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1

Diurnal seismic ambient noise and seismic station performance characterization in the Bengal Basin, Bangladesh

Zannat Naharin, Farazi Atikul Haque, Kamal A. S. M. Maksud, Rahman Md. Zillur, Hossain Md. Shakhawat

Geology, Geophysics and Environment

|

2023

|

Vol. 49, no. 3

209--224

EN

Seismic ambient noise (SAN) energy can potentially blur regional and teleseismic arrivals as well as various microearthquakes at specific frequencies. Therefore, quantification of the SAN energy level in a region is required to optimize seismic station distribution for seismological investigations. Moreover, evaluation of station performance and noise source is possible from observation of SAN energy levels. The SAN energy distribution from seismic stations in the Bengal Basin (BB), Bangladesh has not yet been estimated. At the same time, this tec-tonically active and complex region is less studied using seismic methods. This study aims to quantify SAN energy and characterize its diurnal variation along with evaluating station performance at 11 seismic stations, which were temporarily installed in the deeper portion of the BB. Herein, the daily SAN energy level was determined within the period range of 0.02–30 s by estimating the power spectral density (PSD) of seismic data for 7 continuous days. SAN energy and its variation over time were observed using the probability density functions (PDFs) of PSDs and spectrograms, respectively. The sources of SAN energies at different period bands were also investigated by comparing the PSDs with daily variations in human activities, nearby noise sources, local meteorological factors (i.e., air temperature and precipitation), and sea level height. The insights from this study could be useful for the future deployment of seismic networks as well as seismological studies in the BB.

2

Flame analysis by selected methods in the frequency domain

Grądz Żaklin, Klimek Jacek, Kozak Czesław

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

|

2022

|

T. 12, nr 4

87--89

EN

Diagnostics of pulverized coal combustion can be carried out in the field of process monitoring and analysis of measurement data. The information about changes in the flame is presented in the form of time series, which can be analyzed in the time and frequency domain. The paper presents an analysis of signals of changes in the intensity of the flame glow during pulverized coal combustion using power spectral density. On the basis of the periodograms determined using the Welch method, it was possible to determine the frequency components present in the signal.

PL

Diagnostyka spalania pyłu węglowego może być przeprowadzana w zakresie monitorowania przebiegu procesu oraz analizy danych pomiarowych. Informacje o zmianach zachodzących w płomieniu przedstawione są w postaci szeregów czasowych, które mogą być analizowane w dziedzinie czasu i czestotliwości. W artykule przedstaiono analize sygnałów zmian intesnywności świecenia płomenia podczas spalania pyłu węglowego przy użyciu gęstości widmowej mocy. Na podstawie periodogramów wyznaczonych z zastosowaniem metody Welcha możliwe było określenie składowych czestotliwościowych występujących w sygnale.

3

Evaluation procedure for blowing machine monitoring and predicting bearing SKFNU6322 failure by power spectral density

Castilla-Gutiérrez Javier, Fortes Garrido Juan Carlos, Davila Martín Jose Miguel, Grande Gil Jose Antonio

Eksploatacja i Niezawodność

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2021

|

Vol. 23, no. 3

522--529

EN

This work shows the results of the comparative study of characteristic frequencies in terms of Power Spectral Density (PSD) or RMS generated by a blower unit and the SKFNU322 bearing. Data is collected following ISO 10816, using Emonitor software and with speed values in RMS to avoid high and low frequency signal masking. Bearing failure is the main cause of operational shutdown in industrial sites. The difficulty of prediction is the type of breakage and the high number of variables involved. Monitoring and analysing all the variables of the SKFNU322 bearing and those of machine operation for 15 years allowed to develop a new predictive maintenance protocol. This method makes it possible to reduce from 6 control points to one, and to determine which of the 42 variables is the most incidental in the correct operation, so equipment performance and efficiency is improved, contributing to increased economic profitability. The tests were carried out on a 500 kW unit of power and It was shown that the rotation of the equipment itself caused the most generating variable of vibrational energy.

