Amplitude Power Spectral Density Research Articles

Ensemble power spectral density of SDSS quasars in UV/optical bands

Context. Quasar variability has proven to be a powerful tool to constrain the properties of their inner engine and the accretion process onto supermassive black holes. Correlations between UV/optical variability and physical properties have been long studied with a plethora of different approaches and time-domain surveys, although the detailed picture is not yet clear. Aims. We analysed archival data from the SDSS Stripe-82 region to study how the quasar power spectral density (PSD) depends on the black hole mass, bolometric luminosity, accretion rate, redshift, and rest-frame wavelength. We developed a model-independent analysis framework that could be easily applied to upcoming large surveys such as the Legacy Survey of Space and Time (LSST). Methods. We used light curves of 8042 spectroscopically confirmed quasars, observed in at least six yearly seasons in five filters ugriz. We split the sample into bins of similar physical properties containing at least 50 sources, and we measured the ensemble PSD in each of them. Results. We find that a simple power law is a good fit to the power spectra in the frequency range explored. Variability does not depend on the redshift at a fixed wavelength. Instead, both PSD amplitude and slope depend on the black hole mass, accretion rate, and rest-frame wavelength. We provide scaling relations to model the observed variability as a function of the physical properties, and discuss the possibility of a universal PSD shape for all quasars, where frequencies scale with the black hole mass, while normalization and slope(s) are fixed (at any given wavelength and accretion rate).

Preliminary Results on Low Frequency Passive Seismic (LFPS) Study in Lake Toba

Sumatra Island is an island located in the subduction zone of the Indo-Australian plate towards Eurasia. The geological structure on the island of Sumatra is the Semangko Fault. There is active volcanic activity, such as the Bukit Barisan Mountains, which makes Sumatra Island vulnerable to volcanic eruptions. The study was conducted in Lake Toba, North Sumatra, using earthquake data from the IRIS station. The purpose of this study is to investigate the amplitude in determining the presence of fluid reservoirs (magma) and to analyze the volcanics of the Lake Toba region using the Low Frequency Passive Seismic (LFPS) method by utilizing attributes such as maximum amplitude Vertical-to-Horizontal Spectral Ratio (VHSR), maximum amplitude of Power Spectral Density (PSD) Z, and the maximum amplitude spectrum of the Z component, which are used as indicators to connect the subsurface fluid reservoir by looking at the spectrum curve. Previous research has linked the presence of a reservoir to the peak amplitude spectrum in the vertical component in the frequency range 1-6 Hz. Based on the research results from the analysis of all attribute parameters obtained, the maximum anomaly of the maximum VHSR amplitude spectrum, the maximum PSD Z amplitude, and the maximum Z component amplitude spectrum indicate that the location with the highest subsurface fluid reservoir potential is in the Northwest-Southeast around Lake Toba and Samosir island. These results support previous research. Volcanic activity in Lake Toba is relatively lower because the amplitude spectrum values of all attribute parameters are not too high.

Spectral features of non-nutritive suck dynamics in extremely preterm infants.

Non-nutritive suck (NNS) is used to promote ororhythmic patterning and assess oral feeding readiness in preterm infants in the neonatal intensive care unit (NICU). While time domain measures of NNS are available in real time at cribside, our understanding of suck pattern generation in the frequency domain is limited. The aim of this study is to model the development of NNS in the frequency domain using Fourier and machine learning (ML) techniques in extremely preterm infants (EPIs). A total of 117 EPIs were randomized to a pulsed or sham orocutaneous intervention during tube feedings 3 times/day for 4 weeks, beginning at 30 weeks post-menstrual age (PMA). Infants were assessed 3 times/week for NNS dynamics until they attained 100% oral feeding or NICU discharge. Digitized NNS signals were processed in the frequency domain using two transforms, including the Welch power spectral density (PSD) method, and the Yule-Walker PSD method. Data analysis proceeded in two stages. Stage 1: ML longitudinal cluster analysis was conducted to identify groups (classes) of infants, each showing a unique pattern of change in Welch and Yule-Walker calculations during the interventions. Stage 2: linear mixed modeling (LMM) was performed for the Welch and Yule-Walker dependent variables to examine the effects of gestationally-aged (GA), PMA, sex (male, female), patient type [respiratory distress syndrome (RDS), bronchopulmonary dysplasia (BPD)], treatment (NTrainer, Sham), intervention phase [1, 2, 3], cluster class, and phase-by-class interaction. ML of Welch PSD method and Yule-Walker PSD method measures revealed three membership classes of NNS growth patterns. The dependent measures peak_Hz, PSD amplitude, and area under the curve (AUC) are highly dependent on PMA, but show little relation to respiratory status (RDS, BPD) or somatosensory intervention. Thus, neural regulation of NNS in the frequency domain is significantly different for each identified cluster (classes A, B, C) during this developmental period. Efforts to increase our knowledge of the evolution of the suck central pattern generator (sCPG) in preterm infants, including NNS rhythmogenesis will help us better understand the observed phenotypes of NNS production in both the frequency and time domains. Knowledge of those features of the NNS which are relatively invariant vs. other features which are modifiable by experience will likewise inform more effective treatment strategies in this fragile population.

