Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate generalized Poisson regression

Poisson regression is used to model the data with the response variable in the form of count data. This modeling must meet the equidispersion assumption. That is, the average value is the same as the variance. However, this assumption is often violated. Violation of the equidispersion assumption in Poisson regression modeling will result in invalid conclusions. These violations are an overdispersion and an underdispersion of the response variable. Generalized Poisson Regression (GPR) is an alternative if there is a violation of the equidispersion assumption. If there are two correlated response variables, modeling will use the Bivariate Generalized Poisson Regression (BGPR). However, in the panel data with the observation unit in the form of an area, BGPR is not quite right because there is spatial and temporal heterogeneity in the data. Geographically and Temporally Weighted Bivariate Generalized Poisson Regression (GTWBGPR) is a method for modeling spatial and temporal heterogeneity data. GTWBGPR is a development of GWBGPR. In GTWBGPR, besides accommodating spatial effects, it also accommodates temporal effects. This research will discuss the parameter estimation and test statistics for the GTWBGPR model. Parameter estimation uses Maximum Likelihood Estimation (MLE), but the result is not closed-form, so it is solved by numerical iteration. The numerical iteration used is Newton-Raphson. The test statistic for simultaneous testing uses the Maximum Likelihood Ratio Test (MLRT). With large samples, then this test statistic has a chi-square distribution approximation. So the test statistic for the partial test uses the Z test statistic.

ELECTRICAL POTENTIAL BETWEEN NON-PARALLEL FLAT ELECTRODES – SIMULATION OF A CELL USED WITH TOMATO

The equipotential lines of the field generated by the cell used in dielectric measurements of whole fruit tomato are plotted. This cell consists of two inclined electrodes, at inverse potentials, and is an adaptation made in the Dielectric Laboratory of the cell used by Varlan-Sansen. To obtain the graphs, the Laplace equation was solved by finite differences and a program in Fortran language was written, which performs the calculations by numerical iteration. The field generated by the cell at different electrode separation distances was analyzed.

Kinematic Analysis and Performance Test of a 6-DOF Parallel Platform with Dense Ball Shafting as a Revolute Joint

To meet the special requirements of the third mirror adjustment system for an optical telescope, a 6-P-RR-R-RR parallel platform using offset RR-joints is designed with high precision, a large load-to-size ratio and high stiffness. In order to improve the adjustment accuracy and the stiffness of the whole mechanism, each rotating joint in the subchain is designed as a zero-gap bead shaft system. When compared with a traditional Hooke joint, the offset RR joint has certain characteristics, including large carrying capacity and easy processing and adjustment, that effectively reduce the risk of interference with the joint during rotation and increase the working space of the entire machine. Because of the additional variables introduced by the offset joints, the kinematics problem becomes much more complicated. Regarding the P-RRRRR series subchain, the kinematics model is established using the Denavit–Hartenberg parameter method and then solved by the numerical iteration method. The stiffness of the parallel platform is analyzed and tested, including static and fundamental frequency. Motion performance testing of the parallel platform is performed.

Flow Continuity of Isothermal Elastohydrodynamic Point-Contact Lubrication under Different Numerical Iteration Configurations

Elastohydrodynamic Lubrication (EHL) in point contacts can be numerically solved with various iteration methods, but so far the flow continuity of such solutions has not been explicitly verified. A series of closed regions with the same inlet side boundary is defined and two treatments to total all flows related to the other boundaries of the closed regions are defined to enable flow continuity verifications. The multigrid method and the traditional single mesh method with different relaxation configurations are utilized to solve different cases to evaluate computation efficiencies. For the multigrid method, the combination of a pointwise solver together with hybrid relaxation factors is identified to perform better than other combinations. The single mesh method has inferior degrees of flow continuity than the multigrid method and needs much smaller error control values of pressure to achieve a decent level of flow continuity. Because flow continuity has a physical meaning, its verifications should be routinely included in any self-validation process for any EHL results. Effects of control errors of pressure, mesh sizes, differential schemes and operating conditions on flow continuities are studied. Then, trends of film thickness with respect to speed are briefly discussed with meshes up to 4097 by 4097.

