Describing a Set of Points with Elliptical Areas: Mathematical Description and Verification on Operational Tests of Technical Devices

The purpose of this article was to present an algorithm for creating an ellipse for any data set represented on a two-dimensional reference frame. The study objective was to verify the developed method on real results of experimental tests with different subject matter. This article contains a mathematical algorithm to describe a set of points with elliptical areas. In addition, four results of tests with different subject matter are cited, based on which the developed method was verified. The verification of the method included checking the deviation of the geometric dimensions of the ellipse, the number of points contained within the ellipse, and the area of the ellipse. The implemented research methodology allowed to demonstrate the possibility of using the method of describing a set of points with elliptical areas, in order to determine quantitative parameters evaluating the results of the test. The presented results show the method’s applicability for the results obtained in four different operational tests: measurement of the human body’s gravity center position for a person propelling a wheelchair, measurement of marker position using motion capture methods, measurement of particulate emissions when using equipment powered by an internal combustion engine, and measurement of the muscle activity of the upper limb when propelling a hybrid manual-electric wheelchair. The performed experiments demonstrated that the method allows to describe about 85% of all measurement points with an ellipse.

Analysis of Aircraft Operation System Regarding Readiness—Case Study

The aim of the study was to develop a model of the readiness and reliability of an aircraft to perform an air task. The applied research method uses quantitative statistical methods and Markov processes in order to create a mathematical algorithm to exploit a selected aircraft type. The paper presents a case study of the TS-11 “Iskra” aircraft. The results show that even if the probability of being on stand-by is low, the tasks can be completed by operating the entire fleet properly.

Математический алгоритм для обнаружения утечек малой интенсивности

The operating principle of leak detection systems, based on registration of transported medium hydroacoustic fluctuations, appearing due to pipeline loss of containment, consists of identification of hydraulic impulse, originating in case of leakage, using acoustic dynamic pressure measuring sensors - hydrophones. However, during pumping at pipeline stationary operating mode hydrophones also register background noises, which can mask the leakage signal. To separate the useful leakage signal it is important to construct an algorithm that allows lowering the noise component of the signals. Within the scope of experimental research, two pairs of hydrophones were used, which were installed at the functioning main oil pipeline at a distance of 20 km of each other. The distance between the adjacent paired hydrophones was no more than 1 km. Leaks were imitated by draining the product (diesel fuel) in the middle of control section. Authors considered the methods of noisy signals filtration and possible methods of cleared signals processing to determine the leak parameters. Mathematical algorithm that allows minimizing the influence of signal noise by filtration and mutual hydrophone readings compensation was proposed. It is established, that the developed algorithm allows detecting the leakages of low intensity (up to 0.1 % of actual flow) in cases of stationary pipeline operating mode and pumping stop mode. Принцип работы систем обнаружения утечек, основанных на регистрации гидроакустических колебаний транспортируемой среды, возникающих из-за разгерметизации трубопровода, состоит в идентификации гидравлического импульса, возникающего при образовании утечки, с помощью акустических датчиков измерения динамического давления – гидрофонов. Однако гидрофоны в процессе перекачки при стационарном режиме работы трубопровода регистрируют в том числе фоновые шумы, которые могут маскировать сигнал от утечки. Для выделения полезного сигнала утечки актуально построение алгоритма, позволяющего понизить шумовые составляющие сигналов. В рамках экспериментальных исследований использовались две пары гидрофонов, которые устанавливались на действующем магистральном нефтепродуктопроводе на расстоянии 20 км друг от друга. Расстояние между соседними гидрофонами в паре составляло не более 1 км. Утечки имитировались путем выполнения натурных сливов продукта (дизельного топлива) в середине контрольного участка. Авторами рассмотрены методы фильтрации зашумленных сигналов и возможные способы обработки очищенных сигналов с целью определения параметров утечки. Предложен математический алгоритм, позволяющий минимизировать влияние шумовых составляющих сигналов путем фильтрации и взаимной компенсации показаний пар гидрофонов. Установлено, что разработанный алгоритм позволяет обнаруживать утечки малой интенсивности (до 0,1 % от фактического расхода) в условиях стационарного режима работы трубопровода и режима остановленной перекачки.