4

Assessment and recognition of pre and co seismic electromagnetic signatures from magnetotelluric data: a case study from Koyna–Warna seismoactive region, India

Vijaya Kumar P. V., Rawat Vishal S., Patro Prasanta K., Gupta A. K., Babu Narendra

Acta Geophysica

|

2021

|

Vol. 69, no. 1

1--15

EN

Continuously monitored magnetotelluric (MT) time series data were used to identify the short-term earthquake co-seismic and pre-seismic electromagnetic phenomenon. The co-seismic behavior of the MT time series data recorded at 15 Hz sampling frequency is analyzed for the earthquake that occurred on November 24, 2007, of Mw =4.6. The wavelet analysis of the MT time series data shows signifcant enhancement at 3–6 Hz frequency band in the scalogram during the earthquake in comparison with pre- and post-time. The signifcant enhancement in the scalogram is related to the onset of the main shock of the earthquake. In this paper, we have also shown the precursory signatures of several earthquake magnitudes (Mw) ranging from 3.9 to 4.9 and the focal depth extending from 5 to 10 km mainly dominated by normal and strike-slip faulting. The spectral polarization ratio technique was implemented on these events to identify the precursory signatures. A few days before the earthquake, a signifcant anomaly was identifed for most of the earthquakes using this technique. This prominent anomaly is correlated with Dst index, which provides information about the ionosphere and magnetosphere responses in the presence of the solar wind and interplanetary magnetic feld. We inferred the unusual behavior prior to the earthquake is related to the precursory signature, but not related to the solar-terrestrial efect. The complex tectonic settings in the study region suggest that both electrokinetic and seismic dynamo mechanisms are the probable mechanisms playing an important role in generation of co- and pre-seismic electromagnetic signals.

5

Application of probabilistic power spectral density technique to monitoring the long-term vibrational behaviour of cern seismic network stations

Łacny Łukasz, Ścisło Łukasz, Guinchard Michael

Vibrations in Physical Systems

|

2020

|

Vol. 31, nr 3

art. no. 2020311

EN

In this paper, a statistical method called Probabilistic Power Spectral Density based on the standard spectral density plots is presented and utilized. The practical application and utility of this method are shown based on the seismic data collected over a long period from three seismic stations connected within the so-called CERN Seismic Network. The analysis was used to observe and monitor the increase in ambient vibration levels over a long period during the heightened heavy machinery work close to LHC Point 1 (ATLAS detector).

6

Teoretyczne i przydatne eksperymentalnie modele szumów

Kowalczyk Adam

Przegląd Elektrotechniczny

|

2020

|

R. 96, nr 11

45--49

PL

W artykule zwrócono uwagę na potrzeby badawcze w określeniu przydatnych teoretycznie i praktycznie modeli sygnałów stochastycznych. Przedstawiono modele teoretyczne mało przydatne praktycznie: szum biały i szum biały po przejściu przez układ inercyjny. Opisano modele teoretyczne szumów dolnopasmowych przydatne praktycznie. Podano przykładowe charakterystyki teoretyczne i eksperymentalne szumów.

EN

The article brings to attention the research needs in determining theoretically and practically useful models of stochastic signals. It presents theoretical models of little practical use: white noise and white noise after passing through an inertial system. Practically useful theoretical models of low-band noises were described. Examples of theoretical and experimental characteristics of noises were provided.

7

Surface micromorphology analysis of Cu/Ni nanocomposite thin films by power spectra density and fractal geometry

Nikpasand Kimia, Elahi Seyed Mohammad, Sari Amir Hossein, Boochani Arash

Materials Science Poland

|

2020

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Vol. 38, No. 2

328--333

EN

Copper (Cu) and nickel (Ni) nanoparticles have been grown simultaneously on glass and silicon substrates by RF sputtering method to form three Cu/Ni nanocomposites at different deposition times. The existence of Cu and Ni peaks in the X-ray diffraction (XRD) profiles confirms the crystalline structure of samples with Cu and Ni atomic content which have also been characterized by Rutherford backscattering (RBS) method. Moreover, the structural and morphological properties of the prepared nanocomposites have been compared with respect to their morphologies by means of atomic force microscopy (AFM) analysis. In order to compare the surface roughness over different spatial frequency ranges and evaluate surface quality, power spectral density (PSD) of each sample has been extracted from AFM data and also, the experimental and theoretical results have been compared. The fractal nature of these nanocomposites has been finally discussed.

8

Nowy impuls ultra szerokopasmowy i jego właściwości

Witenberg A.

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

|

2018

|

nr 6

297--299, CD

PL

Ultra szerokopasmowa technika modulacji i przesyłania sekwencji ultrakrótkich impulsów jest intensywnie rozwijającą się technologią komunikacji bezprzewodowej. Zastępuje ona tradycyjną technikę radiową transmisją impulsów o bardzo małej energii w szerokim zakresie częstotliwości na odległość do 10 metrów. Powszechnie stosuje się impulsy o kształcie pochodnych funkcji Gaussa. W pracy zaproponowano nowy impuls ultra szerokopasmowy o kształcie zmodyfikowanej funkcji rozkładu Cauchy'ego. Przedstawiono jego właściwości i porównano z impulsami Gaussa.

