Dispersive Fourier transformation is an emerging measurement technique that overcomes the speed limitations of traditional optical instruments and enables fast continuous single-shot measurements in ...optical sensing, spectroscopy and imaging. Using chromatic dispersion, dispersive Fourier transformation maps the spectrum of an optical pulse to a temporal waveform whose intensity mimics the spectrum, thus allowing a single-pixel photodetector to capture the spectrum at a scan rate significantly beyond what is possible with conventional space-domain spectrometers. Over the past decade, this method has brought us a new class of real-time instruments that permit the capture of rare events such as optical rogue waves and rare cancer cells in blood, which would otherwise be missed using conventional instruments. In this Review, we discuss the principle of dispersive Fourier transformation and its implementation across a wide range of diverse applications.
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Intelligent fault diagnosis methods based on signal analysis have been widely used for bearing fault diagnosis. These methods use a pre-determined transformation (such as empirical mode ...decomposition, fast Fourier transform, discrete wavelet transform) to convert time-series signals into frequency domain signals, the performance of dignostic system is significantly rely on the extracted features. However, extracting signal characteristic is fairly time consuming and depends on specialized signal processing knowledge. Although some studies have developed highly accurate algorithms, the diagnostic results rely heavily on large data sets and unreliable human analysis. This study proposes an automatic feature learning neural network that utilizes raw vibration signals as inputs, and uses two convolutional neural networks with different kernel sizes to automatically extract different frequency signal characteristics from raw data. Then long short-term memory was used to identify the fault type according to learned features. The data is down-sampled before inputting into the network, greatly reducing the number of parameters. The experiment shows that the proposed method can not only achieve 98.46% average accuracy, exceeding some state-of-the-art intelligent algorithms based on prior knowledge and having better performance in noisy environments.
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•A transient thermal model is proposed for the study of the frictional sliding contact between rough surfaces.•The problem is solved with optimization techniques and the Fast Fourier Transform.•With ...this model, the rise of surface temperature and heat distribution are calculated considering surface roughness.•Several parametric analyses are performed with the aim to identify the most influent parameters on the thermal contact phenomena.
Surface temperature in sliding contact systems has a considerable effect on friction and wear mechanisms, and thus the system performances. Hence its knowledge is crucial for the design of these systems. This is a complex challenge since real surfaces are rough and the contact area depends on several factors. Thus, the aim of this paper is to present an efficient thermal contact model allowing to study the transient rise of temperature and heat partition in sliding contact systems considering surface roughness. This model is based on the heat source theory. The produced heat is computed based on a contact mechanics model considering roughness. In addition to roughness, a thermal interface layer made of wear debris is considered within micro-contact zones which leads to a discontinuity of temperature at the scale of asperities. If the interface layer is considered, heat is generated within it. Otherwise, the generation of heat is at the top of surface asperities and the continuity of temperature is assumed. The numerical problem is solved using optimization techniques and the Fast Fourier Transform to accelerate calculations. A parametric study is presented with the aim to highlight the effects of material properties, roughness, velocity and the interface layer on the partition of heat and surface temperature.
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The forecast of electricity consumption plays an essential role in marketing management. In this study, a random forest (RF) model coupled with ensemble empirical mode decomposition (EEMD) named ...EEMD-RF is presented for forecasting the daily electricity consumption of general enterprises. The candidate data is first decomposed into several intrinsic mode functions (IMFs) by the EEMD. Through fast Fourier transformation, the features in each IMF are extracted in the time-frequency domain, then simulated and predicted by the RF model. Finally, the results of each IMF are integrated into the overall trend of the daily electricity consumption for those enterprises. The proposed method was applied to two enterprises located in the Jiangsu High-Tech Zone, and the period of collected data was from January 1, 2015 to May 3, 2016. To show the applicability and superiority of the EEMD-RF approach, two basic models (a back-propagation neural network (BPNN) and least squares support vector regression (LSSVM) and five model experiments (EEMD-BPNN, EEMD-LSSVM, RF, BPNN and LSSVM) were selected for comparison. Among these approaches, the proposed model exhibited the best forecast performance in terms of mean absolute error, mean absolute percentage error, and root-mean-square error.
•A random forest model coupled with ensemble empirical mode decomposition (EEMD-RF) is proposed.•The EEMD is applied for extracting complex features of different modes.•The RF is applied for modeling the changes of different modes.•The EEMD-RF has high accuracy in enterprise electricity consumption forecasting.
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•A M-band flexible wavelet transform with high frequency resolution is constructed.•The wavelet filter bank is designed by the frequency domain method.•The fast numeric implementation algorithm of ...the proposed transform is presented.•This method can be well applied to diagnose the faults of planetary gearboxes.