Experimental on the fatigue failure areas of wind turbine blades’ rotating fundamental frequency

The dominant type of vibration in wind turbine blades is flapwise vibration, which causes fatigue loading owing to the out-of-plane alternating load, with blade breakage occurring when the load is below the strength limit. Consequently, the mechanism and distribution of alternating-load generation must be understood to reduce the fatigue load. The strain data in the flapwise direction at the characteristic position of the operating wind turbine were collected to learn the characteristics of the spanwise distribution of the strain power spectral density (PSD) amplitude, to explore the fatigue damage-prone area and the generation mechanism, and to reveal the influence of the rotational speed on the spanwise distribution of the strain. It was evident that linked torsional and edgewise vibrations were predominant and that the strain PSD amplitude of the 1P loading component was nonlinear because of the Brazier effect in the transition region. The fatigue failure susceptible region of the rotating blade is more accurately identified. Except for the 0.10 R position, the blade 1P component 0.70–0.75 R spanwise region is more prone to failure. The rotation speed increases the dynamic fluctuation of spanwise strain.

Operation of Diamond Solution-Gated Field-Effect Transistor in the Frequency Domain

Here, the effect of frequency-domain sensing with diamond solution-gated field-effect transistors (SGFET) was investigated, where a sine wave with different frequencies (3, 30, 300, and 3 kHz) was applied at the gate. Variation of the power spectral density (PSD) amplitudes of the drain-source current was examined by using the NaCl gate electrolyte with various concentrations. With the increase of NaCl concentration, the PSD amplitudes basically increase for hydrogen-terminal diamond SGFET, however, the change of PSD amplitudes is not so obvious. When the diamond surface is partially oxidized by the UV radiation in the atmosphere, the PSD amplitudes increase first and then decrease with the concentration of NaCl aqueous solution. And the sensitivity of oxidized diamond SGFET is higher than that of hydrogen-terminated and increases with the increase of oxidation degree.

Origins of subdiffractional contrast in optical coherence tomography.

We demonstrate that OCT images quantify subdiffractional tissue structure. Optical coherence tomography (OCT) measures stratified tissue morphology with spatial resolution limited by the temporal coherence length. Spectroscopic OCT processing, on the other hand, has enabled nanoscale sensitive analysis, presenting an unexplored question: how does subdiffractional information get folded into the OCT image and how does one best analyze to allow for unambiguous quantification of ultrastructure? We first develop an FDTD simulation to model spectral domain OCT with nanometer resolution. Using this, we validate an analytical relationship between the sample statistics through the power spectral density (PSD) of refractive index fluctuations and three measurable quantities (image mean, image variance, and spectral slope), and have found that each probes different aspects of the PSD (amplitude, integral and slope, respectively). Finally, we found that only the spectral slope, quantifying mass scaling, is monotonic with the sample autocorrelation shape.

Fatigue strain signal reconstruction technique based on selected wavelet decomposition levels of an automobile coil spring

This study aims to assess the fatigue life analysis of strain signals with the implementation of a reconstruction of the signals of the discrete wavelet transform (DWT) decomposition technique. The process involves the time and frequency information used in fatigue life analysis. Strain signals, also known as original signals, were measured based on different road conditions. The DWT method was applied to the original signals to assess the time–frequency domain characteristics. As a result, 14 decomposition signals were obtained and the fatigue life of each signal was evaluated. The decomposition signals contained lower fatigue life, which is below 108 cycles determined at levels 6 to 9. The reconstructed signals were obtained based on these selected levels. The frequency information obtained from the power spectral density (PSD) shows the elimination of high frequency, with low PSD amplitude in the reconstructed signal. The frequency range with high PSD amplitude obtained from this reconstructed signal at 20 Hz was the same as the original signal. Good fatigue life correlation between the reconstructed and original signals enable the prediction of similar fatigue life values, which are at 107 and 105 cycles for the highway and bumpy road conditions, respectively. It can be concluded that the implementation of this technique was able to provide good agreement of strain signals in fatigue life analysis.

