Traditional Fourier Analysis Research Articles

Tidal and residual currents in the inner shelf of East China Sea detected from underway ADCP observations

Characterizing the spatial variability of net flow transport in a tide-dominated area like the East China Sea (ECS) is key to understanding the material and heat budget as well as their impacts on local ecosystem. However, the residual circulation in the ECS was much less confirmed by observations as it can only be derived from very sparse mooring data. Here for the first time we obtain the spatial patterns of tidal and residual currents in the inner ECS shelf from ADCP underway measurements conducted in 12 cruises using a spatial least squares (SLS) fitting technique. The SLS method is validated with the traditional harmonic analysis using numerical simulation results and then implemented with the observational data. The tidal current is dominated by two semidiurnal components M2 and S2 in this area, with the major axis of tidal ellipse along northwest-southeast direction. The ADCP-derived tide parameters are in good agreement with those from the mooring data and barotropic tide model. The annual spatial pattern of residual circulation is characterized by a southward coastal current and a northward shelf current, which are identified as the East China Sea Coastal Current (ECSCC) from Changjiang River runoff and the Taiwan Warm Current (TWC) originated from Taiwan Strait and Kuroshio. Their magnitudes are comparable but of one order smaller than tides. The vertical structure of TWC shows a subsurface-intensified feature in line with previous mooring observations. The north limit of TWC is approximately at 31.5°N around the submerged valley, beyond which the northward TWC becomes almost invisible. By a series of virtual cruise experiments, we show that the observation data length is the most crucial factor controlling the SLS fitting accuracy, while the role of other factors like sampling frequency is secondary. With a fixed-length dataset, the degree of polynomial function used for SLS fitting must be properly determined to minimize the under-fitting and over-fitting error, and there is also a trade-off in the fitting accuracy between tidal and residual currents depending on the fitting strategy.

Tropical and Subtropical South American Intraseasonal Variability: A Normal-Mode Approach

Instead of using the traditional space-time Fourier analysis of filtered specific atmospheric fields, a normal-mode decomposition method was used to analyze South American intraseasonal variability (ISV). Intraseasonal variability was examined separately in the 30–90-day band, 20–30-day band, and 10–20-day band. The most characteristic structure in the intraseasonal time-scale, in the three bands, was the dipole-like convection between the South Atlantic Convergence Zone (SACZ) and the central-east South America (CESA) region. In the 30–90-day band, the convective and circulation patterns were modulated by the large-scale Madden–Julian oscillation (MJO). In the 20–30-day and 10–20-day bands, the convection structures were primarily controlled by extratropical Rossby wave trains. The normal-mode decomposition of reanalysis data based on 30–90-day, 20–30-day, and 10–20-day ISV showed that the tropospheric circulation and CESA–SACZ convective structure observed over South America were dominated by rotational modes (i.e., Rossby waves, mixed Rossby-gravity waves). A considerable portion of the 30–90-day ISV was also associated with the inertio-gravity (IGW) modes (e.g., Kelvin waves), mainly prevailing during the austral rainy season. The proposed decomposition methodology demonstrated that a realistic circulation can be reproduced, giving a powerful tool for diagnosing and studying the dynamics of waves and the interactions between them in terms of their ability to provide causal accounts of the features seen in observations.

Quantifying network behavior in the rat prefrontal cortex.

The question of how consciousness and behavior arise from neural activity is fundamental to understanding the brain, and to improving the diagnosis and treatment of neurological and psychiatric disorders. There is significant murine and primate literature on how behavior is related to the electrophysiological activity of the medial prefrontal cortex and its role in working memory processes such as planning and decision-making. Existing experimental designs, specifically the rodent spike train and local field potential recordings during the T-maze alternation task, have insufficient statistical power to unravel the complex processes of the prefrontal cortex. We therefore examined the theoretical limitations of such experiments, providing concrete guidelines for robust and reproducible science. To approach these theoretical limits, we applied dynamic time warping and associated statistical tests to data from neuron spike trains and local field potentials. The goal was to quantify neural network synchronicity and the correlation of neuroelectrophysiology with rat behavior. The results show the statistical limitations of existing data, and the fact that making meaningful comparison between dynamic time warping with traditional Fourier and wavelet analysis is impossible until larger and cleaner datasets are available.