EN

UWB is a modulation and data transmission method which has potential to charge the wireless technique. It is interesting technology for wireless communications. It can replace traditionally carrier-band radio transmission by pulse-based transmission using ultrawideband frequency, but a very low energy, over distances at about 10 meters. The Gaussian monocycle (first derivative of the Gaussian pulse) and his derivatives are commonly used for UWB. In this paper we propose a new ultrawideband impulse, named Cauchy impulse, with the shape of the modified Cauchy distribution function. Its properties are presented and compared to Gaussian pulses.

9

Effect of Feature Extraction on Automatic Sleep Stage Classification by Artificial Neural Network

Prucnal M., Polak A. G.

Metrology and Measurement Systems

|

2017

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Vol. 24, nr 2

229--240

EN

EEG signal-based sleep stage classification facilitates an initial diagnosis of sleep disorders. The aim of this study was to compare the efficiency of three methods for feature extraction: power spectral density (PSD), discrete wavelet transform (DWT) and empirical mode decomposition (EMD) in the automatic classification of sleep stages by an artificial neural network (ANN). 13650 30-second EEG epochs from the PhysioNet database, representing five sleep stages (W, N1-N3 and REM), were transformed into feature vectors using the aforementioned methods and principal component analysis (PCA). Three feed-forward ANNs with the same optimal structure (12 input neurons, 23 + 22 neurons in two hidden layers and 5 output neurons) were trained using three sets of features, obtained with one of the compared methods each. Calculating PSD from EEG epochs in frequency sub-bands corresponding to the brain waves (81.1% accuracy for the testing set, comparing with 74.2% for DWT and 57.6% for EMD) appeared to be the most effective feature extraction method in the analysed problem.

10

Numerical synthesis of the track alignment and applications. Part I: The synthesis method

Dumitriu M.

Transport Problems

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2016

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T. 11, z. 1

19--28

EN

This paper features a method to synthesize the track irregularities, by which the alignment may be analytically represented by a pseudo-stochastic function, as well as the implementation of such method in the numerical simulation of the dynamic behaviour of the railway vehicles. The method thus suggested allows a convenient formulation of the limits of the interval specific to the wavelengths of the track lateral irregularities, so that it will be representative for the frequency range of the vehicle lateral vibrations. The Part I of this paper demonstrates the method to synthesize the track alignment and its basic elements –the power spectral density of the track irregularities, as per ORE B176 and the values associated with the track quality levels, mentioned in the UIC 518 Leaflet. The Part II introduces the results of the numerical simulations regarding the dynamic behaviour of the railway vehicle during the circulation on a tangent track with lateral irregularities, synthesized as in the method herein.

FR

L’article présente une méthode pour la synthèse des irrégularités de la voie, aveclaquelle le dressage peut être représenté analytiquement par une fonction pseudoaléatoire et aussi l’application de cette méthode dans la simulation numérique du comportement dynamique latérale des véhicules ferroviaires. La méthode proposée permet de choisir convenablement les limites d’intervalles spécifiques des longueurs d’onde des irrégularités latérales de la voie, de sort qu’elles sont représentativespour le domaine de fréquence de la vibration latérale du véhicule. La Partie I de l’article, analyse la méthode de synthèse du dressage de la voie et donne ses éléments de base –la densité spectrale de puissance décrite conformant ORE B176 et les quantités associées de la voie précisées dans la Fiche UIC 518. La Partie II présente les résultats des simulations numériques du le comportement dynamique latéral du véhicule pendant la circulation sur une voie en alignement avec des irrégularités latérales synthétisées en utilisant la méthode présentée.

11

A new baroreflex sensitivity index based on improved Hilbert–Huang transform for assessment of baroreflex in supine and standing postures

Singh A., Saini B. S., Singh D.

