Stochastic model of the gearbox pair vibration

The model of vibration signal of gearbox pair in the form of periodically correlated non-stationary random process is considered. It is shown that hidden periodicities in biperiodic correlated random process mean and covariance function, characterizing the vibrations of gearbox pair can be detected using the component and least square methods. Seven particular cases of the bi-rhythmic hidden periodicity for different modulation modes are analyzed.

Determination of Periodic Variations in Sub-Daily GPS Positions of Volcanic Areas

Deformation caused by a volcano (e.g., from volcanic activity) can be a good indicator of volcanic processes; ground deformation measurements using geodetic tools can be useful to monitor this movement. This study concentrates on detecting short-term movements occurring during both low activity periods and the eruptive stages of a volcano on the island of Montserrat by using sub-daily (epoch-by-epoch) GPS data processing approaches. The GPS data are obtained from UNAVCO for stations surrounding the Soufrière Hills Volcano during the May 20, 2006, volcanic eruption period and during the Fall 2012 period (a period of lower activity). In order to analyze hidden periodicities within the data, Least Squares Spectral Analysis has been used. Our results show that the sub-daily peaks are located at near diurnal and semidiurnal tidal constituents (K1 and K2) with up to 5 mm amplitude.

Design Wind Speeds Using Fast Fourier Transform

In this chapter, a study on the effects of transforming wind speed data, from a time series domain into a frequency domain via Fast Fourier Transform (FFT), is presented. The wind data is first transformed into a stationary pattern from a non-stationary pattern of time series data using statistical software. This set of time series is then transformed using FFT for the main purpose of the chapter. The analysis is done through MATLAB software, which provides a very useful function in FFT algorithm. Parameters of engineering significance such as hidden periodicities, frequency components, absolute magnitude and phase of the transformed data, power spectral density and cross spectral density can be obtained. Results obtained using data from case studies involving thirty-one weather stations in Malaysia show great potential for application in verifying the current criteria used for design practices.