Spectral analysis method of electrophysical non-destructive testing data

A computational method for spectral analysis of the electrophysical test results based on sequential mathematical algorithm transformations using a discrete linear response function has been developed. The procedure for constructing spectral functions has a certain order and is aimed at obtaining adequate results of the experimental sample approximation in the frequency domain. It is shown that use of the low-frequency FIR filter function as part of the convolution, together with the fast Fourier transform, gives accurate results for structural inhomogeneities localization in welded joints.

Detection of radio signals against the background of strong electromagnetic noise in transport

The problem of detecting a useful signal in the presence of a strong background noise is considered. To solve it, a statistical approach is used, based on a change in the level of chaos in the system when an additional random or deterministic process occurs, which is probabilistically independent from a set of stochastic phenomena that form background noise. It is shown that the occurrence of this process changes the level of entropy of the measured signal; this fact is the basis of the applied mathematical algorithm. It is based on the elements of the Fourier transform apparatus for the probability density with an appropriate choice of a nonlinear function of the random process under study. The proposed approach, based on variations in the randomness in the system in the presence of a useful signal, makes it possible to record its presence against the background of noise components even at low signal-to-noise ratios. The effectiveness of the method is confirmed both by theoretical justification and by the calculations presented in this work. The condition for the implementation of the technique described in the article, which does not impose restrictions on the studied physical fields and frequency ranges, is the comparability of the width of the probabilistic distribution of the desired useful signal with several intervals of discreteness of the measuring equipment. One of the results of this work is a high sensitivity to the emergence of independent random components.

Application of Fuzzy Mathematics Algorithm in Computer Speech Recognition

Speech recognition, as one of the key artificial intelligence technologies in modern development, plays an important role in any aspect. However, there are still problems in practical application, such as poor anti-interference and low degree of perfection. Therefore, this paper aims at the content of existing computer speech recognition technology, grasps fuzzy mathematical algorithm, and analyzes how to use this algorithm to better study computer speech recognition.

Research on Task-Service Network Node Matching Method Based on Multi-Objective Optimization Model in Dynamic Hyper-Network Environment

In order to reduce the cost of manufacturing and service for the Cloud 3D printing (C3DP) manufacturing grid, to solve the problem of resources optimization deployment for no-need preference under circumstance of cloud manufacturing, consider the interests of enterprises which need Cloud 3D printing resources and cloud platform operators, together with QoS and flexibility of both sides in the process of Cloud 3D printing resources configuration service, a task-service network node matching method based on Multi-Objective optimization model in dynamic hyper-network environment is built for resource allocation. This model represents interests of the above-mentioned two parties. In addition, the model examples are solved by modifying Mathematical algorithm of Node Matching and Evolutionary Solutions. Results prove that the model and the algorithm are feasible, effective and stable.

CenetBiplot: a new proposal of sparse and orthogonal biplots methods by means of elastic net CSVD

In this work, a new mathematical algorithm for sparse and orthogonal constrained biplots, called CenetBiplots, is proposed. Biplots provide a joint representation of observations and variables of a multidimensional matrix in the same reference system. In this subspace the relationships between them can be interpreted in terms of geometric elements. CenetBiplots projects a matrix onto a low-dimensional space generated simultaneously by sparse and orthogonal principal components. Sparsity is desired to select variables automatically, and orthogonality is necessary to keep the geometrical properties that ensure the biplots graphical interpretation. To this purpose, the present study focuses on two different objectives: 1) the extension of constrained singular value decomposition to incorporate an elastic net sparse constraint (CenetSVD), and 2) the implementation of CenetBiplots using CenetSVD. The usefulness of the proposed methodologies for analysing high-dimensional and low-dimensional matrices is shown. Our method is implemented in R software and available for download from https://github.com/ananieto/SparseCenetMA.