Abstract
A diagnostic system was developed for spectrally resolved, three-dimensional tomographic reconstruction of Hall thruster plasmas, and local intensity profiles of Xe I and Xe II emissions ...were reconstructed. In this diagnostic system, 28 virtual cameras were generated using a single, fixed charge-coupled device camera by rotating the Hall thruster to form a sufficient number of lines of sight. The Phillips–Tikhonov regularization algorithm was used to reconstruct local emission profiles from the line-integrated emission signals. The reconstruction performance was evaluated using both azimuthally symmetric and asymmetric synthetic phantom images including 5% Gaussian white noise, which resulted in a root-mean-square error of the reconstruction within an order of 10
−3
even for a 1% difference in the azimuthal intensity distribution. Using the developed system, three-dimensional local profiles of Xe II emission (541.9 nm) from radiative decay of the excited state 5p
4
(
3
P
2
)6p
2
3°
5/2
and Xe I emission (881.9 nm) from 5p
5
(
2
P°
3/2
)6p
2
5/2
3
were obtained, and two different shapes were found depending on the wavelength and the distance from the thruster exit plane. In particular, a stretched central jet structure was distinctively observed in the Xe II emission profile beyond 10 mm from the thruster exit, while gradual broadening was found in the Xe I emission. Approximately 10% azimuthal nonuniformities were observed in the local Xe I and Xe II intensity profiles in the near-plume region (<10 mm), which could not be quantitatively distinguished by analysis of the frontal photographic image. Three-dimensional Xe I and Xe II intensity profiles were also obtained in the plume region, and the differences in the structures of both emissions were visually confirmed.
The capacitance of capacitive energy storage devices cannot be directly measured, but can be estimated from the applied input and measured output signals expressed in the time or frequency domains. ...Here the time-domain voltage–charge relationship of non-ideal electrochemical capacitors is treated as an ill-conditioned convolution integral equation where the unknown capacitance kernel function is to be found. This comes from assuming a priori that in the frequency domain the charge is equal to the product of capacitance by voltage, which is in line with the definition of electrical impedance. The computation of a stable solution to this problem particularly when dealing with experimental data is highly sensitive to noise as it may lead to an oscillating result even in the presence of small errors in the measurements. In this work, the problem is treated using Tikhonov’s regularization method, where a degree of damping is added to each singular value decomposition (SVD) component of the solution, thus effectively filtering out the components corresponding to the small singular values. The regularized time-domain capacitance of a commercial electric double-layer capacitor is found to be in good agreement with the frequency-to-time transformed capacitance obtained from impedance spectroscopy.
•Time-domain charge in EDLC is treated as convolution of capacitance by voltage.•Use of Tikhonov regularization for extraction of capacitance function.•Computed time-domain capacitance verifies frequency-to-time frequency-domain capacitance.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•A novel discrete GM(2,1) model with a polynomial term is proposed.•The generalization and adaptability of the proposed model were validated from the theoretical and practical perspectives.•The ...newly-designed model is applied to predict per capita living electricity consumption.
The forecast of electrical energy demand has played an increasingly relevant role in sustainable electrical power system. This paper develops a new method for forecasting China's per capita living electricity consumption by grey modelling technique. Considering the multiple and mixed change patterns, a novel discrete grey model with polynomial term (abbreviated as DGM(2,1,kn)) is proposed in this study. Firstly, the polynomial term is introduced into the discrete DGM(2,1) model. Secondly, the Tikhonov regularization method is employed to solve the overfitting problem. Lastly, two published cases and China's per capita living electricity consumption are used to validate the generalization and adaptability of the newly-designed model. The numerical results of such experiments show that the proposed model outperforms other competitive models in terms of accuracy level. Therefore, the projections of China's per capita living electricity consumption in 2020 and 2025 have been made for providing a solid reference for the formulation of electrical power strategies.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•Two types of inverse problems for diffusion equations involving Caputo fractional derivatives in time and fractional Sturm-Liouville operator for space are given.•Two types of inverse problems are ...proved to be ill-posed in the sense of Hadamard whenever an additional condition at a final time is given.•A new fractional Tikhonov regularization method is used for the reconstruction of the stable solutions.•An error estimates between the exact and it regularize solutions are obtained.
In this research, we deal with two types of inverse problems for diffusion equations involving Caputo fractional derivatives in time and fractional Sturm-Liouville operator for space. The first one is to identify the source term and the second one is to identify the initial value along with the solution in both cases. These inverse problems are proved to be ill-posed in the sense of Hadamard whenever an additional condition at the final time is given. A new fractional Tikhonov regularization method is used for the reconstruction of the stable solutions. Under the a-priori and the a-posteriori parameter choice rules, the error estimates between the exact and its regularized solutions are obtained. To illustrate the validity of our study, we give numerical examples. A final note is utilized in the ultimate section.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In a recent paper of Zhang et al. (2016) a variation of the Tikhonov regularization method for calculating the distribution of relaxation times (DRT) in relation to analysis of the electrochemical ...impedance spectroscopy data has been proposed. The novelty of the proposed method is that it is free from the regularization parameter, the adjusting of which usually causes the main issue when applying the Tikhonov regularization method. In the present paper, we investigate by means of numerical experiments the frequency resolution of the method by Zhang et al. and its robustness to resist noise embedded in the impedance spectra. In doing so, we also consider how changing certain matrices used in the method affects the results. In addition, the DRT function calculation for a real electrochemical object by means of this new approach is shown.
•The ability of the new method to resolve overlapping relaxation processes is studied.•The results depend on intrinsic parameters of the method implementation.•The method potentially has a higher robustness to resist noise in EIS.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
This note is concerned with a computational method for an inverse problem for Helmholtz equation. It seeks to recover a subsurface material property based on data collected at the boundary. The major ...improvement in this method is that it does not require the linearization of the working equations. The method is quite simple and requires only one set of data to obtain a good approximation of the unknown material property. Additional set of data can improve the quality of the recovered function. A number of numerical examples, both one-D and 2-D, are used to study the applicability of the method in the presence of noise
•The algorithm requires no linearization.•The method works for real and complex Helmholtz problem in various domains.•The method requires fewer sets of data compared to previous methods.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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