Evolutionary numerical approach for solving nonlinear singular periodic boundary value problems

In this approximation study, a nonlinear singular periodic model in nuclear physics is solved by using the Hermite wavelets (HW) technique coupled with a numerical iteration technique such as the Newton Raphson (NR) one for solving the resulting nonlinear system. The stimulation of offering this numerical work comes from the aim of introducing a consistent framework that has as effective structures as Hermite wavelets. Two numerical examples of the singular periodic model in nuclear physics have been investigated to observe the robustness, proficiency, and stability of the designed scheme. The proposed outcomes of the HW technique are compared with available numerical solutions that established fitness of the designed procedure through performance evaluated on a multiple execution.

Distributed Analytical Formation Control and Cooperative Guidance for Gliding Vehicles

This paper addresses the analytical formation control and cooperative guidance problem for multiple hypersonic gliding vehicles under distributed communication. The gliding flight of the hypersonic gliding vehicle is divided into formation control phase and time coordination phase. In formation control phase, based on the idea of path tracking, the formation controller is designed using the second-order consensus protocol with normal positions as the coordination variables. In time coordination phase, based on the quasi-equilibrium gliding condition and the assumption of uniform deceleration motion, the analytical expression of time to go is derived. Then, the cooperative guidance method is developed using the first-order consensus protocol with time to go as the coordination variable. The proposed method takes full consideration of the characteristics of hypersonic gliding vehicle, such as complex nonlinear dynamics, no thrust, and quasi-equilibrium gliding condition, and no online numerical iteration is needed, which is well applicable for hypersonic gliding vehicles. Simulation results demonstrate the effectiveness of the formation control and cooperative guidance method.

Algorithm Used to Detect Weak Signals Covered by Noise in PIND

Detection of the loose particles is urgently required in the spacecraft production processes. PIND (particle impact noise detection) is the most commonly used method for the detection of loose particles in the aerospace electronic components. However, when the mass of loose particles is smaller than 0.01 mg, the weak signals are difficult to be detected accurately. In this paper, the aperiodic stochastic resonance (ASR) is firstly used to detect weak signals of loose particles. The loose particle signal is simulated by the oscillation attenuation signal. The influences of structure parameters on the potential height and detection performance of ASR are studied by a numerical iteration method. The cross-correlation coefficient C1 between input and output is chosen as a criterion for whether there is an existing a particle or not. Through normalization, the loose particle signal-labeled high frequency of 135 kHz is converted into the low-frequency band, which can be detected by the ASR method. According to the algorithm, weak signals covered by noise could be detected. The experimental results show that the detection accuracy is 66.7%. This algorithm improves the detection range of weak loose particle signals effectively.

Numerical iteration for nonlinear oscillators by Elzaki transform

Iteration methods are widely used in numerical simulation. This paper suggests the Elzaki transform in the variational iteration method for simple identification of the Lagrange multiplier. The Elzaki transform is a modification of the Laplace transform, and it is extremely useful for treating with nonlinear oscillators as illustrated in this paper, a single iteration leads to a high accuracy of the solution.

An effective approach for robust design optimization of wind turbine airfoils with random aerodynamic variables

The robust design optimization of an airfoil needs to continuously realize the probability-based aerodynamic simulation for various combinations of geometry and wind climate parameters. The simulation time is lengthy when a full aerodynamic model is embedded for the numerical iteration. To this end, a second-order polynomial-based response surface model is first presented to relate the airfoil performance indicator with geometry and random aerodynamic variables. This allows to quickly evaluate the response moments and optimization constraints. Then, the robust design optimization is formulated to simultaneously maximize the mean aerodynamic performance and minimize the variance of design results due to the variation of geometry and aerodynamic parameters. The robust design optimization based on the NACA63418 and the DU93-W-210 airfoils with random Mach and Reynolds numbers is presented to demonstrate potential applications of this proposed model. Results have shown that the mean-value aerodynamic indicator is generally improved, whereas the variance is minimized to archive the robust design objective. The proposed approach is simple and accurate, suggesting an attractive tool for robust design optimization of airfoils with random aerodynamic variables.

Analysis of a Vibrating Motor Considering Electrical, Magnetic, and Mechanical Coupling Effect

A vibrating motor is a multi-physics product in which there is coupling between electrical, magnetic, and mechanical domains. To obtain a more accurate analysis, nonlinear parameters, such as inductance, speedance, and force factor, are considered as functions of current and displacement based on the finite element method. By solving a voltage equation using a numerical iteration method, current and displacement at each frequency of the vibrating motor can be calculated. The validity of the analysis method was demonstrated by comparing the results of the experiment with those of the simulation and they were found to be similar.