Wavelet Power Spectrum Analysis Research Articles

Study on Nonlinear Cutting Forces Phenomenon of Difficult-to-Machining Materials

To investigate the nonlinear phenomena of cutting forces when machining difficult-to-machining materials in the high-speed cutting process, system experiments by factorial design and Latin hypercube sampling design were conducted. The cutting force nonlinear characteristics were analyzed in time domain and frequency domain through wave-let analysis and power spectrum analysis. Experiments indicated that in the high-speed milling process, the characteristic curves of primary cutting forces could not strictly maintain their linearity with the variation of cutting parameters, the effect of one cutting parameter on primary cutting forces is sensitive to the combination of cutting parameters, and a lower frequency periodic signal appears when the cutting speed is above 471 m/min (spindle speed is 3000 r/min).

Responses of the Zhe-Min coastal current adjacent to Pingtan Island to the wintertime monsoon relaxation in 2006 and its mechanism

In conjunction with synchronous remotely sensed winds and sea surface temperature (SST), the spatiotemporal features of the Zhe-Min coastal current (ZMCC), especially responses of the ZMCC adjacent to Pingtan Island (PT) to the wintertime monsoon relaxation in 2006 and corresponding mechanism are investigated based on the field observations. In situ data are acquired from Conductivity-Temperature-Depth (CTD) cruise and Bottom-Mounted Moorings (BMM), which are conducted during a comprehensive survey for the Chinese Offshore Investigation and Assessment Project in winter 2006. It is revealed that the ZMCC is well mixed vertically in winter 2006. The ZMCC (<14°C) recedes during the relaxation of the wintertime monsoon and is accompanied by the enhanced northward shift of the warm, saline Taiwan Strait Mixed Water (TSMW, higher than 14°C and is constituted by the Taiwan Strait Warm Water and the Kuroshio Branch Water). And greatly enhanced southward intrusion of the ZMCC can be detected when the wintertime monsoon restores. Correspondingly, the thermal interface bounded by the ZMCC and the TSMW moves in the northwest/southeast direction, leading to periodic warm/cold reversals of the near-seabed temperature adjacent to the PT. By EOF (Empirical Orthogonal Function) analysis of the large-scale wind fields and wavelet power spectrum analysis of the water level, ocean current and the near-seabed temperature, responses of the ZMCC off the PT to wintertime monsoon relaxation are suggested to be attributed mainly to the southward propagating coastally trapped waves triggered by the impeding atmospheric fronts. As a result, ocean current and near-seabed temperature demonstrate significant quasi-5 d and quasi-10 d subtidal oscillations. By contrast, the onshore/offshore water accumulation resulted from Ekman advection driven by the local winds has minor contributions.

Time evolution of short and intermediate term periodicities of electrons at geosynchronous orbit during solar cycle 23 and 24: A wavelet approach

In this paper, we investigate short and intermediate-term periodicities and their time variations in energetic> electron flares at geosynchronous altitude in two different energy bands for the complete solar cycle 23 and a part of the current cycle 24 using data from Geostationary Operational Environmental Satellites (GOES). The wavelet power spectrum analysis method has been invoked to investigate time variation of the main quasi-periodicities present in the electron flux data. The wavelet power spectrum analysis shows a number of quasi-periodic oscillations in both data sets. In high frequency range, a prominent period of 22–35day including 27day oscillation is detected. Other quasi-periods in the range of 40–60day, 90–100day, near Rieger periods of 130–140, 180–190day, Rieger period 150–160day, ∼250day, 350–370day and 1.2–1.4yr are found in different phases of cycle 23. In solar cycle 24, apart from other periods, we have detected the presence of best known “Rieger period” in both data sets. Possible explanations of the observed periodicities are discussed in terms of previous results and r-mode oscillations.

