Stochastic Properties of Confidence Ellipsoids after Least Squares Adjustment, Derived from GUM Analysis and Monte Carlo Simulations

In this paper stochastic properties are discussed for the final results of the application of an innovative approach for uncertainty assessment for network computations, which can be characterized as two-step approach: As the first step, raw measuring data and all possible influencing factors were analyzed, applying uncertainty modeling in accordance with GUM (Guide to the Expression of Uncertainty in Measurement). As the second step, Monte Carlo (MC) simulations were set up for the complete processing chain, i.e., for simulating all input data and performing adjustment computations. The input datasets were generated by pseudo random numbers and pre-set probability distribution functions were considered for all these variables. The main extensions here are related to an analysis of the stochastic properties of the final results, which are point clouds for station coordinates. According to Cramer’s central limit theorem and Hagen’s elementary error theory, there are some justifications for why these coordinate variations follow a normal distribution. The applied statistical tests on the normal distribution confirmed this assumption. This result allows us to derive confidence ellipsoids out of these point clouds and to continue with our quality assessment and more detailed analysis of the results, similar to the procedures well-known in classical network theory. This approach and the check on normal distribution is applied to the local tie network of Metsähovi, Finland, where terrestrial geodetic observations are combined with Global Navigation Satellite System (GNSS) data

Designing nanomaterials with desired mechanical properties by constraining the evolution of their grain shapes

Grain shapes are acknowledged to impact nanomaterials' overall properties. Research works on this issue include grain-elongation and grain-strain measurements and their impacts on nanomaterials' mechanical properties. This paper proposes a stochastic model for grain strain undergoing severe plastic deformation. Most models deal with equivalent radii assuming that nanomaterials' grains are spherical. These models neglect true grain shapes. This paper also proposes a theoretical approach of extending existing models by considering grain shape distribution during stochastic design and modelling of nanomaterials' constituent structures and mechanical properties. This is achieved by introducing grain 'form'. Example 'forms' for 2-D and 3-D grains are proposed. From the definitions of form, strain and Hall-Petch-Relationship to Reversed-Hall-Petch-Relationship, data obtained for nanomaterials' grain size and conventional materials' properties are sufficient for analysis. Proposed extended models are solved simultaneously and tested with grain growth data. It is shown that the nature of form evolution depends on form choice and dimensional space. Long-run results reveal that grain boundary migration process causes grains to become spherical, grain rotation coalescence makes them deviate away from becoming spherical and they initially deviate away from becoming spherical before converging into spherical ones due to the TOTAL process. Percentage deviations from spherical grains depend on dimensional space and form: 0% minimum and 100% maximum deviations were observed. It is shown that the plots for grain shape functions lie above the spherical (control) value of 1 in 2-D grains for all considered grain growth mechanisms. Some plots lie above the spherical value, and others approach the spherical value before deviating below it when dealing with 3-D grains. The physical interpretations of these variations are explained from elementary principles about the different grain growth mechanisms. It is observed that materials whose grains deviate further away from the spherical ones have more enhanced properties, while materials with spherical grains have lesser properties. It is observed that there exist critical states beyond which Hall-Petch Relationship changes to Reversed Hall-Petch Relationship. It can be concluded that if grain shapes in nanomaterials are constrained in the way they evolve, then nanomaterials with desired properties can be designed

Analysis of characteristics of random microstructures of nanomaterials

Predicting and manipulating materials macroscopic properties from the knowledge of their microstructure characteristics are attracting significant attention in the field of Materials Science and Engineering. Nowadays, Nanoscience and Nanotechnology are engaged in these studies. Nanomaterials constituents, called herein unambiguously microstructures, have inherently random features/characteristics. In the research reported in this thesis the tools of stochastic processes and stochastic differential equations theory have been used as they offer a sound approach to understanding and analysing microstructures characteristics. This research adopts the approach of first delineating the necessary mathematical formulations, followed by their applications. Substantial number of atoms at nanomaterial Grain Boundaries, GBs, lowers the material thermal stability leading to grain growth. The growth of individual grain size, d, in a nanomaterial is apprehended to be jointly caused by Grain Boundary Migration, GBM, and Grain Rotation- Coalescence, GRC, mechanisms. A model is established that includes the previously ignored GRC in the expression for increment of d and, further, considering the fact that the energy required to activate GBM increases during grain growth. The stochastic counterpart of the expression is obtained by adding two fluctuation terms; to account for the random fluctuations in d caused by GBM and GRC. Results show that nanomaterials low stabilities are also due to their grains’ high rotational mobilities at low grain size dispersion, CV(d). Using information about microstructure size evolution, its probability density function, pdf, is determined using the generalised Fokker-Planck-Kolmogorov equation. Results demonstrate that the type of scaling state pdf depends on the nature of the fluctuation terms. Grain growth parameters are calibrated in such a way that the pdf evolves lognormally throughout. Microstructure-property dependence has for long been given by the Hall-Petch to Reverse Hall- Petch relationship, HP-RHPR, (a relationship between mechanical property and mean grain size, E(d), only). A modified model for this dependence is established using complete information about microstructure size distribution. Results suggest that both E(d) and CV(d) are central in designing materials with required properties. Reasons for conventional, homologous and anomalous temperature dependences of yield stress are revealed. Thus, implementing desired stochastic “properties” of microstructures entails designing required materials mechanical properties

Stochastic Effect of Grain Elongation on Nanocrystalline Materials Strain and Strain Rate Produced by Accumulative Roll-Bonding and Equal Channel Angular Pressing

Severe plastic deformation techniques are acknowledged to produce elongated grains during fabrication of nanostructured materials. Previous models relating grain size to mechanical properties considered only equivalent radius, thus ignoring other approaches of measuring grain sizes such as semiminor axis, semimajor axis, and major axis radii that determine true grain shape. In this paper, stochastic models of nanomaterials mechanical properties that include the ignored parameters have been proposed. The proposed models are tested with data from nanocrystalline aluminum samples. The following facts were experimentally observed and also revealed by the models. Grain elongates to a maximum value and then decreases with further grain refinement due to grain breakages. Materials yield stress increases with elongation to a maximum and then decreases continuously. The varying approaches of measuring grain radius reveal a common trend of Hall-Petch and Reverse Hall-Petch Relationship but with different critical grain sizes. Materials with high curvature grains have more enhanced yield stress. Reducing strain rates leads to materials with more enhanced yield stress, with critical strain rates values beyond which further reductions do not lead to yield stress enhancement. It can be concluded that, by considering different approaches of measuring grain sizes, reasons for different yield stress for nanomaterials that were observed but could not be explained have been dealt with

Experimental Research on Performances of Air Turbines for a Fixed Oscillating Water Column-Type Wave Energy Converter

A fixed oscillating water column (OWC)-type wave energy converter is composed of an air chamber for primary conversion and an air turbine for secondary conversion. In the optimal design method of a fixed OWC-type wave energy converter, it is necessary to develop a design method which can consider the characteristics of incident wave motion, the motion of the internal free surface affected in the structure such as a partly submerged wall, the fluctuation of air pressure in an air chamber, the rotation of the air turbine. In this paper, the 2-dimensional wave tank tests in regular waves for the performance evaluation of the air turbines in a fixed OWC-type wave energy converter were conducted to obtain the data needed to make this design method. As the results, the effects of the impulse turbine specification such as the rotor inlet/outlet angle, the guide vane's number and the vane's setting angle on the primary and secondary conversion efficiencies are clarified experimentally. Furthermore, the performances of the Wells turbines with different number of blade are presented for comparison of the operating condition

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