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Climate change and human activities have led to nonstationarity in hydrological series. To systematically consider nonstationarity in regional frequency analysis (RFA), the features accounting for temporal variability of data series were developed and a nonstationary index flood model considering the trend and jump mutations was proposed in this study. The features extracted by empirical mode decomposition (EMD) were regarded as attributes to identify homogeneous regions. The fuzzy c-means clustering (FCM) and the combination of the self-organizing feature map and Ward’s agglomerative hierarchical clustering (SOM+Ward) were compared. Then the complete nonstationary RFA was applied to the annual maximum daily precipitation (AMDP) of Jiangxi province, China. The results indicate that the regionalization with the attributes reflecting temporal variability of the data series is more detailed. Moreover, the performance of SOM+Ward is better than FCM. The comparison results of precipitation quantiles, which were estimated by stationary and the proposed nonstationary index model, indicate that ignoring nonstationarity in RFA affects the choice of the best-fit distribution and the determination of index flood. In addition, the complete framework of nonstationary RFA developed in this study can provide more proper information when stations with trend and jump mutations exist in the region.

Las crecientes son los gastos máximos anuales de un río y su análisis de frecuencias son técnicas estadísticas que permiten estimar valores asociados con bajas probabilidades de ser excedidos. Tales predicciones permiten el diseño y la revisión hidrológica de las obras hidráulicas. La etapa fundamental del análisis de frecuencias consiste en seleccionar y ajustar, a los datos o muestra disponible, una función de distribución de probabilidades para realizar las predicciones. La distribución general de valores extremos (GVE) tiene bases teóricas que la convierten en un modelo probabilístico adecuado a crecientes, niveles máximos del mar, velocidades extremas de viento, etcétera. Debido a su génesis, la GVE procesa un dato por año, el máximo. Esta desventaja fue superada con el método de los r eventos máximos anuales. Tal procedimiento se describe y aplica al ajuste de la función GVE, a través del método de máxima verosimilitud, utilizando al algoritmo Complex de múltiples variables restringidas, para la maximización numérica. Se integraron cinco registros de crecientes con cinco eventos por año, en estaciones hidrométricas de la Región Hidrológica No. 10 (Sinaloa), México. Además, se procesaron dos registros de niveles máximos del mar con r = 5, tomados de la literatura especializada; uno de ellos es no estacionario al presentar tendencia. Se analizaron los resultados y se contrastaron las predicciones del ajuste de la GVE con r eventos anuales contra las de los métodos clásicos de momentos L y LH. Por último, se formulan las conclusiones, las cuales destacan la conveniencia del método descrito y señalan las ventajas del uso del algoritmo Complex como técnica numérica; debido a lo anterior, se recomienda la aplicación sistemática del procedimiento descrito.

To understand the principal functioning of binaural beats signals and the way it can affect the brain, eight drugs were used. This study was carried out on three groups: the first one contains four binaural beats signals, each one refers to a specific tone: alpha, beta, theta, and delta waves. The second group holds three records, representing three separate meditation binaural beats; however, the third one contains only one record that stands for the Marijuana e-drugs. Two types of analyses were performed on these groups, the temporal and the frequency analyses. In the first one, Hilbert transform was used to detect the envelope of the signal; we then determined the cross correlation function to understand the relationship between the two signals of the left and the right ears. However, in the frequency analysis, Fast Fourier Transform (FFT) was applied to extract binaural and carrier frequencies. The obtained results are very satisfactory and show that there is a delay between the two signals of the left and the right ears. Nevertheless, the frequency analysis shows that in the second group, Solfeggio frequencies lambda, theta and delta waves are used to obtain the meditation state, were gamma, lambda, alpha, and delta waves are applied to get the Marijuana effect in the third group.

In this research, the main aim is to formulate a mathematical model describe the relationship between annual probable maximum precipitation (PMP) for the city of Najaf and other hydrological variables such as temperature, relative humidity and evaporation rates depending on hydrologic data for the period between 1980 to 2005. All the calculations of the values of annual probable maximum precipitation were made depending on Hershfield's method, which is depended on the general equation of hydrologic frequency analysis and calculating the frequency factor for a group of data. The model was derived by the help of the program (SPSS 21). The study demonstrated a relative correlation between the previous independent variables, as a group, and the dependent variable (PMP) in one hand and the correlation between each independent variable with the value of PMP in the other hand. The coefficient of determination (R2) obtained from the statistical analysis for four equations were derived for each case with very suitable values. http://dx.doi.org/10.30572/2018/kje/090306

