GEOMETRIC MODELING OF ADAPTIVE ALGEBRAIC CURVES PASSING THROUGH PREDETERMINED POINTS

In this paper, the geometric theory of multidimensional interpolation was further developed in terms of modeling and using adaptive curves passing through predetermined points. A feature of the proposed approach to modeling curved lines is the ability to adapt to any initial data for high-quality interpolation, which excludes unplanned oscillations, due to the uneven distribution of parameter values, the source of which are the initial data. This is the improvement of the previously proposed method for constructing and analytically describing arcs of algebraic curves passing through predetermined points, obtained on the basis of Bezier curves, which are compiled taking into account the expansion coefficients of the Newton binomial. The paper gives an example of using adaptive algebraic curves passing through predetermined points for geometric modeling of the stress-strain state of membrane coatings cylindrical shells using two-dimensional interpolation. The given example an illustrative showed the advantages of the proposed adaptation of algebraic curves passing through predetermined points and obtained on the basis of Bezier curves for geometric modeling of multifactor processes and phenomena. The use of such adaptation allows not only to avoid unplanned oscillations, but also self-intersection of geometric objects when generalized to a multidimensional space. Adaptive algebraic curves can also be effectively used as formative elements for constructing geometric objects of multidimensional space, both as guide lines and as generatrix’s.

GEOMETRIC MODELING OF MULTI-FACTOR PROCESSES BASED ON VARIABLE POINT ALGORITHMS

In this paper, the geometric theory of multidimensional interpolation was further developed. It has been established that the geometric models of multivariate processes obtained using multidimensional interpolation are characterized by variability, which is a consequence of the multiplicity of choice of reference lines in the process of developing a geometric modeling scheme. At the same time, all possible variations of geometric interpolants fully satisfy the initial experimental and statistical data, but have different curvature between the node points of the interpolation. As the dimension of the space increases, the number of variations increases significantly. The variable approach to geometric modeling of multifactorial processes generates a number of scientific problems that require further research, such as: comparison of geometric objects of multidimensional space, development of criteria for choosing the best solutions, construction of averaged geometric objects as one of the tools for optimizing the results of modeling, etc. The article also presents the results of a computational experiment on geometric modeling of the dependence of the physical and mechanical properties of fine-grained concrete on the composition of the combined aggregate based on variable point algorithms with the subsequent construction of an averaged response surface, the current point of which is the center of gravity of a multidimensional tetrahedron, for which the dimension of space depends on the amount possible interpolation options.

DQ-Frame Admittance Estimation of Three-Phase Converters with a Wide Range of Operating Points

The <i>dq</i>-frame admittance of closed-loop controlled three-phase converters is a linearized model that is dependent on the operating points of the system. Yet, it is impractical to measure the converter admittance at all operating points. This paper, thus, proposes an approach to estimating the <i>dq</i>-frame admittance of three-phase converters at a wide range of operating points. The method applies multidimensional interpolation to a given set of admittance data, which is measured from the pre-defined operating points. The accuracy of interpolation is then evaluated by using the posterior error estimation method. The number of pre-defined operating points is next adjusted to find a good compromise between the accuracy and efficiency of the approach. Simulations and experimental results verify the effectiveness of the approach.<div><br></div>

DQ-Frame Admittance Estimation of Three-Phase Converters with a Wide Range of Operating Points

The <i>dq</i>-frame admittance of closed-loop controlled three-phase converters is a linearized model that is dependent on the operating points of the system. Yet, it is impractical to measure the converter admittance at all operating points. This paper, thus, proposes an approach to estimating the <i>dq</i>-frame admittance of three-phase converters at a wide range of operating points. The method applies multidimensional interpolation to a given set of admittance data, which is measured from the pre-defined operating points. The accuracy of interpolation is then evaluated by using the posterior error estimation method. The number of pre-defined operating points is next adjusted to find a good compromise between the accuracy and efficiency of the approach. Simulations and experimental results verify the effectiveness of the approach.<div><br></div>

Development of a MOX equivalence Python code package for ANICCA

The basis of the MOX (Mixed OXide) energy equivalence principle is keeping the in-core fuel management characteristics (cycle length, feed size, etc.) of a nuclear reactor unchanged when replacing UOX (Uranium OXide) fuel assemblies by MOX. If the effect of the loading pattern is neglected, such an equivalence is obtained by tuning the Pu content in the MOX fuel, while considering the specific Pu isotopic vector at the time of the core reload to obtain a crossing of the reactivity curves of UOX and MOX at the end-of-cycle core average burnup. It is proposed in this work to extend the fuel cycle analysis tool ANICCA (Advanced Nuclear Inventory Cycle Code) with a MOX equivalence Python code package, which automatically governs the supply and demand of Pu vector isotopes required to obtain MOX equivalence. This code package can determine the reactivity evolution for any given Pu vector by means of a multidimensional interpolation on a directive grid of pre-calculated data tables generated by WIMS10, covering the physically accessible Pu vector space. A fuel cycle scenario will be assessed for a representative evolution of the Pu vector inventory available in spent UOX fuel as a demonstration case, defining the interim fuel storage building dimensional requirements for different reprocessing strategies.