Analysis on Food Crispness Based on Time and Frequency Domain Features of Acoustic Signal

Crispness is an important indicator of crunchy food. However, it cannot be easily quantified by sensory evaluation, due to the high subjectivity of evaluators; instrument measurement of this indicator requires much manpower and time. To improve the efficiency of food crispness prediction, this paper attempts to build a rapid, convenient, and accurate crispness analysis model. Starting with the fracturing sound of crunchy food, the authors collected the fracturing acoustic signal, conducted wavelet denoising, analyzed the eigenvalues in time and frequency domains, and constructed crispness prediction models based on multiple linear regression (MLR) and neural network, respectively. Through fracturing test and acoustic test, cluster analysis was adopted to select the typical eigenvalues of acoustic signal, including the peak amplitude of power spectral density (PSD) curve, amplitude difference, and waveform index. Based on these eigenvalues, a crispness analysis model was established, and used to predict the crispness of four kinds of food, namely, potato, sweet potato, carrot, and turnip. The results show that the BP neural network had a smaller relative error than the MLR; when the threshold was 5%, the BP neural network maintained a prediction accuracy of >90%, and achieved 100% prediction accuracy on two types of food. To sum up, this paper reveals the relationship between the food chewing sound features and food quality, laying the theoretical basis for the research of food chewing sound mechanism.

A Physical Model for Volcanic Eruption Tremor

AbstractSeismic waves are commonly used to monitor unrest before, during, and after volcanic eruptions. The source of seismic tremor during a sustained explosive volcanic eruption is not well understood. Recent observations of the 2016 eruption of Pavlof Volcano, Alaska, revealed a change in the relationship (hysteresis) between ash plume height and seismic amplitude over time. Based on similarities in physical processes and observed seismic tremor in rivers, we explore two key sources of seismic energy in the volcanic conduit: (1) forces exerted by particle impacts and (2) dynamic pressure changes by the turbulent flow. We develop a physical model calculating the seismic power spectral density (PSD), where forces on the conduit wall are convolved with the Green's function for Rayleigh waves. Using reasonable eruption parameters, the model is able to reproduce the frequency spectrum from the Pavlof eruption, although the modeled amplitudes are generally lower. We test the relative importance of different eruption parameters, including grain size, velocity, and conduit dimensions. We find that turbulence generally dominates over particle impacts. However, to reach the PSD amplitude during the Pavlof eruption, large grain sizes are required, as they have the greatest relative influence on the modeled amplitude. The hysteresis between plume height and seismic amplitude can then potentially be explained by grain size changes. The PSD shape is mostly determined by the Rayleigh‐wave quality factor Q, and substantial variations in seismic amplitude can be modeled assuming a constant mass eruption rate.

Frontal Alpha Asymmetry and Theta Oscillations Associated With Information Sharing Intention.

Social media has gained increasing importance in many aspects of everyday life, from building relationships to establishing collaborative networks between individuals worldwide. Sharing behavior is an essential part of maintaining these dynamic networks. However, the precise neural factors that could be related to sharing behavior in online communities remain unclear. In this study, we recorded electroencephalographic (EEG) oscillations of human subjects while they were watching short videos. The subjects were later asked to evaluate the videos based on how much they liked them and whether they would share them. We found that, at the population level, subjects watching videos that would not be shared had higher power spectral density (PSD) amplitudes in the theta band (4–8 Hz), primarily over the frontal and parietal sites of the right hemisphere, than subjects watching videos that would be shared. Previous studies have associated task disengagement with an increase in scalp-wide theta activation, which can be interpreted as a mind-wandering effect. This might suggest that the decision to not share the video may lead to a more automatic/effortless neural pattern. We also found that watching videos that would be shared was associated with lower PSD amplitudes in the alpha band (8–12 Hz) over the central and right frontal sites, and with more negative scores of frontal alpha asymmetry (FAA) index scores. These results may be related to previous work linking right-sided frontal EEG asymmetry to the pursuit of social conformity and avoidance of negative outcomes, such as social isolation. Finally, using support vector machine (SVM) algorithms, we show that these EEG parameters and preference rating scores can be used to improve the predictability of sharing information behavior. The information sharing-related EEG pattern described here could therefore improve our understanding of the neural markers associated with sharing behavior and contribute to studies about stimuli propagation.

