Rubric: "2.3.1. System analysis, management and information processing (physical and mathematical sciences)"
519.2 Polynomial chaos and regression based on KolmogorovGabor polynomials: comparative modeling
Oblakova T. V. (Bauman Moscow State Technical University), Pham Q. (-)
doi: 10.18698/2309-3684-2023-4-93108
The application of the generalized expansion of polynomial chaos (PC) and models based on Kolmogorov-Gabor polynomials in regression problems is considered. When choosing PC expansion, the Wiener-Askey scheme was used, which sets the correspondence between the feature distribution law and the orthogonal polynomial basis. To calculate the expansion coefficients, non-intrusive methods were used: least squares, elastic network, as well as Ivakhnenko's inductive evolutionary algorithm. Kolmogorov-Gabor polynomials are used as a reference function of a polynomial neural network. Model errors and performance were calculated on a test set. Models were compared on a linear transport problem under uncertainty: the diffusion coefficient and drift were modeled by uniformly distributed random variables. It is shown that with a small interval of variation in the values of random variables, both models give good efficiency, but the PC model demonstrates a smaller spread of errors and is faster in time. For the de-cay equation with random coefficients distributed according to the Gaussian law, the influence of the correlation of these coefficients on the rate of convergence is studied. It is shown that with dependent coefficients, the best performance is observed in higher-order PC models. On the basis of comparative modeling, it has been established that the use of PC is unambiguously preferable in the following cases: a small dimension of the space of input features, a known law of distribution of input data, and correlated features. It is also shown that the use of PC with a large dimension of the space of input features is inefficient due to the rapid increase in the number of terms in the expansion, leading to a sharp increase in the time to process the task. In this case, the regression model based on the Kolmogorov-Gabor polynomials in combination with the GMDH turned out to be clearly preferable.
Облакова Т.В., Фам Куок Вьет. Сравнительное моделирование на основе многочленов Колмогорова-Габора в задачах полиномиального хаоса и регрессии. Математическое моделирование и численные методы, 2023, № 4, с. 93–108.
Valishin A. A. (Bauman Moscow State Technical University), Zaprivoda A. V. (Bauman Moscow State Technical University), Klonov A. S. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-1-93109
With the development of forecasting methods, the exclusion of random effects from the initial information and the studied processes becomes essential. These effects are associated not only with the impossibility of taking into account all factors, but also with the fact that some of them are often not taken into account at all. It is important not to forget about random measurement errors. In the predicted values, due to these effects, a kind of random offset or "noise" is created. Filtering (exclusion) of noise should, of course, increase the reliability and justifiability of forecasts. This article discusses the principles of real-time data filtering. The problem statement is given, as well as the main evaluation criteria that must be met to obtain a satisfactory result. In addition, the principle of operation of the two most common types of filters – absolutely optimal and conditionally optimal - is analyzed, their advantages and disadvantages are described. The application of Kalman and Pugachev filters to a model with two sensors is considered. Some conclusions and recommendations are presented on in which cases it is better to use one or another filter.
Валишин А.А., Запривода А.В., Клонов А.С. Математическое моделирование и сравнительный анализ численных методов решения задачи непрерывнодискретной фильтрации случайных процессов в реальном времени. Математическое моделирование и численные методы, 2024, № 1, с. 93–109.
519.7 Modeling and efficiency analysis of perceptual hash functions for segmented image search
Valishin A. A. (Bauman Moscow State Technical University), Zaprivoda A. V. (Bauman Moscow State Technical University), Tsukhlo S. S. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-2-4667
This research paper explores the use of perceptual hash functions to improve the retrieval efficiency of aerial photography and satellite remote sensing images segmented by a convolutional neural network. This paper describes three hashing algorithms. The first algorithm is based on the use of a low-pass filter and is aimed at reducing image detail in order to highlight the most stable image features. The second algorithm uses a two-dimensional discrete cosine transform to create an image hash. The third algorithm is based on the Radon transform, which allows you to extract information about the directions of lines in the image, as well as provide maximum invariance to the rotation transformation of the input image. The article also tests these algorithms, including analysis of their invariance to transformations for rotation, scaling and shifting of the source image. Test results show that the algorithm based on the Radon transform exhibits good rotation invariance, but is sensitive to the quality of segmentation, which can lead to frequent collisions when searching for similar images. Algorithms using a two-dimensional discrete cosine transform and an algorithm using a low-pass filter turned out to be more stable and have a smaller spread of values. However, it should be noted that algorithms using a low-pass filter and 2D discrete cosine transform may not be applicable to rotated images. Based on the results of analysis and comparison of the performance of the algorithms, it is recommended to give preference to either the second or third algorithm, because each of them has its own advantages and disadvantages, and the decision to use a specific algorithm in the task of finding the most similar image must take into account the specific conditions and limitations of the problem, as well as the requirements for the quality of image comparison.
Валишин А.А., Запривода А.В., Цухло С.С. Моделирование и сравнительный анализ эффективности перцептивных хеш-функций для поиска сегментированных изображений. Математическое моделирование и численные методы, 2024, № 2, с. 46-67.