Research on harmonic resonant fault mechanism and suppression measures of oilfield power grid based on fast mode analysis method

In recent years, with the use of electric drilling rig, electric fracturing pump, and other equipment, the harmonic resonance problem of oilfield power grid is becoming more and more serious. In view of the high time and space complexity and long calculation time of the traditional harmonic resonance analysis method, the improved power iteration method is combined with the traditional modal analysis method, and the harmonic resonance problem of the oilfield power grid is analyzed by the fast modal analysis method. At the same time, a new set of harmonic resonance amplification index is derived and verified, and the harmonic content amplification times in the resonant influence region and different busbars are revealed. And then a passive filter is used to suppress harmonic resonance, and the effectiveness of the scheme is verified by field tests. The results show that, in the frequency range of 0–1000 Hz, the resonant frequency points in the oil field are mainly related to the rectifier pulse number of the drilling rig and the frequency conversion device for fracturing. The proposed fast modal analysis method has the advantages of fast convergence speed and memory saving, which is helpful to accurately detect the harmonic resonance region caused by the multi-pulse frequency conversion device, and the harmonic resonance can be effectively suppressed by installing a filter at the main excitation bus of the resonant frequency.

Analysis and Exploration of the Impact of Average Sea Level Change on Navigational Safety in Ports

The primary clientele of a harbor is vessels, and vessels are primarily influenced by external forces such as wind (on the water surface), currents (underwater), and waves (affecting vessel stability). Therefore, it is necessary to comprehensively consider safety factors such as marine environmental forces and port characteristics. As ship sailing falls under applied science, acquiring marine meteorological information regarding ship routes can enhance port navigational safety. However, in the face of changes in the environmental conditions of harbor waters, it is essential to fully consider the impact of the external environment on ship maneuvering. One can effectively navigate complex operating environments by devising reasonable ship-handling plans. In the context of sea level rise caused by extreme climatic events, long-term variations, trends, and random factors are at play. Previous assessments of sea level rise have often relied on linear regression and the least squares method to determine coefficients. However, these methods fail to accurately capture the actual trend of sea level rise. Additionally, traditional harmonic analysis methods are unable to analyze sea level rise as well. Therefore, in this study, the techniques of simple moving average (SMA), empirical mode decomposition (EMD), and ensemble empirical mode decomposition (EEMD) were applied to analyze sea level rise. The obtained results of sea level rise under different analysis conditions were integrated with a hydrodynamic model that incorporates both wave and tidal characteristics to calculate the overall coastal dynamics parameters, which are crucial for ship navigation. The research findings contribute to the study of ship navigational safety issues by examining the distribution characteristics of port meteorology under climate change conditions. They offer valuable insights for mariners to assess navigational safety and devise maneuvering strategies based on the actual water flow conditions. Furthermore, the findings help identify and address potential risks and issues, ultimately ensuring the safety of navigation.

Discrete-time analysis of optimized Schwarz waveform relaxation with Robin parameters depending on the targeted iteration count

We propose a new approach that provides new results in the convergence analysis of optimized Schwarz waveform relaxation (OSWR) iterations for parabolic problems, and allows to define efficient optimized Robin parameters that depend on the targeted iteration count, a property that is shared by the actual observed optimal parameters, while traditional Fourier analysis in the time direction leads to iteration independent parameters. This new approach is based on the exact resolution of the time semi-discrete error equations. It allows to recommend a couple (number of iterations, Robin parameter) to reach a given accuracy. While the general ideas may apply to an arbitrary space dimension, the analysis is first presented in the one dimensional case. Numerical experiments illustrate the performance obtained with such iteration-dependent optimized Robin parameters.