Tracing the accretion history of supermassive black holes through X-ray variability: results from the ChandraDeep Field-South

We study the X-ray variability properties of distant AGNs in the Chandra Deep Field-South region over 17 years, up to $z\sim 4$, and compare them with those predicted by models based on local samples. We use the results of Monte Carlo simulations to account for the biases introduced by the discontinuous sampling and the low-count regime. We confirm that variability is an ubiquitous property of AGNs, with no clear dependence on the density of the environment. The variability properties of high-z AGNs, over different temporal timescales, are most consistent with a Power Spectral Density (PSD) described by a broken (or bending) power-law, similar to nearby AGNs. We confirm the presence of an anti-correlation between luminosity and variability, resulting from the dependence of variability on BH mass and accretion rate. We explore different models, finding that our acceptable solutions predict that BH mass influences the value of the PSD break frequency, while the Eddington ratio $\lambda_{Edd}$ affects the PSD break frequency and, possibly, the PSD amplitude as well. We derive the evolution of the average $\lambda_{Edd}$ as a function of redshift, finding results in agreement with measurements based on different estimators. The large statistical uncertainties make our results consistent with a constant Eddington ratio, although one of our models suggest a possible increase of $\lambda_{Edd}$ with lookback time up to $z\sim 2-3$. We conclude that variability is a viable mean to trace the accretion history of supermassive BHs, whose usefulness will increase with future, wide-field/large effective area X-ray missions.

The effect of denture installation at mandibular rest position on unsteady motion of the centre of pressure in postural sway

Wearing dentures has been believed to decrease the instability of the postural sway using the total length of centre of pressure (CoP) trajectory or the magnitude of its variability. However, the physical aspects of the postural sway have not been taken into account while evaluating the CoP in patients who wear dentures. The CoP fluctuations are found to show a random walk process. Therefore, changes in the random movement of CoP caused by wearing dentures should be examined by nonlinear dynamics that enables analysis of the characteristics found in the random movement. We evaluated the effect of complete denture installation on CoP sway for twenty-six edentulous patients by performing the following steps. First, we excluded subjects who did not show crossover in spectral analyses. Then, we evaluated the spectral characteristics and phase shifts of the velocities of CoP sway for the subjects who showed crossover. We found that wearing complete dentures decreased the fluctuations in the high-frequency part of the power spectral density (PSD) and the phase shift in the mediolateral direction. On the other hand, we also found that the use of complete dentures decreased the fluctuations of PSD amplitude in the anteroposterior direction. From the point of view of the kinetic energy of the musculoskeletal system, we suggested that the use of complete dentures could reduce the energy consumption for the standing posture.

Random vibration reliability of BGA lead-free solder joint

Solder joint fatigue failure under vibration loading has been a great concern in microelectronic industry. High-cycle fatigue failure of lead-free solder joints has not been adequately addressed, especially under random vibration loading. This study aims to understand the lead-free solder joint behavior of BGA packages under different random vibration loadings. At first, non-contact TV Laser holography technology was adopted to conduct experimental modal analysis of the test vehicle (printed circuit board assembly) in order to understand its dynamic characteristics. Then, its first order natural frequency was used as the center frequency and narrow-band random vibration fatigue tests with different kinds of acceleration power spectral density (PSD) amplitudes were respectively carried out. Electrical continuity through each BGA package is monitored during the vibration event in order to detect the failure of package-to-board interconnects. The typical dynamic voltage histories of failed solder joints were obtained simultaneously. Thirdly, failed solder joints were cross-sectioned and metallurgical analysis was applied to investigate the failure mechanisms of BGA lead-free solder joints under random vibration loading. The results show that the failure mechanisms of BGA lead-free solder joint vary as the acceleration PSD amplitude increases. Solder joint failure locations are changed from the solder bump body of the PCB side to the solder ball neck, finally to the Ni/intermetallic compound (IMC) interface of the package side. The corresponding failure modes are also converted from ductile fracture to brittle fracture with the increase of vibration intensity.

