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1

Diagnosis of ITSC fault in the electrical vehicle powertrain system through signal processing analysis

Ouamara Dehbia, Boukhnifer Moussa, Chaibet Ahmed, Maidi Ahmed

Diagnostyka

|

2023

|

Vol. 24, No. 1

art. no. 2023113

EN

The three-phase induction motor is well suited for a wide range of mobile drives, specifically for electric vehicle powertrain. During the entire life cycle of the electric motor, some types of failures can occur, with stator winding failure being the most common. The impact of this failure must be considered from the incipient as it can affect the performance of the motor, especially for electrically powered vehicle application. In this paper, the intern turn short circuit of the stator winding was studied using Fast Fourier transform (FFT) and Shor-Time Fourier transform (STFT) approaches. The residuals current between the estimated currents provided by the extended Kalman filter (EKF) and the actual ones are used for fault diagnosis and identification. Through FFT, the residual spectrum is sensitive to faults and gives the extraction of inter-turn short circuit (ITSC) related frequencies in the phase winding. In addition, the FFT is used to obtain information about when and where the ITSC appears in the phase winding. Indeed, the results allow to know the faulty phase, to estimate the fault rate and the fault occurrence frequency as well as their appearance time.

2

Analysis of the backlash in the single stage cycloidal gearbox

Król Roman

Archive of Mechanical Engineering

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2022

|

LXIX, nr 4

693--711

EN

In this paper the analysis of backlash influence on the spectrum of torque at the output shaft of a cycloidal gearbox has been performed. The model of the single stage cycloidal gearbox was designed in the MSC Adams. The analysis for the excitation with the torque and the analysis with constant angular velocity of the input shaft were performed. For these analyses, the amplitude spectrums of the output torque for different backlashes was solved using FFT algorithm. The amplitude spectrums of the combined sine functions composed of the impact to impact times between the cycloidal wheel and the external sleeves were computed for verification. The performed studies show, that the backlash has significant influence on the output torque amplitude spectrum. Unfortunately the dependencies between the components of the spectrum and the backlash could not be expressed by linear equations, when vibrations of the output torque in the range of (350 Hz – 600 Hz) are considered. The gradual dependence can be found in the spectrum determined for the combined sine functions with half-periods equal impact-to-impact times. The spectrum is narrower for high values of backlash.

3

Intelligent system of noise control of the technical condition of railroad tracks

Aliev Telman, Babayev Tofig, Alizada Tahir, Alibayli Elnur, Ahmedov Heybatulla

Transport Problems

|

2021

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T. 16, z. 1

65--73

EN

It is shown that modern geometry cars, flaw detector cars and other track test cars provide reliable control of the technical condition of all hauls of the railroad track at “certain intervals of time”. Their number is limited and therefore “continuous monitoring” of all hauls is almost impossible. At the same time, in real life, due to the impact of various factors, such as seismic processes, certain changes take place even a day after control. The authors consider one option for continuous monitoring of the beginning of changes in the technical condition of the track using intelligent tools, which allow one, by analyzing the useful signal and the noise from the soil vibrations caused by the rolling stock, to create informative attributes for identifying the technical condition of the track. The application of traditional technologies of correlation and spectral analysis and other methods for this purpose does not allow ensuring adequacy of the control results. This paper proposes a technology for extracting and analyzing useful vibration signals, the noise of vibration signals and the relationship between them. The estimates of both correlation and spectral characteristics of the useful signal and the noise are used as the main carriers of diagnostic information. Due to the simplicity and the reliability of implementation of the proposed technical tools, they can be easily installed in one of the cars of all rolling stocks, providing control of the beginning of changes in the technical condition of the track during their movement in all hauls

4

Rotor faults diagnosis by adjustable window function

Koura Mohamed Boudiaf, Boudinar Ahmed Hamida, Bendiabdellah Azeddine, Aimer Ameur Fethi, Gherabi Zakaria

Przegląd Elektrotechniczny

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2021

|

R. 97, nr 3

123--129

EN

Several recent studies dealing with new diagnosis methods criticize the classical method of Power Spectral Density by periodogram technique for its drawbacks related to frequency resolution. This is reflected by the appearance of a smoothing and a negative effect following the selected window function. Indeed, this technique is less efficient in the detection of frequency signatures of faults close to a high amplitude harmonic. In addition, it is unable to detect an incipient fault. However, this method has several advantages such as a low computation time and easy programming. To avoid these drawbacks while considering the method advantages, this paper proposes a simple procedure to define precisely the shape parameters of a new window belonging to the raised-cosine family. This procedure uses the characteristics of the stator current spectrum to ensure reliable diagnosis in the case of an incipient fault, while maintaining a quick processing time. The experimental tests carried out prove the effectiveness of the suggested approach in the diagnosis of incipient fault affecting an induction motor.