Twelve commonly used probability distributions are evaluated to identify the most suitable model that could provide accurate extreme rainfall estimates in Egypt. Three popular parameter estimation methods are applied: the method of moments, L-moments and maximum likelihood. The performance of the models is evaluated based on several numerical and graphical goodness-of-fit criteria. The proposed procedure is applied to annual maximum daily rainfall data from a network of 31 stations located in Egypt. The results indicate that no single distribution performed the best at all stations. Log-Normal, Log-Pearson Type III and Exponential are the top three distributions for the frequency analysis of daily annual extreme rainfalls in Egypt, i.e. they are selected as the “optimum” models for 23%, 19% and 19% of the total stations, respectively. In contrast, the distributions: Normal, Gumbel, Logistic and Generalized Logistic are not suitable for describing the extreme rainfalls in the country. The performances of both L-moments and maximum likelihood methods are almost equal and much better than that of the method of moments. Additionally, Depth-Duration-Frequency curves were established for 18 stations by using the “optimum” model, which can support the design of hydraulic structures. The findings from this study would be helpful for rainfall frequency analysis in similar arid countries.

The paper analyzes the statistical and temporal seasonal and decadal variability of the atmospheric pressure field in the Arctic region of Russia. Schemes for the frequency analysis of probability transitions for characteristics of stochastic-diffusion processes were used as the main research method. On the basis of the given series of 60 years long from 1948 to 2008, such parameters of diffusion processes as the mean (drift process) and variance (diffusion process) were calculated and their maps and time curves were constructed. The seasonal and long-term variability of calculated fields was studied as well as their dependencies on a discretization of the frequency intervals. These characteristics were analyzed and their geophysical interpretation was carried out. In particular, the known cycles of solar activity in 11 and 22 years were revealed. Numerical calculations were performed on the Lomonosov-2 supercomputer of the Lomonosov Moscow State University.

Nonlinear dynamic volatility has been observed in many financial time series. The recently proposed quantile periodogram offers an alternative way to examine this phenomena in the frequency domain. The quantile periodogram is constructed from trigonometric quantile regression of time series data at different frequencies and quantile levels, enabling the quantile-frequency analysis (QFA) of nonlinear serial dependence. This paper introduces some spectral measures based on the quantile periodogram for diagnostic checks of financial time series models and for model-based discriminant analysis. A simulation-based parametric bootstrapping technique is employed to compute the p-values of the spectral measures. The usefulness of the proposed method is demonstrated by a simulation study and a motivating application using the daily log returns of the S&P 500 index together with GARCH-type models. The results show that the QFA method is able to provide additional insights into the goodness of fit of these financial time series models that may have been missed by conventional tests. The results also show that the QFA method offers a more informative way of discriminant analysis for detecting regime changes in financial time series.

Assessment of human balance is one of the most common diagnostic tests, both in medical applications and during sports training. Many new methods of measuring are introduced in these studies; however, the analysis of results is still carried out mainly based on the values determined in the time domain – the average COP speed or the ellipse field of the prediction. The aim of the current work is to present the possibilities for the practical application of frequency analyses in assessment of the ability to maintain body balance as a method supplementing standard analyses. As part of the study, measurements of the ability to maintain balance in sensory conflict conditions introduced in the form of an oscillating, three-dimensional, virtual scenery were carried out. 27 healthy volunteers (13 women and 14 men) took part in the study. The three-dimensional scenery, presented by means of the Oculus system, oscillated in the sagittal plane with frequencies equal to 0.7 Hz and 1.4 Hz. The frequency value during the measurement was constant or changed in the middle of the test. Measurements were conducted on the FDM Zebris platform. The results were analyzed using developed coefficients determined on the basis of the Short-time Fourier transform (STFT). The use of frequency-domain analyses confirmed that in the COP movement, one can observe a cyclical component corresponding to following the scenery, as well as the appearance of other cyclical components whose observation is important in terms of assessing the ability to maintain balance. It has been shown that the changes in the average COP speed that occur during the measurement can result from changes related to the movement of following the scenery as well as additional body movements indicating a greater or lesser loss of balance. It has been shown that there are differences in the COP movement provoked by the movement of the surrounding scenery, which depend on the parameters of the introduced disturbances – something that can only be observed in results obtained in the frequency domain. The conducted research shows that in measurements involving the ability to maintain one’s balance conducted in sensory conflict conditions, standard time-domain analyses should be supplemented with other types of data analysis, e.g. frequency domain analyses.

