Fourier Techniques Research Articles

The SINC way: a fast and accurate approach to Fourier pricing

The goal of this paper is to investigate the method outlined by one of us (P. R.) in Cherubini, U., Della Lunga, G., Mulinacci, S. and Rossi, P. [Fourier Transform Methods in Finance, 2009 (John Wiley & Sons Inc.).] to compute option prices. We name it the SINC approach. While the COS method by Fang, F. and Oosterlee, C.W. [A novel pricing method for european options based on Fourier-cosine series expansions. SIAM. J. Sci. Comput., 2009, 31(2), 826–848.] leverages the Fourier-cosine expansion of truncated densities, the SINC approach builds on the Shannon Sampling Theorem revisited for functions with bounded support. We provide several results which were missing in the early derivation: (i) a rigorous proof of the convergence of the SINC formula to the correct option price when the support grows and the number of Fourier frequencies increases; (ii) ready to implement formulas for put, Cash-or-Nothing, and Asset-or-Nothing options; (iii) a systematic comparison with the COS formula for several log-price models; iv) a numerical challenge against alternative Fast Fourier specifications, such as Carr, P. and Madan, D. [Option valuation using the fast Fourier transform. J. Comput. Finance, 1999, 2(4), 61–73.] and Lewis, A.L. [Option Valuation Under Stochastic Volatility with Mathematica Code, 2000 (Newport Beach: Finance Press).]; (v) an extensive pricing exercise under the rough Heston model of Jaisson, T. and Rosenbaum, M. [Limit theorems for nearly unstable Hawkes processes. Ann. Appl. Probab., 2015, 25(2), 600–631.]; (vi) formulas to evaluate numerically the moments of a truncated density. The advantages of the SINC approach are numerous. When compared to benchmark methodologies, SINC provides the most accurate and fast pricing computation. The method naturally lends itself to price all options in a smile concurrently by means of Fast Fourier techniques, boosting fast calibration. Pricing requires resorting only to odd moments in the Fourier space.

Enhanced separation performance of microfiltration carbon membranes for oily wastewater treatment by an air oxidation strategy

An air oxidation strategy was developed for the first time to modify the microstructure and separation performance of microfiltration carbon membranes (MFCMs) for oily wastewater treatment. The structure and property of MFCMs were characterized by the techniques of Fourier transform infrared spectroscopy, scanning electron microscope, pore size distribution, porosity, X-ray diffraction, nitrogen adsorption and water contact angle. The results have shown that the oxidation can effectively modulate the porous structure, surface property and separation performance of MFCMs by varying air oxidation temperature and holding time. The optimal separation performance was respectively achieved to 554.5 kg m−2 h−1 for water permeation flux and 99.0% for oil rejection when MFCMs were oxidized at 80 °C for 30 min. Meanwhile, the anti-fouling ability of MFCMs was substantially improved by two-fold for the flux recovery ratio after oxidation modification. In brief, the work has been proved that the air oxidation is one of the most promising strategies for tailoring MFCMs to efficiently remove the emulsified oil from wastewater.

A comparative study of multidimensional Fourier reconstruction of 2D prestack seismic data

Multidimensional regularization and interpolation methods are an essential component of seismic data processing. Fourier reconstruction algorithms are efficient and straightforward to implement. Minimum Weighted Norm Interpolation (MWNI), Anti-Leakage Fourier Transform (ALFT), and Matching Pursuit Fourier Interpolation (MPFI) are examples of classical Fourier reconstructions techniques for prestack seismic data. MWNI estimates the Fourier coefficients that synthesize spatial data via a regularized inversion method. The MPFI and ALFT algorithms belong to the family of greedy algorithms, which determine Fourier coefficients iteratively. We provide an overview of the three Fourier based reconstruction algorithms mentioned above and compare them to access their strengths and weakness for processing prestack 2D land data. We conduct tests that highlight the capacity of Fourier techniques to reconstruct sparse seismic data and low-quality noisy land seismic data. We pay particular attention to adopting Fourier interpolation for data preconditioning before prestack time migration. We present a processing flow that can be utilized for new and vintage 2D onshore datasets, where preconditioning is essential to obtain high-quality migrated sections. In addition to synthetic examples, we present a real data study that corresponds to a vintage line from the Tacutu Basin, Northern Brazil, which was reprocessed and preconditioned with Fourier interpolation to improve prestack time migration images.

Enhancing resin-dentin bond durability using a novel mussel-inspired monomer.