VARIATIVE GEOMETRIC ALGORITHMS FOR MODELING MULTIFACTOR PROCESSES

The work is investigated by the influence of variable geometric algorithms in modeling multifactor processes using multidimensional interpolation. Geometric models of multifactorial processes obtained using multidimensional interpolation inherent variability, which is a consequence of the multiplicity of the choice of reference lines during the development of geometric modeling schemes. At the same time, all possible variations of geometric interpolyns are fully satisfying the initial data. It has been established that the number of variations of geometric schemes directly depends on the number of current parameters and the dimension of the space in which the simulated geometrical object is located. Thus, a variable approach to geometrical modeling of multifactor processes generates a number of scientific tasks, the main one is the need to determine the effect of the variability of geometric algorithms on the final results of the computational experiment and, as a result, the choice of the best modeling results. To this end, the article presents the studies of variable geometric algorithms and computational experiments on the example of 2-parametric geometric interpolyns. A classification of 2-parametric geometric interpolytesses, which were conditionally divided into 3 types. Depending on the geometric scheme of constructing interpolynta, the square geometric scheme, a rectangular geometric scheme, a mixed geometric scheme. As a result of computational experiments, it was found that for a square geometric scheme, the variability does not affect the final results, in rectangular geometric schemes, the variability has a slight influence, and mixed geometric schemes may have significant differences and require additional research to select the highest quality geometric process model. Comparison of geometric models were performed by the methods of scientific visualization by overlaying the response surfaces on each other.

An Approach to Comparing Multidimensional Geometric Objects

The paper proposes an approach to the comparison of multidimensional geometric objects, which is used to assess the variational geometric models of multifactor processes and phenomena obtained using the geometric theory of multidimensional interpolation. The proposed approach consists of two stages, the first of which consists in the discretization of multidimensional geometric objects in the form of a set of discretely given points, and the second is in comparing the obtained discrete point sets using a criterion that is essentially similar to the coefficient of determination. In this case, one of the discrete point sets is taken as a reference for comparison with another point set. For a correct comparison of multidimensional geometric models in the form of point equations, which are reduced to a system of parametric equations, it is necessary to perform interconnection of parameters. A computational experiment was carried out on the example of comparing geometric models of the physical and mechanical properties of fine-grained concrete. It showed the possibility of using the proposed approach for comparing multidimensional geometric objects and the reliability of the results obtained in comparison with scientific visualization methods. On the same example, it was found that for an accurate comparison of the investigated geometric models of the physical and mechanical properties of fine-grained concrete, it is enough to discretize 100 points. A further increase in the set of discrete points of the compared geometric objects has no significant effect on the criterion for assessing their similarity.

Sval_Imp: a gridded forcing dataset for climate change impact research on Svalbard

We present Sval_Imp, a high-resolution gridded dataset designed for forcing models of terrestrial surface processes on Svalbard. The dataset is defined on a 1 km grid covering the archipelago of Svalbard, located in the Norwegian Arctic (74–82∘ N). Using a hybrid methodology, combining multidimensional interpolation with simple dynamical modeling, the atmospheric reanalyses ERA-40 and ERA-Interim by the European Centre for Medium-Range Weather Forecasting have been downscaled to cover the period 1957–2017 at steps of 6 h. The dataset is publicly available from a data repository. In this paper, we describe the methodology used to construct the dataset, present the organization of the data in the repository and discuss the performance of the downscaling procedure. In doing so, the dataset is compared to a wealth of data available from operational and project-based measurements. The quality of the downscaled dataset is found to vary in space and time, but it generally represents an improvement compared to unscaled values, especially for precipitation. Whereas operational records are biased to low elevations around the fringes, we stress the hitherto underused potential of project-based measurements at higher elevation and in the interior of the archipelago for evaluating atmospheric models. For instance, records of snow accumulation on large ice masses may represent measures of seasonally integrated precipitation in regions sensitive to the downscaling procedure and thus providing added value. Sval_Imp (Schuler, 2018) is publicly available from the Norwegian Research Data Archive NIRD, a data repository (https://doi.org/10.11582/2018.00006).

Numerical Analysis on the Effectiveness of Gurney Flaps as Power Augmentation Devices for Airfoils Subject to a Continuous Variation of the Angle of Attack by Use of Full and Surrogate Models

The disclosing of new diffusion frontiers for wind energy, like deep-water offshore applications or installations in urban environments, is putting new focus on Darrieus vertical-axis wind turbines (VAWTs). To partially fill the efficiency gap of these turbines, aerodynamic developments are still needed. This work in particular focuses on the development of a mathematical model that allows predicting the possible performance improvements enabled in a VAWT by application of the Gurney flaps (GFs) as a function of the blade thickness, the rotor solidity and geometry of the Gurney flap itself. The performance of airfoil with GFs was evaluated by means of detailed simulations making use of computational fluid dynamics (CFD). The accuracy of the CFD model was assessed against the results of a dedicated experimental study. In the simulations, a dedicated method to simulate cycles of variation of the angle of attack similar to those taking place in a cycloidal motion (rather than purely sinusoidal ones) was also developed. Based on the results from CFD, a multidimensional interpolation based on the radial basis functions was conducted in order to find the GF design solution that provides the highest efficiency for a given turbine in terms of airfoil and solidity. The results showed that, for the selected study cases based on symmetric airfoils, the GF positioned facing outwards from the turbine, which provides the upwind part of the revolution, can lead to power increments ranging from approximately 30% for the lower-solidity turbine up to 90% for the higher-solidity turbine. It was also shown that the introduction of a GF should be coupled with a re-optimization of the airfoil thickness to maximize the performance.