Geometrical-Analysis-Based Algorithm for Stereo Matching of Single-Lens Binocular and Multi-Ocular Stereovision System

A geometrical analysis based algorithm is proposed to achieve the stereo matching of a single-lens prism based stereovision system. By setting the multi- face prism in frontal position of the static CCD （CM-140MCL） camera, equivalent stereo images with different orientations are captured synchronously by virtual cameras which are defined by two boundary lines： the optical axis and CCD camera field of view boundary. Subsequently, the geometrical relationship between the 2D stereo images and corresponding 3D scene is established by employing two fundamentals： ray sketching in which all the pertinent points, lines, and planes are expressed in the 3D camera coordinates and the rule of refraction. Landing on this relationship, the epipolar geometry is thus obtained by fitting a set of corresponding candidate points and thereafter, stereo matching of the prism based stereovision system is obtained. Moreover, the unique geometrical properties of the imaging system allow the proposed method free from the complicated camera calibration procedures and to be easily generalized from binocular and tri-oeular to multi-ocular stereovision systems. The performance of the algorithm is presented through the experiments on the binocular imaging system and the comparison with a conventional projection method demonstrates the efficient assessment of our novel contributions.

Efficient and accurate worm grinding of spur face gears according to an advanced geometrical analysis and a closed-loop manufacturing process

Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the machining accuracy is usually improved by increasing the number of tool paths with more time cost.Differently,this work proposes a generated method to improve the efficiency by dressing the worm surface with only one path,and a closed-loop manufacturing process is applied to ensure the machining accuracy.According to an advanced geometric analysis,the worm surface is practically approximated as a swept surface generated by a planar curve.Meanwhile,this curve is applied as the profile of a dressing wheel,which is used to dress the worm surface.The practical machining is carried out in a CNC machine tool,which was originally used to grind helical gears.Finally,a closed-loop manufacturing process including machining,measurement,and modification is proposed to compensate the machining errors.The proposed method is validated with simulations and practical experiments.

Geometrically Nonlinear Analysis of Structures Using Various Higher Order Solution Methods: A Comparative Analysis for Large Deformation

The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of structures.The applied methods have a better convergence rate than the quadratic Newton-Raphson method.These six methods do not require higher order derivatives to achieve a higher convergence rate.Six algorithms are developed to use the higher order methods in place of the Newton-Raphson method to solve the nonlinear equilibrium equations in geometrically nonlinear analysis of structures.The higher order methods are applied to both continuum and discrete problems(spherical shell and dome truss).The computational cost and the sensitivity of the higher order solution methods and the Newton-Raphson method with respect to the load increment size are comparatively investigated.The numerical results reveal that the higher order methods require a lower number of iterations that the Newton-Raphson method to converge.It is also shown that these methods are less sensitive to the variation of the load increment size.As it is indicated in numerical results,the average residual reduces in a lower number of iterations by the application of the higher order methods in the nonlinear analysis of structures.

Geometric Analysis of Singularity for Single-Gimbal Control Moment Gyro Systems

This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.

Global Geometric Analysis of Ship Rolling and Capsizing in Random Waves

The nonlinear biased ship rolling motion and capsizing in randoro waves are studied by utilizing a global geometric method. Thompson＇ s α-parameterized family of restoring functions is adopted in the vessel equation of motion for the representation of bias. To take into account the presence of randomness in the excitation and the response, a stochastic Melnikov method is developed and a mean-square criterion is obtained to provide an upper bound on the domain of the potential chaotic rolling motion. This criterion can be used to predict the qualitative nature of the invariant manifolds which represent the boundary botween safe and unsafe initial conditions, and how these depend on system parameters of the specific ship model. Phase space transport theory and lobe dynamics are used to demonstrate how motions starting from initial conditions inside the regions bounded by the intersected manifolds will evolve and how unexpected capsizing can occur.

