arXiv subjects

Zezhong Wang

Publications and source records attributed to Zezhong Wang.

41 records · Page 3Linked to original sources

arXiv2021

A plane wave method based on approximate wave directions for two dimensional Helmholtz equations with large wave numbers

In this paper we present and analyse a high accuracy method for computing wave directions defined in the geometrical optics ansatz of Helmholtz equation with variable wave number. Then we define an "adaptive" plane wave space with small dimensions, in which each plane wave basis function is determined by such an approximate wave direction. We establish a best $L^2$ approximation of the plane wave space for the analytic solutions of homogeneous Helmholtz equations with large wave numbers and report some numerical results to illustrate the efficiency of the proposed method.

math.NA↗

arXiv2021

A Change-Point Based Control Chart for Detecting Sparse Changes in High-Dimensional Heteroscedastic Data

Because of the curse-of-dimensionality, high-dimensional processes present challenges to traditional multivariate statistical process monitoring (SPM) techniques. In addition, the unknown underlying distribution and complicated dependency among variables such as heteroscedasticity increase uncertainty of estimated parameters, and decrease the effectiveness of control charts. In addition, the requirement of sufficient reference samples limits the application of traditional charts in high dimension low sample size scenarios (small n, large p). More difficulties appear in detecting and diagnosing abnormal behaviors that are caused by a small set of variables, i.e., sparse changes. In this article, we propose a changepoint based control chart to detect sparse shifts in the mean vector of high-dimensional heteroscedastic processes. Our proposed method can start monitoring when the number of observations is a lot smaller than the dimensionality. The simulation results show its robustness to nonnormality and heteroscedasticity. A real data example is used to illustrate the effectiveness of the proposed control chart in high-dimensional applications. Supplementary material and code are provided online.

stat.ME↗

arXiv2019

A Review of Dispersion Control Charts for Multivariate Individual Observations

A multivariate control chart is designed to monitor process parameters of multiple correlated quality characteristics. Often data on multivariate processes are collected as individual observations, i.e. as vectors one at the time. Various control charts have been proposed in the literature to monitor the covariance matrix of a process when individual observations are collected. In this study, we review this literature; we find 30 relevant articles from the period 1987-2019. We group the articles into five categories. We observe that less research has been done on CUSUM, high-dimensional and non-parametric type control charts for monitoring the process covariance matrix. We describe each proposed method, state their advantages, and limitations. Finally, we give suggestions for future research.

stat.ME↗

arXiv2018

Shock Wave in Leader Discharge Observed Using Mach-Zehnder Interferometry

A leader is an electric discharge mechanism in long-air-gap discharges. In this work, we report the shock wave phenomenon in an air-gap leader discharge observed using a Mach-Zehnder interferometer with a time resolution of several microseconds. The continuous temporal evolution of the shock wave and the plasma channel was recorded and reproduced with a thermo-hydrodynamic model based on the measured current. The wave propagated at nearly the speed of sound, and the simulation results for the shock wave front positions and the plasma channel radius showed good consistency with the experimental measurements. Detailed thermal parameters obtained through the simulation showed that continuous energy injection by the current results in a temporary over-pressure process in the plasma channel and produces the shock wave.

physics.app-ph↗

arXiv2018

The dynamic expansion of positive leaders observed using Mach-Zehnder interferometry in a 1-m air gap

The leader plays an important role in long-air-gap discharges. In this paper, Mach-Zehnder interferometry and a high-speed video camera were used to observe the dynamic expansion process of positive leaders near the anode in a 1 m air gap. The leader diameters under lightning and switching impulse are obtained through the analysis of interference fringes. The influences of the applied voltage, including the amplitude and the front time, as well as the electrode sizes on leader expansion are obtained and analysed. For a 0.5-cm-diameter cone electrode, when the applied voltage amplitudes are 330-419 kV, the diameters of the leaders are 1.5-2.5 mm at time scales of less than 195 μs, and the diameters increase as the voltage rises. The diameters of the leaders are larger and the expansion rates are higher for shorter front times. The average expansion rates are 72.30-9.54, 28.09-5.05, 14.38-3.02 and 5.73-1.44 m/s for front times of 1.2, 40, 100 and 250 μs for a 0.5-cm-diameter cone electrode. A larger electrode size leads to a wider diameter. A numerical model was employed to analyse the expansion of the leaders, and the calculated results are in good agreement with the experimental data. Based on the model, the mechanism underlying the leader expansion is discussed in detail.

physics.app-ph↗