PL

Kilka ostatnich badań dotyczących nowych metod diagnostycznych krytykuje klasyczną metodę gęstości widmowej mocy techniką periodogramu ze względu na jej wady związane z rozdzielczością częstotliwości. Rzeczywiście, ta technika jest mniej skuteczna w wykrywaniu sygnatur częstotliwości uszkodzeń blisko harmonicznej o dużejj amplitudzie. Ponadto nie jest w stanie wykryć początkowej usterki. Jednak ta metoda ma kilka zalet, takich jak krótki czas obliczeń i łatwe programowanie. Aby uniknąć tych wad, biorąc pod uwagę zalety metody, w niniejszym artykule zaproponowano prostą procedurę precyzyjnego zdefiniowania parametrów kształtu nowego okna należącego do rodziny podniesionych cosinusów. Ta procedura wykorzystuje właściwości widma prądu stojana, aby zapewnić niezawodną diagnozę w przypadku początkowej fazy uszkodzenia, przy jednoczesnym zachowaniu szybkiego czasu przetwarzania. Przeprowadzone testy eksperymentalne dowodzą skuteczności sugerowanego podejścia w diagnozowaniu początkowej fazy uszkodzenia występującej w silnik indukcyjny.

5

A new optimization method based on Perry's idea through the use of the matrix power

Hafaidia Imane, Benrabia Noureddine, Ghiat Mourad, Guebbai Hamza

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 4

29--41

EN

The purpose of this paper is to present a new conjugate gradient method for solving unconstrained nonlinear optimization problems, based on Perry’s idea. An accelerated adaptive algorithm is proposed, where our search direction satisfies the sufficient descent condition. The global convergence is analyzed using the spectral analysis. The numerical results are described for a set of standard test problems, and it is shown that the performance of the proposed method is better than that of the CG-DESCENT, the mBFGS and the SPDOC.

6

Diagnostics of transformer insulation by frequency domain spectroscopy

Gutten Miroslav, Korenciak Daniel, Brncal Peter, Cefer Viktor

Przegląd Elektrotechniczny

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2020

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R. 96, nr 8

43--46

EN

The paper deals with the diagnostics of insulation oil-paper in high-voltage transformers by frequency diagnostic spectroscopy. The first part of paper deals with the base information about diagnostics of power transformers. In this part are presented differently insulating methods, for example method of recovery voltage method (RVM), method of polarization and depolarization currents (PDC) and chromatographic analysis. The second part of paper deals use of method of frequency domain spectroscopy (FDS) for high-voltage transformers with insulation oil-paper. This method is used in analysis insulating condition of power transformer with system of oil-paper. It was found, that the results of these tests are highly impacted by the operating temperature during the experimental measurement. Moisture and conductivity between insulating paper and oil in an insulating system are highly dependent from temperature. In the other part, the paper presents experimental results of the frequency diagnostic measurement for a real single-phase high-voltage transformer at different operating temperatures and states (with oil and without). Finally in the last part, the paper presents comparing frequency insulating measurements among several the same single-phase high-voltage transformers.

PL

W artykule przedstawiono metody diagnostyki izolacji olejowo-papierowej w transformatorach wysokiego napięcia. Zastosowano metodę spektroskopii częstotliwościowej. Wyniki analizy znacząco zależały od temperatury pracy. Porównano wyniki dla różnych warunków pracy kilku transformatorów.

7

Concept of social responsibility as an instrument of stabilising the macroeconomic situation of enterprises

Mierzejewski Mateusz, Żak Martyna

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

|

2019

|

z. 137

133--147

EN

The article presents the issue of corporate social responsibility as an instrument of stabilising the macroeconomic situation of a company based on building increased trust and attachment of society to a given company. Developing relationships in a proper way with stakeholders should be a guarantee to make a business an important element of the social structure, thus contributing to mitigating the impact of economic changes on the company's situations. The aim of this work is to examine the impact of selected macroeconomic variables related to the activities of enterprises (in particular. socially responsible enterprises), illustrated in the form of changes in the value of stock market indices (including listed social responsibility indexes). The cross-spectral analysis tool was used to analyse the causality of macroeconomic changes. Changes in the spectral density values of individual variables, as well as the coherence square and phase spectrum values of variables, were analysed. An additional tool was used in the study to create an index of changes in exchange values in order to conduct a comparative analysis of the development of time series relating to individual indices. The data analysed was related to changes in the value of social responsibility indexes, as well as macroeconomic data, for the period from January 2001 to the end of April 2019.