PERTURBATION ANALYSIS FOR MAGNETO-PLASTIC INSTABILITY OF FERROMAGNETIC BEAM-PLATES WITH GEOMETRIC IMPERFECTION

The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic ?eld. After the distribution of magnetic ?elds related to the de?ected con?guration of plate is imaginably divided into two parts, i.e., one is related to the ?at plate and the other dependent on the perturbation of magnetic ?elds for which the plate con?guration changes from the ?at into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic ?elds in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic ?eld, which leads to some analytical formulae/solutions for the magnetic ?elds and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic ?eld is discussed, and the critical magnetic ?eld is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic ?eld. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an ampli?cation function, is obtained by solving the dynamic equation of de?ection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic ?eld is sensitive to the plastic characteristic, e.g., hardening coe?cient, and the instability mode and de?ection of the plate are dependent on the geometrical imperfection as well.

Geometric Covariance Modeling for Surface Variation of Compliant Parts Based on Hybrid Polynomial Approximation and Spectrum Analysis

Part variation characterization is essential to analyze the variation propagation in flexible assemblies. Aiming at two governing types of surface variation,warping and waviness,a comprehensive approach of geometric covariance modeling based on hybrid polynomial approximation and spectrum analysis is proposed,which can formulate the level and the correlation of surface variations accurately. Firstly,the form error data of compliant part is acquired by CMM. Thereafter,a Fourier-Legendre polynomial decomposition is conducted and the error data are approximated by a Legendre polynomial series. The weighting coefficient of each component is decided by least square method for extracting the warping from the surface variation. Consequently,a geometrical covariance expression for warping deformation is established. Secondly,a Fourier-sinusoidal decomposition is utilized to approximate the waviness from the residual error data. The spectrum is analyzed is to identify the frequency and the amplitude of error data. Thus,a geometrical covariance expression for the waviness is deduced. Thirdly,a comprehensive geometric covariance model for surface variation is developed by the combination the Legendre polynomials with the sinusoidal polynomials. Finally,a group of L-shape sheet metals is measured along a specific contour,and the covariance of the profile errors is modeled by the proposed method. Thereafter,the result is compared with the covariance from two other methods and the real data. The result shows that the proposed covariance model can match the real surface error effectively and represents a tighter approximation error compared with the referred methods.

Quantitative morphometric analysis of a deep-water channel in the Taranaki Basin, New Zealand

The morphological changes of deep-water channels have an important influence on the distributions of channel sand reservoirs,so it is important to explore the morphological change process of deep-water channel for the exploration and development of deep-water oil and gas.Based on a typical sinuous Quaternary channel(Channel I)in the Taranaki Basin,New Zealand,a variety of seismic interpretation techniques were applied to quantitatively characterize the morphological characteristics of the Channel I,and the relationships between the quantitative parameters and the morphological changes of the Channel I,as well as the controlling factors affecting those morphological changes,were discussed.The results are as follows:(1)in the quantitative analysis,six parameters were selected:the channel depth,width,sinuosity,and aspect ratio(width/depth),the channel swing amplitude(λ)and the channel bend frequency(ω);(2)according to the quantitative morphological parameters of the channel(mainly including three parameters such as channel sinuosity,ωandλ),the Channel I was divided into three types:the low-sinuous channel(LSC),the high-sinuous channel(HSC),the moderate-sinuous channel(MSC).U-shaped channel cross-sections developed in the LSC,V-shaped channel cross-sections developed in the HSC,including inclined-V and symmetric-V cross-sections,and dish-shaped channel cross-sections developed in the MSC;(3)the morphological characteristics of the LSC and MSC were related to their widths and depths,while the morphology of the HSC was greatly affected by the channel width,a change in depth did not affect the HSC morphology;(4)the morphological changes of the Channel I were controlled mainly by the slope gradient,the restricted capacity of the channel and the differential in fluid properties.

Quantitative Analysis of Flabellophyton from the Ediacaran Lantian Biota, South China: Application of Geometric Morphometrics in Precambrian Fossil Research

As a more efficient quantitative method for morphological analysis, geometric morphometrics is applied to the flabellate fossils Flabellophyton including Flabellophyton lantianensis and Flabellophyton strigata from Neoproterozoic Ediacaran Lantian biota, South China. Both traditional morphometric analysis （including diverging angle, length, and width distribution） and geometric morphometric analysis [including superposition of normalized area analysis, non-metric multidimensional scaling （n-MDS）, Bray-Curtis similarity cluster analysis （CLUSTER） and analysis of similarities （ANOSIM）[ were performed. The results indicate there are great interspecific morphological differences between F. lantianensis and F. strigata, in addition to some intraspecific variations within each species. Here we preliminarily suggest that the previously defined Flabellophyton should be subdivided into 2 genera at least： one marked by the dark transverse striated structure, and the other without. This recharacterization and reclassification work still needs further careful observation and comprehensive analysis with large number of flabeilate fossils combining morphology, structure, population, and community-ecology study.