Biocybernetics and Biomedical Engineering

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2016

|

Vol. 36, no. 2

355--365

EN

The aim of this study is to propose a new baroreflex sensitivity (BRS) index using improved Hilbert–Huang transform (HHT) using weighted coherence (CW) criterion and apply it to assess baroreflex in supine and standing postures. Improved HHT is obtained by addressing the mode mixing and end effect problems associated with empirical mode decomposition which is a required step in the computation of HHT and thus mitigating the unwanted low frequency component from the power spectrum. This study was first performed on synthetic signals generated using integral pulse frequency model and further extended to real RR interval and systolic blood pressure records of 50 healthy subjects, 20 post acute myocardial infarction patients undergoing postural stress from supine to standing position. Evaluation is also performed on standard EuroBaVar database, comprising of 21 subjects, under supine and standing positions. The results are (i) enhanced values of supine-to-standing low frequency BRS index (α-LF) equal to 1.78 and high frequency BRS index (α-HF) equal to 2.48 are obtained using improved HHT compared to standard HHT (α-LF = 1.54, α-HF = 2.36) and traditional power spectral density (α-LF = 1.55, α-HF = 2.34) for healthy subjects, (ii) there is an increased rate of change of LF/HF power ratios from supine to standing positions, and (iii) number of BRS responses obtained using CW criterion are greater than those obtained by using mean coherence criterion. In conclusion, the new BRS index takes into consid-eration the non-linear nature of interactions between heart rate variability and systolic blood pressure variability.

12

Reasons for the experimental research of gas outflows based on the signals of weak interactions between the tested model of the gas pipeline, and tested equalizer

Grądzki R., Golak K., Lindstedt P., Bartoszewicz B.

Journal of KONBiN

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2015

|

No. 2 (34)

39--48

EN

This article applies diagnosing issues outflows of gas pipelines using specialized research equipment - equalizers. Variant with only two measuring devices (equalizers), arranged on the inlet and outlet of the pipeline, and the standard pressure transducers and flow rate were considered. The signals from the system and research equipment (equalizers) are the basis for the development of new method to test outflow of gas pipeline, which is based on the quotient of the power spectral density of signals generated by the equalizer (diagnoser) and signals measured using standard pressure transducers and flow rate. Possible use to analysis the signals power will allow go from signal diagnostic for more effective parametric diagnostic.

PL

Artykuł dotyczy zagadnień diagnozowania wycieków z gazociągów za pomocą dwóch specjalistycznych urządzeń badawczych – korektorów. Rozważany jest wariant tylko z dwoma urządzeniami pomiarowymi (korektorami), rozmieszczonymi na wlocie i wylocie rurociągu oraz zastosowaniu do pomiaru standardowych przetworników ciśnienia i natężenia przepływu. Generowane sygnały układu są podstawą do opracowania nowej metody badania wycieku z gazociągu za pomocą ilorazu gęstości widmowej mocy sygnałów generowanych przez korektor (diagnozer) do sygnałów generowanych przez standardowe przetworniki. Wykorzystanie do analizy mocy sygnałów pozwoli przejść od diagnostyki sygnałowej do skuteczniejszej diagnostyki parametrycznej.

13

Badanie czujników inercjalnych z wykorzystaniem metody analizy widmowej

Paszek J., Kaniewski P.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 9

702--704

PL

W artykule przedstawiono wyniki badań losowych zakłóceń pomiarów czujników inercjalnych z wykorzystaniem metody analizy widmowej. Do uzyskania wyników wykorzystano metodę analizy Gęstości Widmowej Mocy (GWM) sygnału z czujnika w celu wyznaczenia charakterystyk źródeł zakłóceń. Przedstawione zostały wyniki badań eksperymentalnych oraz ich porównanie z wynikami uzyskanymi metodą wariancji Allana (AV). Na koniec dokonano porównania wyników graficznej interpretacji krzywych GWM i AV analizowanych danych.

EN

The accuracy of Inertial Navigation Systems (INS) is limited by the performance of used inertial sensors. The measurement precision of gyroscopes and accelerometers is limited due to systematic and random errors. The systematic errors are deterministic and can be easily removed from measurements using mathematical modeling and calibration. The origin of the random errors is electronic noise which interferes in the full measurement spectrum. Thus, this error cannot be fully removed from the acquired data using filtering. Estimation of the random noise errors can be done using Power Spectral Density (PSD) or Allan Variance (AV) method [1, 2, 4, 6]. Both methods are used to decompose noise to its basic sources described by the power spectral model 1/fn [2, 3]. In this paper, the estimation of random noises using the PSD method is shown. The error model used for sensor analysis and the methodology of experiment are described. The spectral analysis of the random errors of the inertial sensors allows comparing the performance of the sensors made in different technologies i.e. microelectro-mechanical gyroscopes (MEMS) and fiber optic gyroscopes (FOG). The PSD and AV methods give information about noise sources which can be used to model and simulate the inertial sensors noise.