The research has been conducted to determine the Young Modulus value of the fishing line with frequency analysis on a string by using a sound sensor. The fishing line made of Nylon Monofilament and Stainless Steel Nylon Coat. The diameter of the fishing line with each material consisted of 0.25 mm. The fishing line vibration events ware displayed on the graph of the relationship between pressure and time in the Logger pro program. The graph of the relationship between pressure and time was then transformed into an FFT graph of the amplitude relationship to frequency. Then the frequency value which was obtained from the FFT was used to determine the wave velocity value of the fishing line. The average wave velocity value was obtained by graphing the frequency relation to one of each string length. After obtained the average wave velocity value of the fishing line the Modulus Young value can be determined by the equation of the square wave velocity relationship times the mass per length times the cross-sectional area. In this study, the Young Modulus value of Nylon Monofilament fishing line was (1.94±0.09) GPa and the Young Modulus value of the Stainless Steel Nylon Coat fishing line was (45.05±2.05) GPa.

In the present work, for the first time, stochastic normal mode frequency analysis of hybrid angle ply laminated composite skew plate with an opening is attempted by a novel approach. The present n...

The frequency shifting and filtering (FSF) algorithm, a variant of DFT, has the merit of high efficiency for frequency analysis thanks to its simple implementation in the time domain. However, the inevitable white noise injected by various factors leads to inaccurate frequency estimation in practical measurement. This article investigates the influence of a stationary white noise on FSF-based frequency estimation of the power system. The variance expression of the frequency estimator is derived theoretically and compared to its unbiased Cramer–Rao lower bound (CRLB). The obtained results are validated by several computer simulations.

Water resources operational planning, managements or either flood defence infrastructure designs often demand the estimations of flow exceedance probability for visualizing the risk of flood episodes. Numerous literature often incorporated copulas for the development of bivariate joint dependence structure among the flood characteristics, flood peak flow, volume and duration, but it could be more realistic and comprehensive if we focus all the three mutually correlated flood characteristics simultaneously. Actually, the inclusion of more flood characteristics could provide better and much justifiable information in correlation and dependency modelling. In this study, trivariate copulas are incorporated and applied to a case study to analyse flood episodes in the Kelantan River basin at Gulliemard bridge gauge station in Malaysia. Firstly, for describing best-fitted bivariate copulas for establishing the joint dependence structure of each flood attribute pairs, the Gaussian copula is recognized most justifiable model for peak-volume pair and the Frank copula for peak-duration and volume-duration pairs. After that, the trivariate joint distribution is modelled using one Archimedean copula, the Frank copula and one Elliptical copula, the Gaussian copula. Based on Cramer-von-Mises-type statistics, Sn and p-value, the Gaussian copula best representing the trivariate dependence structure of flood and which further employed in the deriving of trivariate joint and conditional return periods.

Train safety and operational efficiency can be improved by investigating the dynamics of the train under varying conditions. Longitudinal train dynamics (LTD) simulations performed for such purposes, usually by utilising a nonlinear time-domain model. This paper covers two modes of LTD results corresponding to the time domain and frequency domain analysis. Time-domain solutions are essential to evaluate the full response used for parameter optimisation and controller design studies while frequency domain solutions can provide significant but straightforward clues regarding system dynamics. An advanced draft gear model, which works under a four-stage process is constructed considering all structural components, geometric relationships, friction modelling and dynamic characteristics such as hysteresis, stiffening, state transition, locked unloading, softening. Then, this model is parametrically reduced and implemented into an LTD simulation. The simulation in the time domain is conducted assuming a locomotive connected with a nine wagon via “ode3” fixed-step solver. The transfer function among the first wagon acceleration (output) and the locomotive force (input) estimated through system identification methodology. Then, the identification results interpreted by investigating step-response characteristic and best response giving parameter set is selected. Next, the modal and spectral analysis performed to reveal the behaviour of the in-train forces and the effects of vibration. This paper discusses a reliable methodology for the longitudinal dynamic analysis of the multi-bodied train in time and frequency domain and clarifies in-train vibration behaviour under the existence of sophisticated draft gear.

One of important thing in locating hypocenter process is determine P and S arrival time of the seismogram. Beside that, frequency analysis by FFT method is needed to know the character of the seismogram, like dominant frequency. For further analysis, FFT method can be a good tools in determine P and S wave arrival time in the spectogram form. This process is called automatic picking.

The Hanning window and interpolation algorithm is used to the frequency estimation for voltage and current signals acquired in transformer terminal unit (TTU), and the algorithm is validated by the frequency estimation for actual voltage signals. On this basis, the influence of signal frequency, harmonic, signal-to-noise ratio (SNR), sampling duration, sampling frequency and quantization of analog digital converter (ADC) on the accuracy of frequency estimation is investigated based on the numerically generated voltage signal. The results reveal that the error is proportional to the difference between the actual signal frequency and the rated value (50 Hz). When the total harmonic distortion (THD) varies in the range of 0~10%, the error is almost independent of THD. The error decreases with SNR, and the rate of decrease reduces with SNR. The sampling frequency has little effect on the error when the sampling duration is kept constant. When the quantization bit varies from 4 to 16, it has little effect on the error. Suggestions on the selection of sampling parameters for TTU frequency analysis using the Hanning window and interpolation algorithm are also given.