Long-term Changes of Water Level Associated with Chlorophyll a Concentration in Lake Baiyangdian, North China

In this study, periodic structures of water level and chlorophyll a (Chl a) concentration in Lake Baiyangdian and their correlations were analyzed using Morlet wavelet transform, wavelet power spectrum and cross wavelet transform analyses. Monthly data of water level (from 1950 to 2009) and Chl a concentration (from 2000 to 2009) were obtained from the Anxin county water conservancy and environmental bureaus, respectively. Results from the Morlet wavelet transform analysis show that water level fluctuations follow intra-annual and 60-month periodicity. In contrast, the wavelet transform analysis shows a water level variation structure of 6 and 16 month periodicity at a high confidence level (>95%). The periodic structure of Chl a concentrations shows 6 and >12 month patterns in continuous wavelet transform analysis whereas the periodic structures generated using wavelet power spectrum analysis exhibit 4 and >12 month variance, with the 4 month periodic change above the 95% confidence level. Comparative cross wavelet and coherence and phase analysis of water levels and Chl a concentrations in the lake results in a 16-month periodic structure that displays a complicated nonlinear relationship between the two parameters. Several short-term periodic nonlinear relationships also appear at other time intervals. In conclusion, we show for the first time that a 16-month periodic structure demonstrates the most robust influence of water level on Chl a concentrations in Lake Baiyangdian. Our results can help in understanding the interactions between specific hydrological changes and their corresponding ecological effects.

Spatial and temporal variability of precipitation concentration index, concentration degree and concentration period in Xinjiang, China

AbstractThis paper studied the spatial and temporal variability of the statistical structures of precipitation across Xinjiang, China, by analysing the time series of daily precipitation from 50 weather stations during the period from 1961 to 2008. Three indices precipitation concentration index (CI), precipitation concentration degree (PCD) and precipitation concentration period (PCP) were used to detect precipitation concentrations and the associated spatial patterns. The results show that higher precipitation CI values were mainly observed in Southern Xinjiang, whereas lower precipitation CI values were mostly detected in Northern Xinjiang. The precipitation CI values are noticeably larger in places where both annual total precipitation and number of rainy days are lower. The Mann–Kendall trend test demonstrates that the most parts of Xinjiang are characterized by no significant trends of precipitation CI at the 0.05 significance level. The periodicity characteristic of precipitation CI time series in Xinjiang could be detected by wavelet power spectrum analysis, and significant periods of that in most of Xinjiang were concentrated on 2–5 years band. The results of PCP reveal that rainfall in Xinjiang mostly occurs in summer, and the rainy season arrives earlier in Eastern Xinjiang than Western Xinjiang, whereas the results of PCD indicate that the rainfall in Northern Xinjiang was more dispersed within a year than that in Southern Xinjiang. Copyright © 2010 Royal Meteorological Society

Response analysis of rainfall–runoff processes using wavelet transform: a case study of the alpine meadow belt

AbstractRainfall–runoff processes appear to be highly nonlinear in Bayinbluk watersheds of the northwestern China. In this study, the time‐scale wavelet transform has been used for the analysis of this nonstationary system. The Haar and Morlet wavelet transform were used to analyse the rainfall–runoff conversion relationship. Wavelet power spectrum and change point methods are also employed to analyse rainfall rates and runoffs measured at daily to half‐hourly sampling rate. The four experimental sites (Luoto, Haer, Kuce and Shengl) are located in the Tianshan Mountains (Xinjiang province, China). Correlation analysis and wavelet transform are first applied to runoff process in different underlying surfaces. Wavelet analyses of rainfall rates and runoffs also give meaningful information on the temporal variability of the rainfall–runoff relationship. Change point and wavelet power spectrum analysis provide simple interpretation of energy distribution between different scales. The results indicate that wavelet transform is a good method for analysing the nonlinear relationship of temporal–spatial responses between rainfall and runoff. This method allowed quantification of the processes affecting runoff and provided an insight into their implications in surface water management. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Changing dependence of Zimbabwean rainfall variability on ENSO and the Indian Ocean dipole/zonal mode