8

Investigation of background noise in the GNSS position time series using spectral analysis – A case study of Nepal Himalaya

Ray Jagat Dwipendra, Vijayan M. Sithartha Muthu, Godah Walyeldeen, Kumar Ashok

Geodesy and Cartography

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2019

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Vol. 68, no. 2

375--388

EN

Position time series from permanent Global Navigation Satellite System (GNSS) stations are commonly used for estimating secular velocities of discrete points on the Earth’s surface. An understanding of background noise in the GNSS position time series is essential to obtain realistic estimates of velocity uncertainties. The current study focuses on the investigation of background noise in position time series obtained from thirteen permanent GNSS stations located in Nepal Himalaya using the spectral analysis method. The power spectrum of the GNSS position time series has been estimated using the Lomb–Scargle method. The iterative nonlinear Levenberg–Marquardt (LM) algorithm has been applied to estimate the spectral index of the power spectrum. The power spectrum can be described by white noise in the high frequency zone and power law noise in the lower frequency zone. The mean and the standard deviation of the estimated spectral indices are […] for north, east and vertical components, respectively. On average, the power law noise extends up to a period of ca. 21 days. For a shorter period, i.e. less than ca. 21 days, the spectra are white. The spectral index corresponding to random walk noise (ca. –2) is obtained for a site located above the base of a seismogenic zone which can be due to the combined effect of tectonic and nontectonic factors rather than a spurious monumental motion. Overall, the usefulness of investigating the background noise in the GNSS position time series is discussed.

9

Oznaczanie fluoru w żywności i produktach codziennego użytku. Cz. 2 - wysokorozdzielcza absorpcyjna spektrometria cząsteczkowa HR CS MAS

Palak Ewelina, Godlewska-Żyłkiewicz Beata

Analityka : nauka i praktyka

|

2019

|

nr 3

28--32

PL

Zaletami metody HR CS MAS są wysoka czułość, niskie granice wykrywalności, szeroki zakres liniowości oraz ograniczenie przygotowania próbki di minimum, a także odporność na interferencje. Z tego powodu można przypuszczać, że wysokorozdzielcza absorpcyjna spektrometria cząsteczkowa z ciągłym źródłem promieniowania może stać się coraz powszechniej stosowaną techniką oznaczania fluoru w laboratoriach analitycznych.

10

Metodyka oceny stanu powierzchni betonowej budowli piętrzącej na podstawie analizy spektralnej wyników naziemnego skanowania laserowego

Zaczek-Peplinska J.

Prace Naukowe Politechniki Warszawskiej. Geodezja

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2018

|

z. 57

3--177

11

Polarization of the longitudinal Pochhammer-Chree waves

Ilyashenko A. V., Kuznetsov S. V.

Mechanics and Mechanical Engineering

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2018

|

Vol. 22, nr 4

1329--1336

EN

The exact solutions of the linear Pochhammer-Chree equation for propagating harmonicwaves in a cylindrical rod, are analyzed. Spectral analysis of the matrix dispersionequation for longitudinal axially symmetric modes is performed. Analytical expressionsfor displacement fields are obtained. Variation of wave polarization on the free surfacedue to variation of Poisson's ratio and circular frequency is analyzed. It is observed thatat the phase speed coinciding with the bulk shear wave speed all the components of thedisplacement eld vanish, meaning that no longitudinal axisymmetric Pochhammer-Chree wave can propagate at this phase speed.

12

Analiza spektralna plazmy w procesach azotowania jarzeniowego tytanu technologią aktywnego ekranu

Betiuk M., Maźniak K., Frączek T., Pawelec E.