Quality discharge measurements and frequency analysis are two major prerequisites for defining a design flood. Flood frequency analysis (FFA) utilizes a comprehensive understanding of the probabilistic behavior of extreme events but has certain limitations regarding the sampling method and choice of distribution models. Entropy as a modern-day tool has found several applications in FFA, mainly in the derivation of probability distributions and their parameter estimation as per the principle of maximum entropy (POME) theory. The present study explores a new dimension to this area of research, where POME theory is applied in the partial duration series (PDS) modeling of FFA to locate the optimum threshold and the respective distribution models. The proposed methodology is applied to the Waimakariri River at the Old Highway Bridge site in New Zealand, as it has one of the best quality discharge data. The catchment also has a history of significant flood events in the last few decades. The degree of fitness of models to the exceedances is compared with the standardized statistical approach followed in literature. Also, the threshold estimated from this study is matched with some previous findings. Various return period quantiles are calculated, and their predictive ability is tested by bootstrap sampling. An overall analysis of results shows that entropy can be also be used as an effective tool for threshold identification in PDS modeling of flood frequency studies.

This study illustrates the frequency analysis and the probability of maximum daily rainfall in Northern region of Saudi Arabia, using rain data recorded during the period 1985–2017 at Tabuk (40375), Rafha (40362), Ar’ar (40357), Al Qurayyat (40360), and Al Jawf (40361) climatic stations. This study integrated several statistical tests, as Shapiro-Wilk test of the Normality, Leven test of the homogeneity variances, and LSD test of the ANOVA. The maximum daily distribution system varies from 16.9 mm, 44.8 mm, 12.9 mm, 17.9 mm, and 15.1 mm at Al Jawf, Al Qurayyat, Ar’ar, Rafha, and Tabuk, respectively. Shapiro-Wilk test displays Normal distribution at the level of significance Sig. > 0.05 in all rainfall classes at all stations. While Levene’s test confirmed the homogeneity of variance at Sig level at Ar’ar and Tabuk. The significance level is less than 0.05 at Al Jawf, Al Qurayyat, and Rafha stations. Also, the results of the ANOVA test showed that the level of significance was Sig. < 0.05 for all stations. The Normal and the Extreme value (type I) are the best distributions in Ar’ar and Tabuk stations, respectively, with the significance level less than 0.05 and the degree of freedom 1. Tabuk was characterized by the highest maximum daily with, respectively, 24.7 mm and 57.1 mm during the 5- and 100-year return period. But, Ar’ar was distinguished by the lowest maximum daily with, respectively, 19.7 mm and 31.7 mm during the 5- and 100-year return period.

The objective of this work is to characterize the signals and noises of Geocenter variations time series obtained from different space geodesy techniques as Global Positioning System (GPS), Doppler Orbitography and Radiopositioning Integrated on Satellite (DORIS), and Satellite Laser Ranging (SLR). The proposed methodology is based on the estimation of periodic signals by performing frequency analysis using FAMOUS software (Frequency Analysis Mapping On Unusual Sampling) and evaluation of level and type of noises by Allan variance technique and Three Corned Hat (TCH) method. The available data concern 13 years (from 1993 to 2006) of weekly series of Geocenter residuals components and scale factor variations, according to ITRF2000. The results estimated are more accurate according to GPS and SLR of about 2-8 mm than DORIS of about 8-42 mm, for Geocenter. Better RMS of scale factor was obtained of about 0.1ppb (0.6mm) for GPS technique than SLR and DORIS with 0.6 and 0.9 ppb (3.6 and 5.4mm), respectively. The estimated seasonal signals amplitudes are in the range of few milimeters per technique with centimetre level for Z Geocenter component of DORIS. The Geocenter motion derived from SLR technique is more accurate and close to the geodynamic models. The noise analysis shows a dominant white noise in the SLR and DORIS Geocenter solutions at a level of 0.6-1 mm and 10-40 mm, respectively. However, the GPS solution is characterized by a flicker noise at millimetre level, relating to mismodeling systematic errors.

This paper reports the precision of shape-from-focus (SFF) imaging according to the texture frequencies and window sizes of a focus measure. SFF is one of various depth measurement techniques for optical imaging, such as microscopy and endoscopy. SFF measures the depth of an object according to focus measure, which is generally computed with a fixed window. The window size affects the performance of SFF and should be adjusted for the texture of an object. In this study, we investigated the precision difference of SFF in texture frequencies and by window size. Two experiments were performed: precision validation in texture frequencies with a fixed window size, and precision validation in various window sizes related to pixel-cycle lengths. The first experimental results showed that a smaller window size could not provide a correct focus measure, and the second results showed that a window size that is approximately equal to a pixel-cycle length of the texture could provide better precision. These findings could potentially contribute to determining the appropriate window size of focus measure operation in shape-from-focus reconstruction.

