piecewise quintic polynomial fitting method is used to fit the motion path. Finally, self-adaptive mutation-based particle swarm optimization is put forward and used to obtain the optimal parameters of the quintic polynomial, which performs better compared with the other two particle swarm optimization algorithms in this study. Experiments suggest that the electronic cam curve generated by the piecewise quintic polynomial fitting has got 55.91% (horizontal motors) and 60.96% (vertical motors) optimization in maximum motor torque compared with curves generated by cubic B-spline interpolations. In addition, the new lower hook mechanism and its moving curve described in this paper improved the theoretical weaving speed of the fishing net-weaving machine, providing a basis for digital improvement of the knotted net-weaving industry.


2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Yi-Yun Tsai ◽  
Yi-Chen Pan ◽  
Jui-Chao Kuo

AbstractA raw electron backscatter diffraction (EBSD) signal can be empirically decomposed into a Kikuchi diffraction pattern and a smooth background. For pattern indexing, the latter is generally undesirable but can reveal topographical, compositional, or diffraction contrast. In this study, we proposed a new background correction method using polynomial fitting (PF) algorithm to obtain clear Kikuchi diffraction patterns for some applications in nonconductive materials due to coating problems, at low accelerated voltage and at rough sample surfaces and for the requirement of high pattern quality in HR-EBSD. To evaluate the quality metrics of the Kikuchi patterns, we initially used three indices, namely, pattern quality, Tenengrad variance, and spatial–spectral entropy-based quality to detect the clarity, contrast, and noise of Kikuchi patterns obtained at 5 and 15 kV. Then, we examined the performance of PF method by comparing it with pattern averaging and Fourier transform-based methods. Finally, this PF background correction is demonstrated to extract the background images from the blurred diffraction patterns of EBSD measurements at low kV accelerating voltage and with coating layer, and to provide clear Kikuchi patterns successfully.


Author(s):  
Jingyi Liu ◽  
Lina Yu ◽  
Min Wu ◽  
Yuerong Tong ◽  
Jian Xu ◽  
...  
Keyword(s):  

Author(s):  
huai fang ◽  
Guobin Chang ◽  
zhi bao ◽  
Kai Chen ◽  
xiannan han

Abstract The attitude algorithm is the most important part of the whole strapdown inertial navigation (SINS) processing. It calculates the attitude of certain parameterization by integrating the gyro outputs or measurements in a specifically tailored way according to the attitude kinematic differential equation. The measurements or some angular velocity models obtained by fitting these measurements are often assumed free of errors in order to assess the numerical errors only. However, the gyro outputs and hence the models from them are by no means free of measurement errors. It is more often than not that the measurement errors dominate the numerical ones in practice. In this study, with coping with the measurement errors as the focus, we aim to improve the angular velocity model which is used as input in an attitude integration algorithm. This is achieved by exploiting the potential of overdetermined least-squares polynomial fitting. In order to avoid reducing the update rate by incorporating more measurements, the moving window trick is employed to re-use measurements in the previous update interval. The conventional attitude algorithm with second-order approximation in solving the differential equation of the equivalent rotation vector is employed as an example; however, the proposed method can be readily applied to other parameterizations such as direction cosine matrix, quaternion or Rodrigues parameters, and other high order approximations in solving the differential equation widely studied recently.


2021 ◽  
Author(s):  
Suraj Raval ◽  
Onder Erin ◽  
Xiaolong Liu ◽  
Lamar O. Mair ◽  
Will Pryor ◽  
...  

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