The Music of Rivers: The Mathematics of Waves Reveals Global Structure and Drivers of Streamflow Regime

AbstractRiver flows change on timescales ranging from minutes to millennia. These vibrations in flow are tuned by diverse factors globally, for example, by dams suppressing multi‐day variability or vegetation attenuating flood peaks in some ecosystems. The relative importance of the physical, biological, and human factors influencing flow is an active area of research, as is the related question of finding a common language for describing overall flow regime. Here, we addressed both topics using a daily river discharge data set for over 3,000 stations across the globe from 1988 to 2016. We first studied similarities between common flow regime quantification methods, including traditional flow metrics, wavelets, and Fourier analysis. Across all these methods, the flow data showed low‐dimensional structure (i.e., simple and consistent patterns), suggesting that fundamental mechanisms are constraining flow regime. One such pattern was that day‐to‐day variability was negatively correlated with year‐to‐year variability. Additionally, the low‐dimensional structure in river flow data correlated closely with only a small number of catchment characteristics, including catchment area, precipitation, and temperature—but notably not biome, dam surface area, or number of dams. We discuss these findings in a framework intended to be accessible to the many communities engaged in river research and management, while stressing the importance of letting structure in data guide both mechanistic inference and interdisciplinary discussion.

Tidal analysis and prediction based on the Fourier basis pursuit spectrum

The high-precision prediction of ocean tides is important for coastal management. Traditional harmonic analysis (HA) regards tides as the cumulative motion of multiple trigonometric functions, ignoring the time-varying characteristics of harmonic constants. Although the time-frequency transformation method can reconstruct the time-varying characteristics of tides, there are problems with tidal component coupling and edge effects. Therefore, we propose a method of reconstructing tidal components based on Fourier basis pursuit (FBP) spectral bandpass filtering (FBPBPF) by combining the Fourier dictionary and the basis pursuit algorithm and apply this method to four tide stations in the Gulf of Maine and Hong Kong station to try to solve the above two problems. The results show that the FBP spectrum can effectively identify and separate the main coupling tidal components. In the Gulf of Maine, FBPBPF can use shorter tide data to obtain better or equivalent prediction results than HA. Especially within 30 days, the prediction accuracy of FBPBPF at the four sites can be improved by 53.5% on average compared with that of HA. At Hong Kong station, FBPBPF has higher prediction accuracy than HA and Inaction Method (IM) in 4 months, but its long-term accuracy is gradually reduced (including all stations). We believe that the frequency resolution is the key factor leading to the divergence of long-term prediction errors.

Principal Component Analysis of azimuthal flow in intermediate-energy heavy-ion reactions

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that the sine and cosine functions chosen a priori in the traditional Fourier analysis are naturally the most optimal basis for azimuthal flow studies according to the data itself. We perform PCA-SVD analyses of mid-central Au+Au collisions at Ebeam/A=1.23 GeV simulated using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model to address the following two questions: (1) if the principal components of the covariance matrix of nucleon azimuthal angle distributions in heavy-ion reactions around 1 GeV/nucleon are naturally sine and/or cosine functions and (2) what if any advantages the PCA-SVD may have over the traditional flow analysis using the Fourier expansion for studying the EOS of dense nuclear matter. We find that (1) in none of our analyses the principal components come out naturally as sine and/or cosine functions, (2) while both the eigenvectors and eigenvalues of the covariance matrix are appreciably EOS dependent, the PCA-SVD has no apparent advantage over the traditional Fourier analysis for studying the EOS of dense nuclear matter using the azimuthal collective flow in heavy-ion collisions.

Real-time polarization measurement based on spatially modulated polarimeter and deep learning

Spatially modulated polarimeter (SMP) can be employed to obtain the polarization states of light by a single shot of intensity image, and it is stable, robust and easy to use. In order to simplify the calculation procedures and improve the measurement speed, we introduce the deep learning (DL) method into SMP. In this work, a convolutional neural network (CNN) based on VGGNet architecture has been trained by simulated samples that are generated by a theoretical model of a spatially modulated system. Then the trained CNN is utilized to evaluate the Stokes parameters of the input light beam according to its spatially modulated image obtained in the real experiment. The mean absolute error between the evaluated values and the true values of the normalized Stokes parameters can be less than 0.02, and the evaluation of each image takes only 0.03–0.04 s. Compared with the traditional Fourier analysis method, the DL method is close in accuracy while greatly enhanced in speed, making real-time polarization measurement achievable.