Wavelet based Neuro-Detector for low frequencies of vibration signals in electric motors

This study presents a Wavelet based Neuro-Detector approach employed to detect the aging indications of an electric motor. Analysis of the aging indications, which can be seen in the low frequency region, is performed using vibration signals. More specifically, two vibration signals are observed for healthy and faulty (aged) cases which are measured from the same electric motor. Multi Resolution Wavelet Analysis (MRWA) is applied in order to obtain low and high frequency bands of the vibration signals. Thus for detecting the aging properties in the spectra, the Power Spectral Density (PSD) of the subband for the healthy case is used to train an Auto Associative Neural Network (AANN). The PSD amplitudes, which are computed for the faulty case, are applied to input nodes of the trained network for the re-calling process of AANN. Consequently, the simulation results show that some spectral properties defined in low frequency region are determined through the error response of AANN. Hence, some specific frequencies of the bearing damage related to the aging process are detected and identified.

Roles of Fast-Cyclotron and Alfvén-Cyclotron Waves for the Multi-Ion Solar Wind

Using linear Vlasov theory of plasma waves and quasi-linear theory of resonant wave-particle interaction, the dispersion relations and the electromagnetic field fluctuations of fast and Alfven waves are studied for a low-beta multi-ion plasma in the inner corona. Their probable roles in heating and accelerating the solar wind via Landau and cyclotron resonances are quantified. We assume that (1) low-frequency Alfven and fast waves have the same spectral shape and the same amplitude of power spectral density; (2) these waves eventually reach ion cyclotron frequencies due to a turbulence cascade; (3) kinetic wave-particle interaction powers the solar wind. The existence of alpha particles in a dominant proton/electron plasma can trigger linear mode conversion between oblique fast-whistler and hybrid alpha-proton cyclotron waves. The fast-cyclotron waves undergo both alpha and proton cyclotron resonances. The alpha cyclotron resonance in fast-cyclotron waves is much stronger than that in Alfven-cyclotron waves. For alpha cyclotron resonance, an oblique fast-cyclotron wave has a larger left-handed electric field fluctuation, a smaller wave number, a larger local wave amplitude, and a greater energization capability than a corresponding Alfven-cyclotron wave at the same wave propagation angle \theta, particularly at $80^\circ$ < \theta < $90^\circ$. When Alfven-cyclotron or fast-cyclotron waves are present, alpha particles are the chief energy recipient. The transition of preferential energization from alpha particles to protons may be self-modulated by differential speed and temperature anisotropy of alpha particles via the self-consistently evolving wave-particle interaction. Therefore, fast-cyclotron waves as a result of linear mode coupling is a potentially important mechanism for preferential energization of minor ions in the main acceleration region of the solar wind.

The Two-Dimensional Power Spectral Density: A Connection Between 2-D Rational Functions and Linear Systems

A derivation of the power spectral density (PSD) matrix of a continuous-time, linear, constant-coefficient system with white Gaussian noise input is given. The assumption of wide-sense stationarity is not made. By transforming the two-dimensional (2-D) autocorrelation function (ACF), a 2-D spectral density is obtained that takes the system's transient behavior into account. The 2-D PSD is a non-separable rational function. The results are applicable to second-order Volterra series representations of nonlinear systems. Simulations are presented for a fourth order system that compare the 2-D PSD amplitude (both theoretical and empirical) with its 1-D counterpart on 50 realizations of a short data segment containing an initial transient.