Development of analysis model for geometric error in turning processes

A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed. In the first analyzing step, the cutting force and the cutting heat for the cutting conditions were obtained using the AdvantEdge. Also, the deformation of a workpiece was estimated in the second step using the ANSYS. The deformation was analyzed for a 150 mm-long workpiece at three different measuring points, such as 10, 70 and 130 mm from a reference point, and the amounts of the deformation were compared through experiments. /n the results of the comparison and analysis, the values obtained from these comparison and analysis represent similar tendencies. Also, it is verified that their geometric errors increase with the increase in temperature. In addition, regarding the factors that affect the deformation of a workpiecc, it can be seen that the geometric error in the lathe is about 15%, the error caused by the cutting force is about 10%, and the deformation caused by the heat is about 75%.

Sensitivity of optimal double-layer grid designs to geometrical imperfections and geometric nonlinearity conditions in the analysis phase

This study focuses on exploring the effects of geometrical imperfections and different analysis methods on the optimum design of Double-Layer Grids(DLGs),as used in the construction industry.A total of 12 notable metaheuristics are assessed and contrasted,and as a result,the Slime Mold Algorithm is identified as the most effective approach for size optimization of DLGs.To evaluate the influence of geometric imperfections and nonlinearity on the optimal design of real-size DLGs,the optimization process is carried out by considering and disregarding geometric nonlinearity while incorporating three distinct forms of geometrical imperfections,namely local imperfections,global imperfections,and combinations of both.In light of the uncertain nature of geometrical imperfections,probabilistic distributions are used to define these imperfections randomly in direction and magnitude.The results demonstrate that it is necessary to account for these imperfections to obtain an optimal solution.It’s worth noting that structural imperfections can increase the maximum stress ratio by up to 70%.The analysis also reveals that the initial curvature of members has a more significant impact on the optimal design of structures than the nodal installation error,indicating the need for greater attention to local imperfection issues in space structure construction.

Geometrodynamical Analysis to Characterize the Dynamics and Stability of a Molecular System through the Boundary of the Hill’s Region

In this paper we study the dynamics and stability of a two-dimensional model for the vibrations of the LiCN molecule making use of the Riemannian geometry via the Jacobi-Levi-Civita equations applied to the Jacobi metric. The Stability Geometrical Indicator for short times is calculated to locate regular and chaotic trajectories as the relative extrema of this indicator. Only trajectories with initial conditions at the boundary of the Hill’s region are considered to characterize the dynamics of the system. The importance of the curvature of this boundary for the stability of trajectories bouncing on it is also discussed.

Geometric Scaling Analysis of Deep Inelastic Scattering Data Including Heavy Quarks

An analytic massive total cross section of photon proton scattering is derived, which has geometric scaling. A geometric scaling is used to perform a global analysis of the deep inelastic scattering data on inclusive structure function F2 measured in lepton-hadron scattering experiments at small values of Bjorken x. It is shown that the descriptions of the inclusive structure function F2 and longitudinal structure function FL are improved with the massive analytic structure function, which may imply the gluon saturation effect dominating the parton evolution process at HERA. The inclusion of the heavy quarks prevent the divergence of the lepton-hadron cross section, which plays a significant role in the description of the photoproduction region.

Complex geometric modeling and tooth contact analysis of a helical face gear pair with arc-tooth

A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.