Inżynieria Powierzchni

|

2018

|

nr 4

9--19

PL

Azotowanie jarzeniowe tytanu i jego stopów jest jedną z obróbek powierzchniowych umożliwiających wytworzenie warstw o wysokich twardościach. Celem pracy było dokonanie analizy porównawczej składu jakościowego widma procesowego uzyskanego na tytanowym ekranie aktywnym, z widmem wzorcowym w rurkach spektralnych. Plazmę procesową tworzyły gazy Ar, N2, H2 wprowadzane w przestrzeń wylądowania jarzeniowego. Analizowano widmo spektralne w trzech etapach technologii azotowania jarzeniowego tytanu którymi były: przygotowanie komory próżniowej i oprzyrządowania do procesu, aktywacja powierzchni tytanu w wyładowaniu jarzeniowym, azotowanie jarzeniowe tytanu. Przedstawiono badania oceny wpływu temperatury azotowania jarzeniowego na zmianę sygnału spektralnego plazmy H2, N2, Ar oraz analizowano oddziaływanie zmiany proporcji reaktywnych gazów H2, N2 na sygnał spektralny plazmy. Badania te doprowadziły do próby zdefiniowania nowego parametru sterującego składem mieszanki gazowej wprowadzanej w obszar wyładowania jarzeniowego. Do realizacji celów pracy wykorzystano analizator spektralny plazmy oraz stanowisko badawcze — komorę próżniową pozwalającą naprowadzenie procesu azotowania jarzeniowego na potencjale katody, plazmy oraz potencjale uzupełniającym.

EN

The glow discharge nitriding of titanium and its alloys is one of the surface treatments enabling the formation of high hardness layers. The aim of the paper was to perform a comparative analysis of the qualitative composition of the process spectrum obtained on the titanium active screen with the reference spectrum in the spectral tubes. The process plasma was formed by the gases: Ar, N2 H2 introduced into the glow discharge space. The spectral spectrum was analyzed in three stages of the technology of glow discharge nitriding of titanium, which were: preparation of the vacuum chamber and process instrumentation, activation of the titanium surface in glow discharge, glow discharge nitriding of titanium. The paper presents the studies on the evaluation of the influence of the glow discharge nitriding temperature on the change in the plasma spectral signal H2,N2, Ar and analyzes the influence of the change in the proportions of reactive gases H2,N2 on the spectral signal of the plasma. These studies led to an attempt to define a new parameter controlling the composition of the gas mixture introduced into the glow discharge area. To achieve the goals of the paper, a plasma spectral analyzer and a test stand were used - a vacuum chamber allowing the glow discharge nitriding process to be carried out at the cathode, plasma and complementary potential.

13

Analiza widmowa składowej odbitej promieniowania słonecznego docierającego do powierzchni pionowej

Knera D., Heim D.

Fizyka Budowli w Teorii i Praktyce

|

2018

|

T. 10, nr 1

25--30

PL

W pracy przedstawiono analizę widmową składowej promieniowania słonecznego odbitego od przeciwległej zabudowy i docierającego do elewacji budynku. Przeanalizowano dwie orientacje fasady, wschodnią i zachodnią, zlokalizowane w środowisku zurbanizowanym. Charakterystykę spektralną promieniowania wykonano dla promieniowania widzialnego oraz bliskiej podczerwieni. Obrazy cyfrowe wykonano z wykorzystaniem filtrów fotograficznych o znanej przepuszczalności promieniowania słonecznego. Analiza została przeprowadzona na podstawie pomiarów wykonanych od sierpnia do marca, dla wytypowanych dni charakteryzujących się nieboskłonem zachmurzonym lub bezchmurnym. Otrzymane wyniki pokazują istotną różnicę w udziale promieniowania o różnych długościach fali w całkowitym promieniowaniu docierającym do fasad, w zależności od warunków nieboskłonu, środowiska zewnętrznego i otaczającej zabudowy.

EN

The paper presents spectral analysis of solar radiation component reflected from opposite buildings and reaching the facades of the building. Two façade orientations were analyzed, eastern and western, located in the urban environment. Spectral characteristics of radiation were made for visible and near infrared radiation. Digital images were made using photographic filters with known solar transmittance. The analysis was based on measurements from August to March, for selected days with clear and overcast skies. The obtained results show a significant difference in the proportion of different wavelengths in the radiation reaching the façades depending on the conditions of the sky, the environment and the surrounding buildings.

14

Wykorzystanie zależnej od czasu widmowej reprezentacji sygnału szumu Barkhausena na potrzeby nieniszczącej oceny elementów stalowych

Psuj G., Maciusowicz M.