A novel approach of using variability as a major descriptive parameter for observational time series is adopted to investigate how southeastern African (Zimbabwe) summer rainfall may have been forced by the El Nino southern oscillation (ENSO) and/or the Indian Ocean dipole/zonal mode (IODZM), concurrently with the changing sea surface temperature (SST) background of the Indo-Pacific region. The period is from 1901 to 2007. Wavelet power spectrum and linear statistical analysis, including simple and partial correlation techniques, are utilized to achieve this end. The results reveal epochal changes in teleconnections and other statistical properties linking southeastern African rainfall variability to the Indo-Pacific SSTs. These epochs conspicuously exhibit the period around 1945/1946, 1960/1961, 1972/1973, and 1997/1998 as demarcating distinct systematic climate turning points during the century. The role of the 1976/1977 climate regime shift seems not to be that apparent but instead, 1960/1961 and 1997/1998 appear to be the major turning points, both in the teleconnections and Indo-Pacific SST temporal characteristics. From the early 1960s to 1997, as much as 28% of the rainfall variability was linearly related to the IODZM while the ENSO hardly explained a quarter of this value. During this period, droughts are especially strongly connected to the positive IODZM events but insignificantly linked to El Nino, thus contradicting the conventional knowledge attributing most of regional rainfall suppression to the warm ENSO phase. However, the post 1997 epoch saw the reversal of the two climate modes’ influences. ENSO influence evidently became activated, attaining the previously assumed dominant role which had proved elusive during the earlier epochs. But this increased ENSO control is attributed to only less than 12% of the rainfall variance while IODZM seem to be largely decoupled from the local rainfall influencing processes by hardly explaining a drastically reduced 1% of the rainfall variance. This transformation occurred despite of neither ENSO nor IODZM SST anomalies showing any statistically significant changes. As far as could be established, this epochal behavior may not be forced by the frequency and magnitude of ENSO and IODZM events but most probably by the slow processes inherent in the SST background, especially of the tropical Indian Ocean. Thus, the apparent simultaneous decoupling of the IODZM and coupling of the ENSO to the regional rainfall controlling mechanisms seems to be the result of the unprecedented warming of the intervening tropical western Indian Ocean SSTs in the last decade. Consequently, the knowledge of the states of epochal Indian Ocean SST background variability should be an important regional scientific issue, since these epochal variations may dictate the nature (and successful prediction) of interannual as well as decadal climate fluctuations over southeastern Africa.

Spatial and temporal characteristics of aerosol optical depth over East Asia and their association with wind fields

AbstractRotated principal component analysis (PC) was performed on monthly Aerosol Optical Depth (AOD) from Moderate Resolution Imaging Spectroradiometer (MODIS) data over East Asia for the period of March 2000–January 2006. The first PC mode is a south–north dipole with a strong positive loading between 30–35°N and 130–150°E over middle latitude East Asia and a weaker negative loading in southern parts over East Asia. The first PC mode explains 32.44% of the total variance. By analysing time series of the PC1‐3, results show the PC‐1 and PC‐3 modes are important and both have distinct changes from the period 2000–2003 to 2004–2006; the former pattern (in middle latitudes over East Asia) is characterized in a decreasing linear trend and the latter (in eastern China) is in an increasing linear trend in the full 71 month evolution. Furthermore, based on the wavelet power spectrum analysis, it is found that the distinct changes of the monthly AOD in middle latitudes over East Asia (the PC‐1 pattern) are connected to the multi‐scale variations at intra‐seasonal (3–6 month) and annual (12 month) scales. While calculating the correlation of the PC‐1 with wind fields at 850 hPa from the NCEP/NCAR reanalysis dataset, it is shown that the PC‐1 is closely related to the U and V (horizontal) components over subtropical East Asia and western north Pacific, which well represents East Asian monsoon features. Finally, by comparing the PC‐1 pattern in May between 2003 and 2004, results show that the higher (lower) AOD in 2003 (2004) is associated with weaker (stronger) U component at 850 hPa in middle latitudes over East Asia. Copyright © 2008 Royal Meteorological Society

Non-stationary temporal characterization of the temperature profile of a soil exposed to frost in south-eastern Canada

Abstract. The objective of this work was to compare time and frequency fluctuations of air and soil temperatures (2-, 5-, 10-, 20- and 50-cm below the soil surface) using the continuous wavelet transform, with a particular emphasis on the daily cycle. The analysis of wavelet power spectra and cross power spectra provided detailed non-stationary accounts with respect to frequencies (or periods) and to time of the structure of the data and also of the relationships that exist between time series. For this particular application to the temperature profile of a soil exposed to frost, both the air temperature and the 2-cm depth soil temperature time series exhibited a dominant power peak at 1-d periodicity, prominent from spring to autumn. This feature was gradually damped as it propagated deeper into the soil and was weak for the 20-cm depth. Influence of the incoming solar radiation was also revealed in the wavelet power spectra analysis by a weaker intensity of the 1-d peak. The principal divergence between air and soil temperatures, besides damping, occurred in winter from the latent heat release associated to the freezing of the soil water and the insulation effect of snowpack that cease the dependence of the soil temperature to the air temperature. Attenuation and phase-shifting of the 1-d periodicity could be quantified through scale-averaged power spectra and time-lag estimations. Air temperature variance was only partly transferred to the 2-cm soil temperature time series and much less so to the 20-cm soil depth.