PURPOSE To implement an outcome-driven frequency filter for improving radiomics-based modeling of human papillomavirus (HPV) for patients with oropharyngeal squamous cell carcinoma (OPSCC). METHODS AND MATERIALS One hundred twenty-eight OPSCC patients with known HPV status (60-HPV+ and 68-HPV-, confirmed by immunohistochemistry-P16 protein testing) were retrospectively studied. A 3D Discrete Fourier Transform was applied on contrast-enhanced computed tomography (CE-CT) images of patient gross tumor volumes (GTVs) to transform intensity distributions to the frequency domain and estimate frequency power spectrums of HPV- and HPV+ patient cohorts. Statistical analyses were performed to rank frequency bands contributing toward the prediction of HPV status. An outcome-driven frequency filter was designed accordingly and applied to GTV frequency information. A 3D inverse discrete Fourier transform was applied to reconstruct HPV-related frequency-filtered images. Radiomics features (11 feature-categories) were extracted from pre- and post-frequency filtered images using our previously published "ROdiomiX" software. Least-absolute-shrinkage-and-selection-operation (Lasso) combined with a generalized linear model (Lasso-GLM) was developed to identify and rank feature subsets with the optimal information for prediction of HPV+/-. Radiomics-based Lasso-GLM classifiers (pre- and post-frequency filtered) were constructed and validated using random permutation sampling and nested cross-validation (CV) techniques. Average area under the receiver operating characteristic (AUC), and positive and negative predictive values (PPV and NPV) were computed to estimate generalization error and prediction performance. RESULTS Among 192 radiomic features, 15 features were found to be statistically significant discriminators between HPV+/- cohorts on post-frequency filtered CE-CT images. Fourteen such radiomic features were observed on pre-frequency filtered datasets. Discriminant features included tumor morphology and intensity contrast. Performances for prediction of HPV for the pre- and post-frequency filtered Lasso-GLM classifiers were as follows: AUC/PPV/NPV = 0.789/0.755/0.805 and 0.850/0.808/0.877, respectively. Nested CV performances for prediction of HPV for the pre- and post-frequency filtered Lasso-GLM classifiers were as follows: AUC/PPV/NPV = 0.814/0.725/0.877 and 0.890/0.820/0.911, respectively. CONCLUSION Albeit subject to confirmation in a larger cohort, this pilot study presents encouraging results on the importance of frequency analysis prior to radiomic feature extraction toward enhancement of model performance for characterizing HPV in patients with OPSCC.

Background In clinical practice, small myelinated sensory fibers conveying pain and other sensations, Aδ-fibers, cannot be examined with available nerve conduction study techniques. New method Equipment available in clinical neurophysiology laboratories is used to record from human sensory nerves multiple averaged responses to non-painful stimulation of intraepidermal nerves. Ten averaged responses are analyzed in all possible pair combinations with an algorithm applied to a 0.45 ms period of amplitude and frequency (power spectrum). The median of the algorithms is compared to control data to identify potentials generated as response to intraepidermal stimulation. Results Median analysis of the algorithm applied to amplitude and frequency of multiple record pairs identifies potentials with conduction velocities of Aδ-fibers. The analysis of frequency (power spectrum) adds data to the analysis of amplitude. Median analysis of multiple record pairs yields more data than analysis of one pair of alternate averages with the same algorithms. Comparison with existing method(s) At present, analysis of one pair of alternate average records with an algorithm is the only method to identify Aδ-fiber generated potentials. Median analysis of the same algorithm applied to the amplitude of multiple record pairs increases the number of Aδ-fiber generated potentials identified. Neither median analysis of amplitude nor frequency of multiple records pairs has ever been used for conduction studies of nerve fibers, including Aδ-fibers. Conclusions Stimulation, recording and data analysis methods used in this study can be applied in the clinical EMG laboratory to identify the conduction velocities of Aδ-fibers in human sensory nerves.