14

Fourier spectrum related properties of vibration signals in accelerated motor aging applicable for age determination

Siljak H., Subasi A.

Eksploatacja i Niezawodność

|

2014

|

Vol. 16, no. 4

616--621

EN

A series of computations based on the Fourier spectrum of vibration signals collected in artificial aging processes have been applied in order to tackle trends existing in the signals' sequence. In this study, features extracted from the (Fourier) spectrum of the vibration signal and expressing monotonic changes with respect to the motor age namely mean frequency, low order statistics of the power spectral density and cepstrum are used. Independence of the time domain data allows independent analysis. Results obtained in case of artificial aging are compared with results in case of controlled bearing faults with increasing severity. Clear distinctions are made and conclusions are drawn from the different behavioural patterns. Future research directions are indicated both in practical and theoretical sense.

PL

Wykonano serię obliczeń opartych na widmie Fouriera sygnałów wibracyjnych zebranych podczas procesów sztucznego starzenia w celu określenia trendów istniejących w sekwencji tych sygnałów. Cechy, jakie można wyodrębnić w (fourierowskim) widmie sygnału drgań, które wykazują monotoniczne zmiany w odniesieniu do wieku silnika wykorzystanego w niniejszym badaniu, to średnia częstotliwość, statystyki niskiego rzędu widmowej gęstości mocy oraz cepstrum. Niezależność danych w dziedzinie czasu umożliwia niezależną analizę. Wyniki sztucznego starzenia porównano z wynikami otrzymanymi podczas dokonywania kontrolowanych uszkodzeń łożyska o rosnącym nasileniu. Wyciągnięto wnioski z obserwowanych, wyraźnie różnych wzorców zachowań. Wskazano przyszłe kierunki badań zarówno w aspekcie praktycznym jak i teoretycznym.

15

Heart rate variability assessment with rational-dilation wavelet transform

Buchner T., Grzyb G., Krzesiński P.

Bio-Algorithms and Med-Systems

|

2013

|

Vol. 9, no. 1

29--35

EN

Wavelet transform on a rational dilation is proposed as a method of assessment of spectral power in low and high frequency (LF and HF, respectively) bands for heart rate variability (HRV) analysis. One of the unique properties of this method is a possibility to align the band limits of certain scales with the limits of ranges LF and HF used in HRV analysis. The method parameters are optimized for use in the context of HRV analysis. Suitable examples are tilt test recordings analyzed using the optimized rational-dilation wavelet transform method.

16

Bedform effect on the reorganization of surface and subsurface grain size distribution in gravel bedded channels

Singh A., Guala M., Lanzoni S., Foufoula-Georgiou E.

Acta Geophysica

|

2012

|

Vol. 60, no. 6

1607-1638

EN

Quantification of river bedform variability and complexity is important for sediment transport modeling as well as for characterization of river morphology. Alluvial bedforms are shown to exhibit highly nonlinear dynamics across a range of scales, affect local bed roughness, and vary with local hydraulic, hydrologic, and geomorphic properties. This paper examines sediment sorting on the crest and trough of gravel bedforms and relates it to bed elevation statistics. The data analysed here are the spatial and temporal series of bed elevation, grain size distribution of surface and subsurface bed materials, and sediment transport rates from flume experiments. We describe surface topography through bedform variability in height and wavelength and multiscale analysis of bed elevations as a function of discharge. We further relate bedform migration to preferential distribution of coarse and fine sediments on the troughs and crests, respectively, measuring directly surface and subsurface grain size distributions, and indirectly the small scale roughness variations as estimated from high resolution topographic scans.

17

Speech Segmentation Algorithm Based on an Analysis of the Normalized Power Spectral Density

Pekar D., Tsikhanenka S.

Journal of Telecommunications and Information Technology

|

2010

|

nr 4

44-49

EN

This article demonstrates a new approach to speaker independent phoneme detection. The core of the algorithm is to measure the distance between normalized power spectral densities in adjacent, short-time segments and verify it based on velocity of changes of values of short-time signal energy analysis. The results of experiment analysis indicate that proposed algorithm allows revealing a phoneme structure of pronounced speech with high probability. The advantages of this algorithm are absence of any prior information on a signal or model of phonemes and speakers that allows the algorithm to be speaker independent and have a low computation complexity.

