Gaining Efficiency of Computational Experiments in Modeling the Flight Vehicle Movement

• Main Author: I. K. Romanova
• Format: Article
• Language: Russian
• Published: MGTU im. N.È. Baumana 2017-01-01
• Series: Nauka i Obrazovanie
• Subjects: multivariate analysis of technical systems; dynamics of flight vehicle; the efficiency of the computational experiments; the optimal grid; Pareto - optimal solutions; the robustness and accuracy of the simulation of flight vehicle movement
• Online Access: http://technomag.edu.ru/jour/article/view/1269

<p>The paper considers one of the important aspects to gain efficiency of conducted computational experiments, namely to provide grid optimization. The problem solution will ultimately create a more perfect system, because just a multivariate simulation is a basis to apply optimization methods by the specified criteria and to identify problems in functioning of technical systems.</p><p>The paper discusses a class of the moving objects, representing a body of revolution, which, for one reason or another, endures deformation of casing. Analyses using the author's techniques have shown that there are the following complex functional dependencies of aerodynamic characteristics of the studied class of deformed objects.</p><p>Presents a literature review on new ways for organizing the calculations, data storage and transfer. Provides analysing the methods of forming grids, including those used in initial calculations and visualization of information. In addition to the regular grids, are offered unstructured grids, including those for dynamic spatial-temporal information. Attention is drawn to the problem of an efficient retrieval of information. The paper shows a relevant capability to run with large data volumes, including an OLAP technology, multidimensional cubes (Data Cube), and finally, an integrated Date Mining approach.</p><p>Despite the huge number of successful modern approaches to the solution of problems of formation, storage and processing of multidimensional data, it should be noted that computationally these tools are quite expensive. Expenditure for using the special tools often exceeds the cost of directly conducted computational experiments as such. In this regard, it was recognized that it is unnecessary to abandon the use of traditional tools and focus on a direct increase of their efficiency. Within the framework of the applied problem under consideration such a tool was to form the optimal grids.</p><p>The optimal grid was understood to be a grid in the N-dimensional cube, where N is the number of variable parameters, the calculations of functions on which meet the specified accuracy.</p><p>In computational experiments the grid sizes have been increased step-by-step, with the data sets being reconstructed and the residuals being calculated. The tolerance values were visualized using the level lines on the functions of errors. Special attention was paid to the pitching moment, which is directly connected with the stability problem of of the body movement. Here not only answering the question on the mean square error of calculations is important, but also the change of the sign of the moment coefficient.</p><p>It turned out that despite the available errors, there was no sign change observed. We have also identified areas of overstatement and understatement of the aerodynamic coefficients (ADC) when using the larger grids. Noted that when preparing the grid, the prerequisite is to identify areas of finding the system at the boundaries of stability.</p><p>The calculation results have shown that as compared to the exact calculations the moment is underestimated. Moreover, taking into account the opposite sign of the dependence on the angle of attack in modulus, the moment is overstated; there are overestimations of the lifting force, resistance in the modulus and damping in the operating range.</p><p>The choice of the optimal grid for evaluation of the mean square error led to a rather small grid, so a capability to introduce a grid of the variable size was considered. It was proposed to divide the grid into two parts. In the region of problem areas an estimate of the allowable increase of size is based on the analysis of a Pareto front of the relative derivative (increment) function. After scaling we have obtained the Nash equilibrium point. For the remaining areas the grid is to be selected either according to the tolerable error (with a constant size) or using an equality principle of the function increments.</p><p>The proposed approach to select the mixed grids enables the significantly reducing number of points used when forming the ADC data arrays.</p><p>A final criterion of the proper grid choice was a simulation of the body movement dynamics with used grid functions of ADC. Formulas for equations in deviations to describe a perturbed movement because of coarsening grids were derived. Analysis based on the information about the deformations when enlarging the grid has shown that the perturbed movement remains stable. Deviations, observed in the first phase of movement occur because of a decreasing oscillation period in coarsening a grid, which is quite understandable because of trends of changing ADC within the dynamic coefficients used in calculations of the oscillation period.</p><p>Thus, the article shows the impact of consolidation of grids on the change nature of aerodynamic coefficients. To estimate were used the dependencies of deviations and normalized standard errors of the indicators of grids consolidation. Special attention was paid to identifying the areas of underestimation and overestimation, including zero crossing for pitching moments and damping ratio. The paper proposes a technique for a reasonable selection of grid sizes in multivariable analysis of the body movement dynamics, including deformed ones, on the basis of Pareto-tests of normalized errors.</p>