Intensity Duration Frequency (IDF) curves are important tools for hydraulic and hydrologic design. Considering that there are different approaches to obtain the rainfall quantiles on which the IDF curves are based, the availability of a method to evaluate their reliability is of great importance. With this aim, in this work the multifractal properties of hourly rainfall data recorded at 23 rain gauges in the Umbria Region (Italy) have been used to select the most appropriate frequency analysis method of extreme annual rainfall at each location. Three methods have been tested: Local Frequency Analysis (by fitting at each station extreme annual rainfall data of different durations by a probability distribution function), Regional Frequency Analysis approach based on L-Moments and flood index method (considering the extreme annual rainfall data from all the stations), and a variant of the latter method known as In-site Regional Frequency Analysis (based on the consideration of the station as a region). Therefore, quantiles of rainfall for different durations and return periods have been obtained. These quantiles have been fitted to the Montana Intensity-Duration-Frequency (IDF) curve. The scaling properties of rainfall have been obtained through out the empirical moments scaling function K(q). Their comparison with some scaling behavior properties of the IDF curves has let the selection of the most adequate quantile estimation method at each site, being the Regional Frequency Analysis the most appropriate one for 14 out of the 23 sites included in the study.

In the present work, defect detection in rolling bearing using empirical mode decomposition of vibration signal data has been done. Higher order statistical parameters viz root mean square, kurtosis, skewness, and crest factor are utilized to diagnose bearing fault. Simulated bearing defects as spall on outer race, on roller, and on inner race are used for the study. For experimental study, four different load and speed combination have been chosen to widen the acceptability of results. The effect of bearing speed on statistical parameters is also studied. Effectiveness of signal decomposition by the empirical mode decomposition method has been established by the results. Kurtosis and crest factor values of decomposed and unprocessed signals have been selected and empirical mode decomposition-based values are shown as effective parameters for defect identification. The crest factor and Kurtosis of outer race defect show greater sensitivity to the load and speed variations, while the skewness of same defect shows its insensitivity to load and speed variations.

Owing to hydrological change and human activities, increasing attention is being paid to the evolution of dependence structure of hydrological characteristics, especially for non-stationary multivariate frequency analysis. In this study, we performed a non-stationary frequency analysis of annual extreme rainfall of four study regions in eastern coastal China. Two indexes separately accounting for rainfall volume and intensity were derived from daily precipitation data recorded by four pairs of gauges. In particular, based on the compatibility of data sets examined by the copula equality test, index series sharing similar dependence structures were merged to enrich data bases for copula modelling. A moving time window of 30 years was applied to the index series for non-stationarity analysis. An investigation of dependence evolution was conducted by detecting trends and change-points in the correlation coefficient series. Time-dependent Archimedean copulas and Generalized Extreme Value (GEV) distribution were employed to model the joint and marginal distributions, respectively. Kendall’s return period was employed to compute the design values of the indexes. Results showed an intensifying tendency of extreme rainfall volume and/or intensity in three of the study regions and uneven spatial and temporal distribution of precipitation. Finally, the occurrence risk of annual extreme rainfall corresponding to different joint return periods (JRPs) was analyzed based on the observed index series. The study highlights incorporating non-stationarity in multivariate hydrological analysis and merging compatible data sets to improve copula inference.

Floods often affect not only a single location, but also a whole region. Flood frequency analysis should therefore be undertaken at a regional scale which requires the considerations of the dependence of events at different locations. This dependence is often neglected even though its consideration is essential to derive reliable flood estimates. A model used in regional multivariate frequency analysis should ideally consider the dependence of events at multiple sites which might show dependence in the lower and/or upper tail of the distribution. We here seek to propose a simple model that on the one hand considers this dependence with respect to the network structure of the region and on the other hand allows for the simulation of stochastic event sets at both gauged and ungauged locations. The new Fisher copula model is used for representing the spatial dependence of flood events in the nested Thur catchment in Switzerland. Flood event samples generated for the gauged stations using the Fisher copula are compared to samples generated by other dependence models allowing for modeling of multivariate data including elliptical copulas, R-vine copulas, and max-stable models. The comparison of the dependence structures of the generated samples shows that the Fisher copula is a suitable model for capturing the spatial dependence in the data. We therefore use the copula in a way such that it can be used in an interpolation context to simulate event sets comprising gauged and ungauged locations. The spatial event sets generated using the Fisher copula well capture the general dependence structure in the data and the upper tail dependence, which is of particular interest when looking at extreme flood events and when extrapolating to higher return periods. The Fisher copula was for a medium-sized catchment found to be a suitable model for the stochastic simulation of flood event sets at multiple gauged and ungauged locations.

Is it true that there is an implicit understanding that Brownian motion or fractional Brownian motion is the driving force behind stock price fluctuations? An analysis of daily prices and volumes of a particular stock revealed the following findings: 1) the logarithms of the moving averages of stock prices and volumes have a strong positive correlation, even though price and volume appear to be fluctuating independently of each other, 2) price and volume fluctuations are messy, but these time series are not necessarily Brownian motion by replacing each daily value by 1 or –1 when it rises or falls compared to the previous day’s value, and 3) the difference between the volume on the previous day and that on the current day is periodic by the frequency analysis. Using these findings, we constructed differential equations for stock prices, the number of buy orders, and the number of sell orders. These equations include terms for both randomness and periodicity. It is apparent that both randomness and periodicity are essential for stock price fluctuations to be sustainable, and that stock prices show large hill-like or valley-like fluctuations stochastically without any increasing or decreasing trend, and repeat themselves over a certain range.