Cloud-covered MODIS LST reconstruction by combining assimilation data and remote sensing data through a nonlocality-reinforced network

Reconstruction of cloud-covered thermal infrared land surface temperature (LST) is vital for the measurement of physical properties in land surface at regional and global scales. In this paper, a novel reconstruction method for Moderate Resolution Imaging Spectroradiometer (MODIS) LST data with a 1-km spatial resolution is proposed by combining assimilation data and remote sensing data through a nonlocality-reinforced network (NRN) model. Firstly, a data grading criterion is introduced to evaluate the importance of the various datasets, forming four combinations of multi-modal datasets for the training and testing of the NRN model. Secondly, the NRN model with a multiscale encoding–decoding structure considering the nonlocality-reinforced module is proposed for LST reconstruction. The results suggest that the proposed method can precisely reconstruct cloud-covered LST, with a mean absolute error (MAE) less than 0.8 K, even when no auxiliary remote sensing LST are used (Combination 1). The best result is the full combination (Combination 4), in which the coefficient of determination is 0.8956, the MAE is 0.5219 K, and the root-mean-square error is 0.7622 K. Compared with the traditional harmonic analysis of time series method, the improved enhanced spatial and temporal adaptive reflectance fusion method and the multiscale feature connected convolutional neural network method for LST reconstruction, the proposed method can achieve superior results. The proposed method with Combination 1 has been implemented to reconstruct the daily LST in the study area for 2019. Referring to the meteorological station observations, the reconstructed bias absolute value is less than 1 K, indicating that the proposed model is very effective and valid for regional cloud-covered LST reconstruction.

Prediction of tide level based on variable weight combination of LightGBM and CNN-BiGRU model

Accurate tide level prediction is crucial to human activities in coastal areas. Many practical applications show that compared with traditional harmonic analysis, long short-term memory (LSTM), gated recurrent units (GRUs) and other neural networks, along with ensemble learning models, such as light gradient boosting machine (LightGBM) and eXtreme gradient boosting (XGBoost), can achieve extremely high prediction accuracy in relatively stationary time series. Therefore, this paper proposes a variable weight combination model based on LightGBM and CNN-BiGRU with relevant research. It uses the variable weight combination method to weight and synthesize the prediction results of the two base models so that the combination model has a stronger ability to capture time series features and fits the data well. The experimental results show that in contrast to the base model LightGBM, the RMSE value and MAE value of the combination model are reduced by 43.2% and 44.7%, respectively; in contrast to the base model CNN-BiGRU, the RMSE value and MAE value of the combination model are reduced by 35.3% and 39.1%, respectively. This means that the variable weight combination model can greatly improve the accuracy of tide level prediction. In addition, we use tidal data from different geographical environments to further verify the good universality of the model. This study provides a new idea and method for tide prediction.

Long-term photometric monitoring and spectroscopy of the white dwarf pulsar AR Scorpii

ABSTRACT AR Scorpii (AR Sco) is the only radio-pulsing white dwarf known to date. It shows a broad-band spectrum extending from radio to X-rays whose luminosity cannot be explained by thermal emission from the system components alone, and is instead explained through synchrotron emission powered by the spin-down of the white dwarf. We analysed NTT/ULTRACAM, TNT/ULTRASPEC, and GTC/HiPERCAM high-speed photometric data for AR Sco spanning almost seven years and obtained a precise estimate of the spin frequency derivative, now confirmed with 50-σ significance. Using archival photometry, we show that the spin-down rate of $P/\dot{P} = 5.6 \times 10^6$ yr has remained constant since 2005. As well as employing the method of pulse-arrival time fitting used for previous estimates, we also found a consistent value via traditional Fourier analysis for the first time. In addition, we obtained optical time-resolved spectra with WHT/ISIS and VLT/X-shooter. We performed modulated Doppler tomography for the first time for the system finding evidence of emission modulated on the orbital period. We have also estimated the projected rotational velocity of the M-dwarf as a function of orbital period and found that it must be close to Roche lobe filling. Our findings provide further constraints for modelling this unique system.