Rapid fluctuation of alkenone temperature in the southwestern Okhotsk Sea during the past 120 ky

Sea-ice expansion in the Okhotsk Sea in winter is sensitively affected by global warming and cooling. Regionally, the southwestern Okhotsk Sea is closely linked to climate change in East Asia, including Japan, because the cold sea surface temperature (SST) in the southwestern Okhotsk Sea influences directly the development of the Okhotsk atmospheric high-pressure system, and the activated Okhotsk high causes cold climatic conditions in northern Japan. Therefore, environmental change in the Okhotsk Sea indicates two-way interactions as a sensitive mirror reflecting global climate change and as a driving force of regional climate change. To better understand how surface environmental changes in the Okhotsk Sea can influence climate change in East Asia, SSTs were estimated in the southwestern Okhotsk Sea for the past 120 ky with millennial to centennial time resolution using the long-chain unsaturated alkyl ketone (alkenone) thermometer. The alkenone temperature, which corresponds to the SST to 20 m depth in autumn, showed repeated abrupt changes at a centennial timescale, especially during the last glacial period, 20–60 ky before present (BP). The alkenone temperature changed concurrently with changes from interstadials (warm events) to stadials (cold events) in the δ 18O record of the ice cores from Greenland, although some interstadials could not be identified in the alkenone temperature record. A wavelet power spectrum analysis showed that a periodicity of about 8 ky was prominent during 10–90 ky BP, and a 4- to 5-ky cycle was characteristic during 30–40 ky BP in the alkenone temperature records. These periodicities were both similar and dissimilar to those in the Polar Circulation Index, which is based on the atmospheric circulation intensity at high latitudes, as recorded by major-ion concentrations in GISP2. Both the similarity and dissimilarity imply that the SST in the southwestern Okhotsk Sea is controlled mainly by the atmosphere–ocean circulation system in the Northern Hemisphere; however, the relationship between the SST in the Okhotsk Sea and the climate in the Greenland is not linear. Anomalously high alkenone temperatures occurred repeatedly in the glacial period. These warm alkenone temperature episodes would have had multiple causes. In particular, high alkenone temperatures during the last glacial maximum (LGM) have been reported previously for locations near this study site. More investigations are necessary to understand what happened in the Okhotsk Sea and in adjacent seas at the time of the LGM.

Ultrasonic vibration dectection with wavelets: Preliminary results

Several arterial disorders are known to cause systolic audio vibrations in tissue: they include stenoses, vasospasm, aneurysms, bleeds and arteriovenous fistulas. High-amplitude vibrations can be discovered with conventional Doppler ultrasound (US) instruments; however, differentiating brief, low-amplitude vibrations from other nonstationary echo sources is difficult. Further, characterizing the frequency and amplitude of vibrations is not feasible with conventional Doppler US. The automated detection and estimation of both the frequency and amplitude of vibrations with durations less than 100 ms and amplitudes of a micrometer or less have remained a signal-processing challenge. These vibrations may be associated with both nonstationary colored noise and strong low-frequency clutter. The normalized continuous Morlet wavelet power-spectrum analysis of quadrature Doppler echoes, followed by a binary hypothesis test for noise, results in simulated detection rates above 99.9%, with 0.1% false alarms for signal-on signal-to-noise ratios (SNRs) as low as one. Two clinical examples are included. (E-mail: mplett@spu.edu)

A Look at the Relationship between the ENSO and the Indian Ocean Dipole.