Frequency analysis is a method for predicting the probability of future hydrological events, based on historical data. Generally, frequency analysis of rainfall data and discharge data is performed using the moment method, but this method has a large bias, variant, and slope, thus there is a possibility of producing inaccurate hydrological design magnitudes. Meanwhile, the L-moment method is a linear combination of Probability Weighted Moment, with the ability to process data concisely and linearly. This study was therefore conducted to discover the L-moment method’s capacity to obtain a regional probability distribution and design rainfall, used as a basis for calculating hydrological planning, in anticipation of disasters. The study location, Mount Merapi, was selected to enable a more accurate prediction of maximum rainfall with the capacity to cause cold lava in the area, and consequently, reduce the risk of loss for people living within close proximity. According to the results, the L-moment regional ratio results were τ2R = 0.203, τ3R = 0.166, and τ4R = 0.169. The homogeneity and heterogeneity tests show all rainfall stations are uniform or homogeneous, and no data were released from the discordance test results. Also, the growth factor value increases in each return period design rainfall prediction. In this study, the suitable regional probability distribution for the research area is the Generalized Logistic distribution with formulated design rainfall equation. Regional design rainfall is able to predict possible rainfall within the area. The Test model showed the minimum RBias = 0.45%, maximum RBias = 41.583%, minimum RRSME = 0.45%, and maximum RRSME = 71.01%. Meanwhile, the L-moment method’s stability was shown by the model test minimum error = 1.64% and maximum error = 16.60%. The higher error value in the higher return period shows L-moment is able to reduce bias data, however, this has limitations in the higher return period.

An algorithm for constructing a dynamic analysis during the formation of a wave field of stand for testing turbines and the effect of the frequency interaction of the stand’s elements on the measurement of its magnitude is described. The research algorithm involves the use of theoretical solutions of nonlinear wave processes using linear oscillations, refined by experiments. The diagnostic model can determine the technical condition of the stand’s elements and also determine the causes of the discrepancies between the calculated and measured turbine power values. To clarify the stiffness coefficients between the stand’s elements, a modal analysis was used to obtain the range of their changes depending on the external dynamic load, which made it possible to assess the impact of changes in the frequency interaction conditions on the turbine power measurement at different test modes. The conditions for amplifying the amplitude of oscillations at their eigenfrequencies are obtained, and the value of the possible deviation of the expected power value at its measurement for specific modes of the turbine is calculated. The algorithm allows to estimate the dynamic state of the stand-in different research modes of turbines and give recommendations for reducing the level of frequency interaction.

The study is an application of L-moments based regional frequency analysis using annual maximum rainfall series of fifteen sites of Sindh, Pakistan. Initial screening reveals that the observed data series at each site has no serial correlation and is randomly and identically distributed. The discordancy measure (Di) show that none of the site in a group of fifteen sites is discordant. The regional heterogeneity measure (H) shows that the region of fifteen sites is homogeneous. L-moment ratio diagram and |ZDIST| statistic are in favor of generalized logistic distribution (GLO) as best-fitted regional distribution. Parameters of GLO distribution and regional as well as at-site quantiles for various return periods have been estimated. Results show that the estimated quantiles of each site are greater than the average values of observed data series at corresponding sites. Random forest regression has been used for the estimation of quantiles at ungauged sites.

Motor learning can improve movement performance and behavioral measurements, such as reaction time, by inducing brain plasticity. In this study, we investigated the effect of training with different task complexity on Electroencephalographic (EEG) signals. Two types of training (‘simple’ and ‘complex’) were performed by two groups of healthy volunteers. The complex training group (CTG) performed a trace tracking task using their dominant foot and the simple training group (STG) executed repetitive ankle dorsiflexion in the training phase. Frequency analysis was performed to study the effect of training on EEG signals. In addition, the coherence between paired-channels investigated to represent changes in brain region connectivity. Results revealed that the power in the Beta (15−31 Hz) was significantly reduced while gamma band power (32−80 Hz) was significantly enhanced in the CTG compared to the STG mainly in the frontal, central and centro-parietal channels. Theta power was also increased after training in fronto-central channel. Moreover, performance variations were mainly correlated to the beta and gamma power changes. Finally, the connectivity of gamma and beta band increased significantly particularly between frontal and central region in CTG while connectivity score of theta and delta band decreased after training. These findings confirm that training-induced brain plasticity depends on the complexity of the task, more complexity.