A Deep Learning Approach to Extract Internal Tides Scattered by Geostrophic Turbulence

AbstractExtraction of internal tidal (IT) signals is central to the interpretation of Sea Surface Height (SSH) data. The increased spatial resolution of future wide‐swath satellite missions poses a challenge for traditional harmonic analysis, due to prominent and unsteady wave‐mean interactions at finer scales. However, the wide swaths will also produce spatially two‐dimensional SSH snapshots which allows us to treat IT extraction as an image translation problem for the first time. We design and train TITE (Toronto Internal Tide Emulator), a conditional Generative Adversarial Network, which, given a snapshot of raw SSH from an idealized eddying simulation, generates a snapshot of the embedded IT component. We test it on data whose dynamical regimes are different from the data provided during training. Despite the diversity and complexity of data, it accurately extracts ITs in most individual snapshots considered and reproduces physically meaningful statistical properties. Predictably, TITE's performance decreases with the intensity of the turbulent flow.

Parametric Circuit Fault Diagnosis Through Oscillation-Based Testing in Analogue Circuits: Statistical and Deep Learning Approaches

Oscillation-based testing of analogue electronic filters removes the need for test signal synthesis. Parametric faults in the presence of normal component tolerance variation are challenging to detect and diagnose. This study demonstrates the suitability of statistical learning and deep learning techniques for parametric fault diagnosis and detection by investigating several time-series classification techniques. Traditional harmonic analysis is used as a baseline for an in-depth comparison. Eight standard classification techniques are applied and compared. Deep learning approaches, which classify the time-series signals directly, are shown to benefit from the oscillator start-up region for feature extraction. Global average pooling in the convolutional neural networks (CNN) allows for Class Activation Maps (CAM). This enables interpreting the time-series signal’s discriminative regions and confirming the importance of the start-up oscillation signal. The deep learning approach outperforms the harmonic analysis approach on simulated data by an average of 11.77% in classification accuracy for the three parametric fault magnitudes considered in this work.

FunCode—Versatile Syntax and Semantics for Functional Harmonic Analysis Labels

Traditional harmonic analysis annotations can be represented in a computer model of a piece of music by plain text strings. But whenever automated processing like analysis, comparison or retrieval is intended, a formal definition is helpful. This should cover not only the syntactic structure, but also the semantics, i.e. the intended meaning, and thus adheres to the technique of mathematical remodelling of existing cultural phenomena. The resulting models can serve as a basis for automated processing, but also help to clarify the communication and discussion among humans substantially. This article proposes such a definition in four layers, which address different problems of encoding and communication: (a) relation of symbol sequences to staff positions, (b) combining functions, (c) chord roots, and (d) interval structure and voice leading. Only one of them is specific to functional (Riemannian) theory and can possibly be replaced to represent scale degree theory. The proposal is configurable to different interval specification methods and open to localisation. Syntax and semantics are defined by precise mathematical means, borrowed from computer science, and thus are unambiguously documented.

Analysis Methods for Aerodynamic Instability Detection on a Multistage Axial Compressor

In order to detect the aerodynamic instability of a multistage axial compressor more accurately and earlier, the harmonic Fourier mean amplitude analysis method and heterotopic variance analysis method are developed. The dynamic instability prediction performance of the two methods is studied on a low-speed and a high-speed two-stage axial compressor. The harmonic Fourier mean amplitude analysis method is suitable for predicting the aerodynamic instability of a multistage axial compressor in the form of a rotating stall. Compared with the traditional harmonic Fourier analysis methods, the harmonic Fourier mean amplitude analysis method can capture the detail of the pressure signal more accurately and it can effectively prevent instability misjudgment. The heterotopic variance analysis method is developed based on the conventional variance analysis method, and it can be used to distinguish whether the compressor is in the rotating stall or the surge state. The heterotopic variance analysis method can predict the aerodynamic instability ahead of the harmonic Fourier mean amplitude analysis method, and fewer circumferential measuring points were employed. The layout of the measuring points also influences the detection of the aerodynamic instability of the compressor. The aerodynamic instability of the high-speed axial compressor can be predicted earlier by employing measuring points at the compressor outlet.