Assessing Brain Pathophysiology through Non-Linear Analysis of MEG in Ιdiopathic Generalized Epilepsy Cases

Background: Non-linear signal analysis has proven to be a technique that is capable of revealing qualitative and quan- titative differentiations between different dynamical systems (biological or otherwise). In the present work it has been demonstrated that this capability reveals quantitative differences in the Magnetoencephalograms (MEG) received from patients with Idiopathic Generalized Epilepsy (IGE) and from healthy volunteers. Method: We present MEG record- ings of 10 epileptic patients with IGE and the corresponding ones from 10 healthy volunteers. A 122-channel SQUID biomagnetometer in an electromagnetically shielded room was used to record the MEG signals and the Grassber- ger-Procaccia method for the estimation of the correlation dimension was applied in the phase space reconstruction of the recorded signal from each patient. Results: The aforementioned analysis demonstrates the existence of spatially diffused low dimensionality in the MEG signals of patients with IGE. Conclusion: The obtained results provide support for the hypothesis that low dimensionality in MEG signals is linked to functional brain pathogeny.

ANALYSIS OF CRITERIA PREDICTING THE TENDENCY OF PILOT INDUCED OSCILLATION FOR LINEAR NON-LINEAR SYSTEM

Some problems encountered in applying Smith's technique to predict the PIO tendency for non-linear pilot-vehicle loop, are thoroughly analyzed. Subsequently, modified PIO predictable criteria are developed, in addition, to make also a certain improvement on Smith's PIO definition and PIO types. These modified criteria are applied to predict PIO tendency of various different configurations on the variable stability aircraft NT-33 in case of supposed non-linearity, and predicted results are compared with the flight tests and analytical results in the case of linear hypothesis given in Ref. (4)

ON USING NON-LINEAR CANONICAL CORRELATION ANALYSIS FOR VOICE CONVERSION BASED ON GAUSSIAN MIXTURE MODEL

Voice conversion algorithm aims to provide high level of similarity to the target voice with an acceptable level of quality.The main object of this paper was to build a nonlinear relationship between the parameters for the acoustical features of source and target speaker using Non-Linear Canonical Correlation Analysis(NLCCA) based on jointed Gaussian mixture model.Speaker indi-viduality transformation was achieved mainly by altering vocal tract characteristics represented by Line Spectral Frequencies(LSF).To obtain the transformed speech which sounded more like the target voices,prosody modification is involved through residual prediction.Both objective and subjective evaluations were conducted.The experimental results demonstrated that our proposed algorithm was effective and outperformed the conventional conversion method utilized by the Minimum Mean Square Error(MMSE) estimation.

Analysis of the Influence of Parafunctional Loads on the Bone-Prosthesis System: A Non-Linear Finite Element Analysis

The present study evaluates the effects of occlusal loading on an implant-supported dental implant with external hexagon dental implant-abutment systems, using the finite element method analysis. Tensile analyses were performed to simulate different axial and obliquous masticatory loads. The influence of the variations in the contouring conditions of the interfaces was analyzed to weigh the osseointegration with linear and non-linear cases, by means of a parametric design. The geometry selected to place the prostheses was a jaw section, considering the properties of the set of cortical and trabecular bones. The results show that for non-linear contour conditions, the stress presents smaller value distributions and signals a different place in the screw-implant interface as the factor of the greater weight in this study. The location indicated that von Mises stress concentrations are not exclusive to the contact regions studied, moving to an area that is not in direct contact with the non-linear contact interfaces. In addition, the direction of load with an angle of 15 degrees presented the highest values of von Mises stress.

Computational Geometric Analysis for <i>C. elegans</i>Trajectories on Thermal and Salinity Gradient

Elegans are one of the best model organisms in neural researches, and tropism movement is a typical learning and memorizing activity. Based on one imaging technique called Fast Track-Capturing Microscope (FTCM), we investigated the movement regulation. Two movement patterns are extracted from various trajectories through analysis on turning angle. Then we applied this classification on trajectory regulation on the compound gradient field, and theoretical results corresponded with experiments well, which can initially verify the conclusion. Our breakthrough is performed computational geometric analysis on trajectories. Several independent features were combined to describe movement properties by principal composition analysis (PCA) and support vector machine (SVM). After normalizing all data sets, no-supervising machine learning was processed along with some training under certain supervision. The final classification results performed perfectly, which indicates the further application of such computational analysis in biology researches combining with machine learning.

Relationships between femoral strength evaluated by nonlinear finite element analysis and BMD,material distribution and geometric morphology

Precisely quantifying the strength of the proximal femur and accurately assessing hip fracture risk would enable those at high risk to be identified so that preventive interventions could be taken.Development of better measures of femoral strength using the clinically