The Intensity-Duration-Frequency (IDF) curve defines the relationship between rainfall intensities at certain durations and with the frequencies. The IDF Curve is extensively used in many applications such as flood modelling and peak discharge estimation. Over the years, the frequent occurrence of flood has become a great challenge in Kelantan river basin. Herein, IDF curves using frequency analyses based on different distributions were developed and compared. The historical rainfall data at eight rainfall stations for the period of 1985-2019 were selected for the assessment purpose. The Gumbel, Normal and Log Pearson Type III distributions were fitted into the annual maximum rainfall series for durations varying from 30 minutes to 24 hours. The goodness of fit tests were then used to evaluate the performances of each frequency distribution. It was found that the Gumbel distribution gave the highest passing rate followed by the Log Pearson Type III and then the Normal distributions. The Gumbel distribution resulted in respective 86% and 75% passing rate since most of the p-values generated by both the K-S and the Mann-Whitney test were greater than 5% of significance level leading to the acceptance of the null hypothesis. Thus, the Gumbel distribution is suggested for the frequency analyses in this study.

This paper proposes a method for tuning the fractional exponent of different types of fractional order resonant controllers for a voltage source converter in a weak AC grid context. The main objective is to ensure the stability of the controlled system in a weak AC grid environment and to achieve an adequate dynamic response under disturbances. Therefore, six commonly used integer order proportional resonant (PR) control structures are selected from the literature and compared with each other according to their frequency behaviour. Afterwards, a rational approximation for the fractional order term is selected based on continuous fraction expansion technique. The inclusion of a fractional exponent in each integer order PR structure generates the fractional order proportional resonant (FPR) control transfer functions. Once the FPR controllers have been obtained, their closed-loop responses are tested via eigenvalue trajectory analysis. For each FPR control structure, a range of the fractional exponent that ensures stability is obtained. The conclusions of eigenvalue trajectory analysis are tested by implementing the FPR control structures in an specific application consisting in a modular multi-level converter (MMC) connected to a weak AC grid with adjustable short-circuit ratio. By means of time-domain simulations, not only the previous eigenvalue analyses are validated, but also new tuning criteria are given for the fractional exponent in combination with other control parameters, such as the damping frequency and the inductance of the complementary feedback branch. Moreover, a sensitivity analysis of the tuning criteria is carried out for other sizes of the AC filter inductance. This work was supported by the Basque Government through the Project of Research Group GISEL under Grant IT1083-16. Besides, TECNALIA is a ‘‘CERVERA Technology Centre of Excellence’’ recognised by the Ministry of Science and Innovation.

In this Chapter, An extension of the existing frequecncy analysis and design techniques is discussed to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems. The Output Frequency Response Function (OFRF) in terms of physical parameters of concern is introduced for the NARX Model with parameters of interest for Design (NARX-M-for-D). Moreover, a new concept known as the Associated Output Frequency Response Function (AOFRF) is introduced for the frequency analysis and design of nonlinear systems.

In this chapter we investigate a big family of Fourier transforms: continuous Fourier transform (CFT), Fourier series (FS), discrete-time Fourier transform (DtFT), and discrete Fourier transform (DFT). The DFT, in its fast form (FFT), is probably one of the most frequently used orthogonal transforms in the world apart from the discrete cosine transform (DCT). We learn that DtFT originates from continuous Fourier transform, while DFT from Fourier series. We become familiar with transform features and understand their strong and weak points. We learn the fundamentals of frequency analysis of discrete-time signals by DtFT and DFT. We see the significance of special signal shaping functions called windows in spectral analysis of signals.

A methodology using the standardised precipitation index is proposed to develop critical drought intensity-duration-frequency (IDF) curves. We define dry periods within which we recognise droughts of different durations. The most severe drought for each drought duration in each year is called the critical drought. The total probability theorem-coupled frequency analysis is used to determine the best-fit probability distribution function of drought severity, which is then converted to intensity. The generalised extreme value probability distribution function is found to best fit the critical drought severity. The methodology is implemented using monthly precipitation data for a meteorological station in Turkey. The critical drought intensity decreases linearly with increasing drought duration, whereas the return period increases exponentially when the drought becomes more severe. The site-specific IDF curves furnished with an empirical relationship between the intensity and return period allow one to characterise the drought not by an index-based intensity but by its return period. This kind of presentation is physically easier to understand, in particular for stakeholders and decision makers in practice., Istanbul Technical University [MUA2019-42094]; Fulbright [Academic Research Scholarship]; Scientific and Technological Research Council of Turkey [2219 Post-doctoral Research Program], This work was supported by the Istanbul Technical University [MUA2019-42094]; Fulbright [Academic Research Scholarship]; and Scientific and Technological Research Council of Turkey [2219 Post-doctoral Research Program].