On Time Scales of Intrinsic Oscillations in the Climate System.

Proxy temperature data records featuring local time series, regional averages from areas all around the globe, as well as global averages, are analyzed using the Slow Feature Analysis (SFA) method. As explained in the paper, SFA is much more effective than the traditional Fourier analysis in identifying slow-varying (low-frequency) signals in data sets of a limited length. We find the existence of a striking gap from ~1000 to about ~20,000 years, which separates intrinsic climatic oscillations with periods ranging from ~60 years to ~1000 years, from the longer time-scale periodicities (20,000 year+) involving external forcing associated with Milankovitch cycles. The absence of natural oscillations with periods within the gap is consistent with cumulative evidence based on past data analyses, as well as with earlier theoretical and modeling studies.

Displacement Estimation of Self-Sensing Magnetic Bearings Based on Biorthogonal Spline Wavelet

By collecting the ripple current in the control coil, the self-sensing magnetic bearings can obtain rotor displacement information without a displacement sensor, which has the advantages of low cost and high integration. According to the problems of incomplete and inaccurate displacement information extraction caused by the traditional displacement estimation method using Fourier method to analyze the ripple current with non-stationary characteristics to estimate the rotor displacement with the Gibbs effect. Therefore, this paper proposes a rotor displacement estimation algorithm based on multiresolution filter bank biorthogonal spline wavelet for a magnetic bearing motor based on two-level switching power amplifier. This algorithm utilizes the biorthogonal spline wavelet with the characteristics of generalized linear phase and tight support, which can accurately demodulate the ripple current in the coil and extract the displacement information in the ripple current. Therefore, it is able to overcome the Gibbs effect in the traditional Fourier analysis estimation algorithm, to reduce the influence of ripple on rotor displacement estimation, and to improve the accuracy and stability of displacement estimation. In order to verify the correctness and effectiveness of the proposed algorithm, this paper establishes a simulation model of magnetic bearing in MATLAB Simulink and designs the proposed displacement estimator. Simulation results demonstrate that the proposed algorithm has higher accuracy and better stability than traditional displacement estimation algorithms. Experimental results show that the maximum deviation rate of the displacement estimation method proposed in this paper does not exceed 1% when the radial magnetic bearing gap is 0.5 mm, which can effectively estimate the rotor displacement.

Shape difference of mud clasts depending on depositional facies: application of newly modified elliptic Fourier analysis to hybrid event beds

ABSTRACT Hybrid event beds are the deposits from sediment gravity flows that change their rheological behavior through their passage, entraining muddy sediments and damping turbulence. Muddy facies of hybrid event beds are often associated with abundant mud clasts which show a wide variety of size and shape. The variation of clast occurrence in hybrid event beds is expected to preserve the information of entrainment and transport processes of muddy sediments in submarine density currents. However, previous analyses of hybrid event beds have focused on describing the overall clast occurrence rather than the statistical size and shape analyses because traditional shape parameters are incapable of characterizing the complex shape of mud clasts. Here, a new quantitative grain-shape analysis of mud clasts is conducted and allows visualization of the spatial variation of clast size and shape, which suggests the wide variety of origin and transport systems of entrained mud clasts. This new method revises the traditional elliptic Fourier analysis, substituting Fourier power spectra (FPS) for traditional elliptic Fourier descriptors to overcome the mirror-wise shape problem. Further, principal-component analysis is shown to capture significant shape attributes more effectively than traditional shape parameters. The proposed method is applied to mud clasts in sediment-gravity-flow deposits in the lower Pleistocene Otadai Formation, central Japan. Results imply that there are distinctive shape and size differences of mud clasts that are strongly associated with depositional facies rather than the distance from the source. The clasts have a higher angularity than other facies in the debrite intervals in hybrid event beds. It is also shown that clasts in sandy, structureless facies have different characteristics in shapes based on elongation and convexity compared to laminated facies. Comparison between different shape-analysis methods demonstrates that none of the traditional methods are able to visualize these trends as effectively as the method presented herein. These results highlight the importance of the quantitative shape analysis of sediment grains and the effectiveness of FPS-based elliptic Fourier analysis.