Badania Nieniszczące i Diagnostyka

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2018

|

nr 4

69--71

PL

Zakres zastosowań metody obserwacji magnetycznego szumu Barkhausena (BN) do nieniszczącego badania stanu lub właściwości materiałów magnetycznych stale rośnie. Z uwagi na stochastyczną naturę efektu Barkhausena niezbędne staje się użycie zaawansowanych metod analizy w celu ilościowej oceny obserwowanych zależności. Wiele czynników może wpływać na różne właściwości sygnałów BN wyrażanych w dziedzinie czasu i częstotliwości. Dlatego też obserwacja zmian dynamiki tego zjawiska wymaga analizy obu reprezentacji podczas procesu ekstrakcji cech. Z tego powodu korzystne staje się stosowanie metod transformacji czasowo-częstotliwościowych (tf) sygnałów. W tym artykule, w celu połączenia informacji dostarczonych w czasie i częstotliwości, zastosowano krótkoczasową transformatę Fouriera (ST FT). Przeprowadzono analizę uzyskanych reprezentacji tf sygnałów BN otrzymanych dla próbek stalowych o różnym stopniu zniszczenia i przedstawiono wyniki.

EN

The scope of applications of the magnetic Barkhausen noise observation (BN) method for non-destructive testing of the state or properties of magnetic materials is constantly increasing. Due to the stochastic nature of the Barkhausen effect, it is necessary to use advanced methods of analysis in order to quantify the observed relationships. Many factors can affect the various properties of BN signals expressed in the domain of time and frequency. Therefore, observation of changes in the dynamics of this phenomenon requires the analysis of both representations during the process of extraction of features. For this reason, it is preferable to use methods for transforming signals into time-frequency (tf) representation. In this article, a Short-Time Fourier Transform (ST FT) was used to combine information provided in time and frequency. The analysis of tf representations of BN signals obtained for steel samples representing various degrees of damage was performed and the results were presented.

15

The effects of anisotropy of marine magnetic anomalies on the Curie point depth estimates from spectral analysis

Wang M., Liu Z.

Acta Geophysica

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2018

|

Vol. 66, no. 5

1019--1030

EN

Azimuthally averaged power spectra are widely used in the Curie point depth (CPD) estimation with the implicit assumption that the magnetization distribution is random and uncorrelated. However, the marine magnetic anomalies are caused by bands of normal and reverse magnetization and show obvious trends. To investigate the effects of the anisotropy of marine magnetic anomalies on the CPD estimates, we develop 3D fractal striped magnetization models to produce lineated marine magnetic anomalies for the first time. We analyze the spectra anisotropy of the lineated magnetic anomalies of the synthetic fractal striped magnetization models and investigate its effects on the CPD estimates. The synthetic models and actual data show that the spectra of the lineated marine magnetic anomalies are directionally anisotropic. The amplitude response is strong and the slope of the logarithmic spectrum is large in a direction perpendicular to the stripes of magnetic anomalies, whereas the amplitude response is weak and the slope of the logarithmic spectrum is small in a direction parallel to the stripes of magnetic anomalies. The depth estimates in the perpendicular direction are close to the actual values, whereas the depths estimates in the parallel direction are significantly lower than the actual values. The actual marine magnetic anomalies of the South China Sea exhibit an anisotropic power spectrum that is consistent with the spectral anisotropy of magnetic anomalies of the synthetic fractal striped magnetization models.

16

Spatio-temporal analysis of annual rainfall in Crete, Greece

Varouchakis E. A., Corzo G. A., Karatzas G. P., Kotsopoulou A.

Acta Geophysica

|

2018

|

Vol. 66, no. 3

319--328

EN

Analysis of rainfall data from the island of Crete, Greece was performed to identify key hydrological years and return periods as well as to analyze the inter-annual behavior of the rainfall variability during the period 1981–2014. The rainfall spatial distribution was also examined in detail to identify vulnerable areas of the island. Data analysis using statistical tools and spectral analysis were applied to investigate and interpret the temporal course of the available rainfall data set. In addition, spatial analysis techniques were applied and compared to determine the rainfall spatial distribution on the island of Crete. The analysis presented that in contrast to Regional Climate Model estimations, rainfall rates have not decreased, while return periods vary depending on seasonality and geographic location. A small but statistical significant increasing trend was detected in the inter-annual rainfall variations as well as a significant rainfall cycle almost every 8 years. In addition, statistically significant correlation of the island’s rainfall variability with the North Atlantic Oscillation is identified for the examined period. On the other hand, regression kriging method combining surface elevation as secondary information improved the estimation of the annual rainfall spatial variability on the island of Crete by 70% compared to ordinary kriging. The rainfall spatial and temporal trends on the island of Crete have variable characteristics that depend on the geographical area and on the hydrological period.