Tlibekov A. T. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-2-112125
The comparison of existing and developed new methods of converting optimality criteria into a scalar function of the goal is performed. New converting methods are used in the problems of interpolation of experimental data by a modified fractional-power Newton–Puiseux series. Coefficients and degrees of a fractional-power series are calculated by evolutionary or infinite-step optimization methods, where the modules of the difference between experimental data and the values obtained by calculating the interpolation polynomial are used as optimality criteria. Under such conditions, the optimization task becomes multi-criteria, for which, during the search process, part of the optimality criteria increases, the rest decrease and reduce the scalar goal function and creating the illusion that the search is effective. For new converting methods, all optimality criteria in the search process are reduced. The errors obtained by interpolating the time of laser cutting of steel sheet and forecasting the production program of parts are shown. The use of modified fractional power series and new methods of converting optimality criteria for the implementation of the neural network learning function is proposed.
Тлибеков А.Х. Сравнительный анализ методов свертывания критериев оптимальности в задачах многокритериальной оптимизации. Математическое моделирование и численные методы, 2024, № 2, с. 112-125.
Ivanov M. Y., Bushuev A. Y. (Bauman Moscow State Technical University), Shcherbakov N. S. (Bauman Moscow State Technical University), Resh G. F.
doi: 10.18698/2309-3684-2024-3-100119
In various technical systems hydraulic devices are widely used to ensure the synchronous movement of executive bodies — unregulated chokes, flow dividers, regulators and/or flow stabilizers. The latter are characterized by the fact that their functioning occurs in the range of pressure drops of liquid amounting to several hundred atmospheres. The issues related to the numerical simulation of non-stationary physical processes in the flow stabilizer the design of which is protected by a patent of the Russian Federation for the invention are considered. The results of computer modeling based on a theoretical model with concentrated parameters, the use of the finite-difference implicit Geer method for solving a system of rigid differential equations are presented. The problem of optimal improvement of the design of such flow stabilizer in accordance with the selected criterion is formulated and solved. This optimization criterion is to ensure the condition of the minimum possible positive statism of the flow-drop (static) characteristic in conditions of wide change in the pressure drop on the device and the effect of the axial component of the hydrodynamic force. The problem of optimal design improvement was solved using one of the widely used evolutionary optimization algorithms — genetic algorithm with real coding. The results of computational experiments in modeling physical processes of the analysis problem correspond to the available experimental data that were previously obtained by the authors of the work. It is shown that improvement of the existing design of the flow stabilizer is possible — the angle of inclination of the flow-drop characteristic to the horizontal axis has decreased almost twofold. At the same time, it was possible to obtain higher accuracy of maintaining volumetric flow rate of the liquid. This accuracy is on the order of ±7,5 % of the nominal (tuning) value of the flow stabilizer. For comparison, the accuracy of maintaining the volume flow rate of the liquid before performing the optimization procedure was about ±10 %.
Иванов М.Ю., Бушуев А.Ю., Щербаков Н.С., Реш Г.Ф. Компьютерное моделирование динамических процессов в гидравлическом стабилизаторе расхода и его оптимизация на основе эволюционного алгоритма. Математическое моделирование и численные методы, 2024, № 3, с. 100-119.
Oblakova T. V. (Bauman Moscow State Technical University), Pham Q. (-)
doi: 10.18698/2309-3684-2024-3-120139
Application of generalized decomposition of polynomial chaos (RPH) in problems of quantitative estimation of uncertainty is considered. A program code has been implemented to study the influence of the input data generation scheme on the quality of the model whose coefficients are calculated by the least squares method. Standard error and sliding control values were used as quality criteria. Along with the classical method of filling the space of the input features on the scheme of the Latin hypercube, two variants of modelling coherent-optimal sample are considered: using the Markov chain and with additional thinning on the D-criterion. While the Latin hypercube sample evenly distributes points across the whole space of random variables, coherent optimum methods aim to distribute samples more densely in areas with greater variance and more rarely in areas with small variance. This approach allows for a better integration of information about the real model, which leads to a reduction in the number of samples in the planning of the experiment and as a result save costly CPU time. The implemented methods were compared on the Ishigami model function and the farm design with random values of physical characteristics. As a result of comparative modeling, it is established that in case of small range of change of random parameters, when their gradients slowly change, the design of the Latin hypercube shows the lowest values of error and sliding control. At the same time, in the case of strong non-linearity, the application of coherent-optimal design leads to a more stable and efficient model, and additional thinning according to the criterion of D-optimality gives the best result and is the most sustainable. It has also been shown that both the planning algorithms of the experiment are unstable and incorrect if there are insufficient samples.
Облакова Т.В., Фам Куок Вьет. Об оптимальной конструкции моделирования разложения полиномиального хаоса в задачах количественной оценки неопределенности. Математическое моделирование и численные методы, 2024, № 3, с. 120–139.