18

Power spectral density in balance assessment. Description of methodology

Syczewska M., Zielińska T.

Acta of Bioengineering and Biomechanics

|

2010

|

Vol. 12, no. 4

89-92

EN

One of the methods used in clinical setting to assess the balance function is the measurement of the centre of pressure trajectory (COP). The COP trajectory is strongly dependent on the body centre of mass trajectory (COM), but in case of balance problems the corrective signals influence this dependence. The aim of the present study is to explore the possibility of using power spectral density function of the COP vs. COM signal in assessing the amount of correction signals. As the aim was a methodological one, only one healthy adult subject participated in the study. This subject performed five balance tasks of increasing difficulty. The COP trajectory was recorded using the Kistler force plate, and COM trajectory was calculated based on the marker trajectories placed on the subject’s body and simultaneously recorded with VICON 460 system. The COM data were subtracted from COP trajectory in anteroposterior (AP) and lateral direction. Next the power spectral density (PSD) was calculated for the new signals. The power spectral density is very low for easiest condition, but increases with the difficulty of task. Moreover, it also provides information in which plane (sagittal or frontal) more correction movements are needed to maintain stability.

19

Badania kawitacji w olejach izolacyjnych

Szmechta M., Zmarzły D.

Przegląd Elektrotechniczny

|

2008

|

R. 84, nr 10

40-43

PL

W artykule zawarto wybrane wyniki analizy spektralnej sygnału emisji akustycznej obserwowanej podczas pobudzania ultradźwiękami szklanej okrąglo-dennej kolby wypełnionej nowym olejem izolacyjnym. Przy odpowiednich wartościach wartości skutecznej i częstotliwości sygnału zaobserwowano pęcherzyki kawitacyjne. Implodujące pęcherzyki są odpowiedzialne za występowanie szerokopasmowego szumu w widmie sygnału emisji akustycznej. Na podstawie wyznaczonych widm zaproponowano wskaźnik kawitacji reprezentujący intensywność zjawiska.

EN

The paper presents some spectral analysis results of acoustic emission observed during ultrasound driven round bottomed fiask with fresh insulating oil inside. At suitable value of signal rms value and freąuency many of cavitation bubbles were observed. Collapsing bubbles were responsible for broadband noise included In acoustic emission signal spectra. To represent the cavitation intensity a simple cavitation indicator based on power spectral densities of acoustic emission signal was proposed. (lnvestigation of cavitation in insulating oils).

20

Possibilities of application of stochastic process theory in evaluation of tribological experiment

Pršan J., Kučera M.

Technical Sciences / University of Warmia and Mazury in Olsztyn

|

2007

|

nr 10

59-68

EN

Mathcad 11, a software product of Mathsoft, was used for random numbers generation. The program enables generating sets of random numbers of various statistical properties. We used random distribution for our application. The set of random numbers had undergone statistical analysis using statistical dynamics methods. We applied low-permeable numeric filter. After filtration, the statistical analysis results have shown, that the power spectrum is relatively low. This has been confirmed also by the Fisher test. There are 15 important frequencies total, ranging in interval of 0.5 Hz - 6.2 Hz. Statistically, the most signifficant frequency is 0.5 Hz. Evaluated and described courses with their frequency spectrums can be used as input parameters of rationalizing and optimizing methods of tools' and machinery's design modification. They can be also used as input data of load in adhesive wear testing within tribologic experiments.

PL

Do wygenerowania zbioru liczb przypadkowych zastosowano produkt Mathcada 11 firmy Mathsoft. Program pozwala na generowanie liczb przypadkowych o różnych właściwościach statystycznych. Na potrzeby eksperymentu przyjęto podział przypadkowy. Zbiór liczb przypadkowych poddano analizie statystycznej z zastosowaniem metod dynamiki statystycznej. W analizie zastosowano dolnoprzepuszczalny filtr liczbowy. Po filtracji analiza statystyczna wykazała, że realizacyjne spektrum częstotliwości jest relatywnie niskie, co potwierdzono również w teście Fishera. Istotnych jest tylko 15 częstotliwości w zakresie 0,5÷6,2 Hz. Statystycznie najbardziej istotna jest częstotliwość 0,5 Hz. Opisywane funkcje i ich spektra częstotliwościowe mogą być wykorzystane jako wstępne parametry metod optymalizowania konstrukcyjnego narzędzi i maszyn, a także jako wstępne parametry obciążeń w badaniach trybologicznych związanych z adhezyjnym zużyciem materiałów.