17

Wieloaspektowa analiza spektralna sygnałów fonokardiograficznych

Lejkowski W., Dobrowolski A. P., Gawron B., Olszewski R.

Przegląd Elektrotechniczny

|

2017

|

R. 93, nr 10

73--76

PL

W artykule przedstawiono koncepcję analizy spektralnej sygnałów fonokardiograficznych. Zaprezentowano wyniki analizy sygnałów zawierających od kilku do kilkunastu uderzeń serca oraz sygnałów krótkich zawierających pojedyncze uderzenie serca. Przedstawiono propozycje kilkudziesięciu widmowych cech dystynktywnych oraz ocenę ich przydatności w diagnostyce schorzeń kardiologicznych.

EN

The article presents the idea of spectral analysis of phonocardiographic signals. The results of analysis of signals containing from several to over a dozen heartbeats and short signals containing only one heartbeat. Proposals dozens of spectral distinctive features and evaluate their usefulness in the diagnosis of cardiac diseases.

18

Calculation of electromagnetic component vibration of brushed direct current machines with structural units defects

Zagirnyak M., Prus V., Kushch I.

Przegląd Elektrotechniczny

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2017

|

R. 93, nr 12

191--194

EN

The special features of taking into account the basic defects of brushed direct current machines influence on the vibration component of electromagnetic nature are scientifically substantiated. It is based on the use of the modern methods for magnetic field calculation. The efficiency of the use of the developed field model and the method for its parameters calculation in the analysis of the structural units typical breakages influence on the magnetic induction vector components distribution is confirmed. The dynamic eccentricity influence on the spectral distribution of forces of magnetic nature acting on the brushed direct current machine basic pole is analyzed. It enables identification of this defect in the future.

PL

Wzięcie pod uwagę wpływu efektów bazowych w szczotkowych silnikach prądu stałego na elektromagnetycznej natury składnik drgań jest naukowo uzasadniony. Opiera się to na użyciu nowoczesnych metod obliczania pola magnetycznego. Efektywność użycia rozwiniętego modelu polowego oraz metody obliczania parametrów w analizie uszkodzeń konstrukcyjnych wpływają na rozkład składowych wektora indukcji magnetycznej została potwierdzona. Przeanalizowano wpływ dynamicznej ekscentryczności na spektralny rozkład sił natury magnetycznej, działających na podstawowy biegun szczotkowej maszyny prądu stałego. Technika ta umożliwia identyfikację defektu w przyszłości.

19

Spectral analysis of business cycles in Poland and its major trading partners

Kijek A.

Operations Research and Decisions

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2017

|

Vol. 27, No. 1

57--75

EN

The properties of business cycles in Poland and its major trading partners have been examined. The business cycle synchronization (BCS) between Poland and other countries was studied in order to assess the impact of international trade on BCS. The author applies a modification of the Fourier analysis to the estimation of cycle amplitudes and frequencies. This allows more precise estimation of the cycle characteristics than the traditional approach. Cross-spectral analysis of the cyclical components of GDP for Poland and its major trading partners enables us to study the relationships between business cycles in these countries. Comparing the international structure of Polish trade with that of EU members with the cross-spectral characteristics of GDP series allows us to investigate the links between international trade and business cycle synchronization.

20

The approximation function of bridge deck vibration derived from the measured eigenmodes

Sokol M., Komorníková M., Bacigál T., Rodríguez M. X.

International Journal of Applied Mathematics and Computer Science

|

2017

|

Vol. 27, no. 4

799--814

EN

This article deals with a method of how to acquire approximate displacement vibration functions. Input values are discrete, experimentally obtained mode shapes. A new improved approximation method based on the modal vibrations of the deck is derived using the least-squares method. An alternative approach to be employed in this paper is to approximate the displacement vibration function by a sum of sine functions whose periodicity is determined by spectral analysis adapted for non-uniformly sampled data and where the parameters of scale and phase are estimated as usual by the least-squares method. Moreover, this periodic component is supplemented by a cubic regression spline (fitted on its residuals) that captures individual displacements between piers. The statistical evaluation of the stiffness parameter is performed using more vertical modes obtained from experimental results. The previous method (Sokol and Flesch, 2005), which was derived for near the pier areas, has been enhanced to the whole length of the bridge. The experimental data describing the mode shapes are not appropriate for direct use. Especially the higher derivatives calculated from these data are very sensitive to data precision.