THE LONGEST TIMESCALE X-RAY VARIABILITY REVEALS EVIDENCE FOR ACTIVE GALACTIC NUCLEI IN THE HIGH ACCRETION STATE

The All Sky Monitor (ASM) onboard the Rossi X-ray Timing Explorer (RXTE) has continuously monitored a number of Active galactic nuclei (AGNs) with similar sampling rates for 14 years from 1996 January to 2009 December. Utilizing the archival ASM data of 27 AGNs, we calculate the normalized excess variances of the 300-day binned X-ray light curves on the longest timescale (between 300 days and 14 years) explored so far. The observed variance appears to be independent of AGN black hole mass and bolometric luminosity, respectively. According to the scaling relation with black hole mass (and bolometric luminosity) from Galactic black hole X-ray binaries (GBHs) to AGNs, the break timescales which correspond to the break frequencies detected in the power spectral density (PSD) of our AGNs are larger than binsize (300 days) of the ASM light curves. As a result, the singly broken power-law (soft-state) PSD predicts the variance to be independent of mass and luminosity, respectively. Nevertheless, the doubly-broken power-law (hard-state) PSD predicts, with the widely accepted ratio of the two break frequencies, that the variance increases with increasing mass and decreases with increasing luminosity, respectively. Therefore, the independence of the observed variance on mass and luminosity suggests that AGNs should have the soft-state PSDs. If taking into account the scaling of breaking timescale with mass and luminosity synchronously, the observed variances are also more consistent with the soft-state than the hard-state PSD predictions. With the averaged variance of AGNs and the soft-state PSD assumption, we obtain a universal PSD amplitude of $0.030\pm0.022$. By analogy with the GBH PSDs in the high/soft state, the longest timescale variability supports the standpoint that AGNs are scaled-up GBHs in the high accretion state, as already implied by the direct PSD analysis.

Identification Fluctuation of Aerostatic Guideway

The fluctuation of gas film of aerostatic guideway has been the main factor of the workpiece waviness in ultra-precision machining. The stiffness equation of a double row orifice of aerostatic guideway is derived by using Reynolds equation in order to analyze the performance of aerostatic guideway,the measurement experiment of corresponding static stiffness of aerostatic guideway is carried out to verify the correctness and feasibility of the established model of stiffness. Dynamic model of aerostatic guideway is established by combining the modal analysis result. The simulated results of stiffness and fluctuation frequency with the variation of thickness of gas film are obtained according to the dynamic model; the effect of fluctuation of gas film on the machining result is analyzed on the basis of the amplitude of vibration. Wavelet transform is used to decompose the measured signal of workpiece into low frequency signal and high frequency signal in every scale,and the power spectral density is used to analyze high frequency signal. Which scale the signal of gas film fluctuation lies in is identified according to the frequency of guideway system,the impact of gas fluctuation on the machining can be derived from the amplitude of power spectral density.

Spectral Analysis of the Selected Accelerations and Orbital Elements for the Goce Satellite Orbit

Spectral Analysis of the Selected Accelerations and Orbital Elements for the Goce Satellite OrbitThe work contains the results of research of the simulated GOCE satellite orbit. For the 30-day orbit determination the Cowell numerical integration of the eighth order was used and the geopotential was described by means of the EGM96 model. The selected accelerations and the Keplerian elements were computed along this orbit. These accelerations included the satellite accelerations due to: the geopotential, the Earth tides and the ocean tides (the radial component for both), the gravitation of the Moon, the gravitation of the Sun, the gravitation of the Venus and the relativity effects.The computed accelerations and Keplerian elements were treated as the input data for the DFT algorithm (Discrete Fourier Transform) to determine their spectral characteristics, i.e. the amplitude power spectral densities (PSD). Additionally, the averages and standard deviations were obtained for the aforementioned accelerations and Keplerian elements.The numerous periodic components were identified. The characteristic resonances with the satellite orbital period, with the Earth's rotation period and with the Moon's synodic period were described.

Ride vibration environment of tracked sidewalk snowploughs: spectral classification

A spectral class is defined in the 0.5 to 40 Hz frequency range to characterise the vibration at or near the seat attachment point in tracked sidewalk snowploughs during normal operating conditions. The spectral class is defined for the vibrational modes involving longitudinal (x-axis), lateral (y-axis) and vertical (z-axis) motions, and angular motions along the roll and pitch axes. The definition of this spectral class for the various vibrational modes is based upon field measured data involving 20 combinations of vehicles (Bombardier SW-48) and operating tasks associated with the use of this type of vehicle by the municipalities. The spectral class is defined by a function which approximates the amplitude of the mean power spectral density (PSD) of measured acceleration in the 0.5– 40 Hz frequency range for the various vibrational modes. A spectral class defining more severe vibration conditions approximating the envelope of maximum PSD amplitude values is further proposed to be considered as input in laboratory seat performance testing. For both mean and severe vibration conditions, the frequency-weighted and unweighted rms accelerations associated with the various modes of vibration characterising the spectral class are also provided based upon the integration of the derived acceleration PSD functions. The determination of crest factors associated with the measured data is also realised on the basis of the probability distribution function of instantaneous acceleration values evaluated for all the segments of acceleration time signals of one minute duration retained to characterise the vibration.