Using observed sea surface temperature data from 1871-1998, and observed wind data from 1958-1998, it is confirmed that the recently discovered Indian Ocean Dipole (IOD) is a physical entity. Many IOD events are shown to occur independently of the El Nino. By estimating the contribution from an appropriate El Nino index based on sea surface temperature anomaly in the eastern Pacific, it is shown that the major fraction of the IOD Mode Index is due to the regional processes within the Indian Ocean. Our circulation analysis shows that the Walker circulation during the pure IOD events over the Indian/ Pacific Ocean is distinctly different from that during the El Nino events. Our power spectrum analysis, and wavelet power spectrum analysis show that the periodicities of El Nino and IOD events are different. The results from the wavelet coherence analysis show that, during the periods when strong and frequent IOD events occurred, the Indian Ocean Dipole Mode Index is significantly coherent with the equatorial zonal winds in the central Indian Ocean, suggesting that these events are well coupled. During the periods when there seems to be some relationship between the equatorial zonal winds in the central Indian Ocean and ENSO index, no significant coherence is seen between the Indian Ocean Dipole Mode Index and the equatorial zonal winds in the central Indian Ocean, except after 1995, suggesting that most of the IOD events are not related to ENSO.

Interannual and decadal variability of the north pacific blocking and its relationship to SST, teleconnection and storm tracks

Climalological features of mid-latitude blocking occurring over the North Pacific Ocean during 52 winters (December to February) of 1948/1949-1999/2000 are statistically analyzed based on NCEP/ NCAR reanalysis data. Significant interannual variation with a period of about 3-7 years as well as decadal variability is found by wavelet analysis and power spectrum analysis. A decreasing trend of the 2-7 year bandscale-averaged variance occurs throughout the 52 years and an abrupt shift from a higher state to a lower state during the 1970s is also found, which suggests an interdecadal variation of the North Pacific blocking. The possible relationship between the variability of blocking and sea surface temperature (SST), storm tracks and teleconnection are shown using composite analysis. In strong blocking anomaly winter (SBW), the geopotential height anomaly at 500 hPa exhibits a typical PNA (Pacific-North American)-like wave-train pattern in the North Pacific. The storm tracks, representing the activity of transient eddies, extend northeastward to the western coast of North America along the mid latitudes of about 40°-50°N, with the SST anomaly exhibiting a Pacific decadal oscillation (PDO) mode at mid-latitude and a La Nina-like pattern along the equator. Contrasting features appear in weak blocking anomaly winter (WBW).

The Wavelet Analysis of the Solar and Cosmic-Ray Data

Results of the wavelet power spectrum (WPS) analysis(which covers the 1969–1998 years) obtained using the daily data of the following parameters: (i) the Mt. Wilson Magnetic Plage Strength index (MPSI), (ii) the solar LDE-type flare index (LDE-FI) and (iii) the Calgary cosmic-ray (CR) intensity, are reported for periods ranging between 64 and 1024 days. The temporal distribution of the WPS during the last three solar activity cycles is extremely discontinuous. A clear resemblance between the CR and LDE-FI WPS is obtained only for the 22nd solar activity cycle. Nevertheless, the CR multiperiod peak, observed in 1982, can well be identified with the WPS peaks obtained in both solar parameters under consideration. In the 21st cycle, we found significant the MPSI periods around 850–880 days (2.3–2.4 yr), while such periods are present in the LDE-FI data of the 22nd cycle. In the CR data we discerned a net periodicity around 650 days (1.7 yr).

Wavelet power spectrum analysis of heterogeneities from sonic velocity logs

The continuous wavelet transform (CWT) is used to evaluate local variations in the power‐law exponents of sonic log data. The resulting wavelet spectrum can be compared with the corresponding global estimates obtained by conventional Fourier transform methods. In Fourier analysis, the fundamental tool used to characterize a fluctuating velocity distribution is the power spectrum. It represents the energy contained in each wavenumber and thus provides information regarding the importance of each scale of heterogeneity. However, important spatial information regarding the location of events becomes implicit in the phase angle of the Fourier transform. In this paper, it is shown how the square of the amplitude of the wavelet transform is related to the Fourier spectrum and how spatial information can be expressed in an explicit manner. Using the conservation of energy, it is shown that the average wavelet power spectrum over the total depth range is equal to the global power spectrum. A Gaussian wavelet is chosen to realize the wavelet transform. Two synthetic sonic logs with exponential and von Karman correlation functions are used to demonstrate the potential of the suggested analysis. Furthermore, the wavelet transform is applied to the KTB (Continental Deep Drilling Program) sonic log data. The wide range of applications of the CWT shows that this transform is a natural tool for characterizing the structural properties of underground heterogeneities. It offers the possibility of separating the multiscale components of heterogeneities.