The fault diagnosis of planetary gear transmission systems is crucial for the safety of machineries and equipment. To identify the underlying fault features in measured signals, a novel M-band flexible wavelet transform is constructed. This transform provides a denser sampling of the time–frequency plane and preserves tunable filter parameters and dilation factors. A perfect reconstruction condition of the proposed transform is established, and its corresponding wavelet filter bank is designed to satisfy the perfect reconstruction condition. A numerical implementation algorithm of M-band flexible wavelet transform is investigated using a multirate filter bank and fast Fourier transform. Denoising the simulation signals demonstrates that the proposed transform exhibits better performance than analytic flexible wavelet transform, orthogonal wavelet transform, and biorthogonal wavelet transform. A new fault diagnosis method for planetary gear transmission systems is proposed on the basis of M-band flexible wavelet transform and spectral negentropy. Experimental and comparative results show that the proposed method can be more effectively and accurately applied to the fault diagnosis of planetary gear transmission systems compared with typical fault diagnosis methods based on analytic flexible wavelet transform, Morlet wavelet transform, and infograms.
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•The Tooth-FFT algorithm is introduced to track time-varying frequency components.•A method to detect incipient and consolidated faults in induction motors is proposed.•The method uses as input the ...current monitored during the motor start-up transient.•Healthy, incipient and consolidated BRB faults are considered in the experimentation.•A percentage of detection of 97.5% is obtained for all the possible motor conditions.
Motor current signals analysis (MCSA) is a widely used approach for fault diagnostics in induction motors (IMs). It consists of detecting a specific signature or pattern associated to a fault condition from current signals. In particular, the fault of broken rotor bars (BRBs) is featured by a V-shaped pattern in the time-frequency domain during the startup transient. Although many techniques and methodologies have been presented in literature, most of them have been focused on analyzing consolidated faults such as one- BRB and multiple BRBs; in contrast, the BRB incipient detection, such as half BRB, has been rarely investigated. Hence, a methodology based on a new technique named Tooth-fast Fourier transform (FFT) to detect both incipient and consolidated BRB conditions is presented in this work. It consists of two windows moving along the analyzed current signal, where the FFT is performed for each window. Next, the spectra are subtracted for minimizing the stationary frequencies and maximizing the moving-ones. The signature of the moving frequencies in the resulting spectrogram has a “teeth” shape, giving the name to the proposed technique. Next, a weight function and a classification stage employing four indicators are presented for automatic diagnostics. The proposal is validated and tested using both synthetic and real signals. For the latter, different levels of BRB, i.e., half BRB, one BRB, and two BRBs, are considered. Results demonstrate the effectiveness and usefulness of the proposal to detect both incipient and consolidated BRB faults in IMs.
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This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this ...book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.
A recently developed extrography separation method fractionates petroleum asphaltenes based on their ionization efficiency, which correlates with polarity, aggregation tendency, and asphaltene ...structure (single-core or island versus multicore or archipelago). Archipelago asphaltenes were recently demonstrated to coexist with island structures in a variety of petroleum samples; however, archipelago compounds ionize much less efficiently than island compounds, making the former difficult to observe by mass spectrometry without prior separation. Highly processed coal-derived asphaltenes have been studied previously to reveal only small, single-core structure asphaltenes; however, the structure(s) of asphaltenes from unaltered coal extracts has not been extensively studied. Thus, this work focuses on the application of the extrography separation to an unaltered Illinois coal No. 6 asphaltene extract to reveal the coexistence of island and archipelago structural motifs by positive-ion (+) atmospheric pressure photoionization (APPI) Fourier transform ion cyclotron resonance mass spectrometry. Asphaltenes from a Wyoming crude oil sample are also characterized for comparison with coal asphaltenes. The results reveal that Wyoming crude oil asphaltenes contain mainly island species, whereas coal asphaltenes contain archipelago and island compounds with high oxygen content. The structural analysis is enabled by a new “multinotch” stored-waveform inverse Fourier transform isolation, which selectively isolates high-aromaticity precursor ions at each of several nominal mass ranges prior to fragmentation by infrared multiphoton dissociation, and enables unambiguous determination of island versus archipelago species in samples that contain compounds with high and low aromaticity. The more polarizable fractions from each asphaltene sample reveal low-aromaticity polyfunctional oxygenated species, with a solubility behavior consistent with asphaltenes but a compositional range typical of maltenes. These atypical asphaltene species, which ionize poorly, are hypothesized to participate in multiple hydrogen bonding interactions and thus exhibit strong adsorption on polar stationary phases such as SiO2. Furthermore, these polarizable polyfunctional species ionize preferentially as protonated cations by (+) APPI, accounting for their capability to hydrogen-bond in solution. Collectively, the results demonstrate the existence of archipelago structures in both coal and petroleum asphaltenes, along with polyoxygenated species with low aromaticity that behave like asphaltenes in terms of solubility, because they can establish stronger intermolecular forces such as hydrogen bonding.
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A more efficient multiscale coupling method is developed to study the progressive damage behavior of three dimensional (3D) braided composite beam. In the mesoscale, the fast Fourier transformation ...(FFT)-based method combining with variational principle is used to overcome the poor convergence for composites with large jumps of material properties. In the macro-scale, the mechanical response of the braided composites is analyzed by using finite element (FE) method, in which the stress and stiffness information of each material point can be transferred from the mesoscale results. It is verified that the predicted strength and dominated failure modes of the braided composites structure obtained by the proposed method combing with anisotropic stiffness degradation model are in good agreement with the experimental results. Meanwhile, the high computation efficiency is attractive for large complex structure taking into account the nonlinear mechanical behavior.
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