Numerous approaches have been developed to improve the resin-dentin bond performance, among which the bio-application of mussel-derived compounds have drawn great attention recently. To assess the performance of N-(3,4-dihydroxyphenethyl)methacrylamide (DMA), a mussel-derived compound, as a functional monomer in dental adhesive, its potential property to cross-link with dentin collagen and polymerize with adhesive will first be evaluated by transmission electron microscopy (TEM), attenuated total reflectance technique of Fourier transform infrared (ATR-FTIR), and atomic force microscopy (AFM) via Peakforce QNM mode. After validating the influence of DMA on collagen and adhesive separately, the overall performance of DMA/ethanol solution as a primer in dentin bonding was examined using micro-tensile bond strength (μTBS) testing, fracture pattern observation, and nanoleakage evaluation both immediately and after 10,000 times thermocycling aging. The inhibitory effect of DMA on endogenous metalloproteinases (MMPs) was evaluated by in situ zymography using confocal laser scanning microscopy (CLSM) and the cytotoxicity of DMA was evaluated using cell counting kit-8. Results demonstrated that DMA successfully cross-linked with dentin collagen via non-covalent bonds and had no influence on the polymerization and mechanical properties of the adhesive. Furthermore, even after 10,000 times thermocycling aging, the μTBS and nanoleakage expression of the DMA-treated groups showed no significant change compared with their immediate values. In situ zymography revealed reduced endogenous proteolytic activities after the application of DMA, and no cytotoxicity effect was observed for DMA concentration up to 25 ​μmol/L. Thus, DMA could be used as a novel, biocompatible functional monomer in dentin bonding.

Comparison of Deterministic Methods to Estimate Sidereal Rotation Period from Light Curves

The importance of determining the sidereal rotation period of an astronomical object on future investigations pertaining to said object has been well documented in the literature. Researchers, however, have differed in their techniques used to estimate and model objects in the space catalog. In this paper, several period-estimation methods will be explored ranging across Fourier and phase-folding techniques. These methods will be tested using ground-based observations of light curve data for various resident space objects that fall under a rigid body context (i.e., asteroids, satellites, probes, rocket bodies) and celestial objects like stars and extrasolar planets. The effect of varying sample size, the inadequacies in unevenly sampled data processing, autonomy of the method, and complexity of parameters are investigated. For the models of artificial space objects that are not open source, a simulation is used to generate synthetic light curves with which all of the above-mentioned techniques are also employed. To account for heterogeneity in method parameters, each technique is tested with a range of values to optimize the rotational period. Results for uniformly sampled asteroid data as well as nonuniformly sampled stellar objects and generic sinusoidal data show variances in accuracy of the methods, but certain methods stand out.

NUDIM: A non-uniform fast Fourier transform based dual-space constraint iterative reconstruction method in biological electron tomography

Electron tomography, a powerful imaging tool for studying 3D structures of macromolecular assemblies, always suffers from imperfect reconstruction with limited resolution due to the intrinsic low signal-to-noise ratio (SNR) and inaccessibility to certain tilt angles induced by radiation damage or mechanical limitation. In order to compensate for such insufficient data with low SNR and further improve imaging resolution, prior knowledge constraints about the objects in both real space and reciprocal space are thus exploited during tomographic reconstruction. However, direct Fast Fourier transform (FFT) between real space and reciprocal space remains extraordinarily challenging owing to their inconsistent grid sampling modes, e.g. regular and uniform grid sampling in real space whereas radial or polar grid sampling in reciprocal space. In order to solve such problem, a technique of non-uniform fast Fourier transform (NFFT) has been developed to transform efficiently between non-uniformly sampled grids in real and reciprocal space with sufficient accuracy. In this work, a Non-Uniform fast Fourier transform based Dual-space constraint Iterative reconstruction Method (NUDIM) applicable to biological electron tomography is proposed with a combination of basic concepts from equally sloped tomography (EST) and NFFT based reconstruction. In NUDIM, the use of NFFT can circumvent such grid sampling inconsistency and thus alleviate the stringent equally-sloped sampling requirement in EST reconstruction, while the dual-space constraint iterative procedure can dramatically enhance reconstruction quality. In comparison with conventional reconstruction methods, NUDIM is numerically and experimentally demonstrated to produce superior reconstruction quality with higher contrast, less noise and reduced missing wedge artifacts. More importantly, it is also capable of retrieving part of missing information from a limited number of projections.

AIEgens-based fluorescent covalent organic framework in construction of chemiluminescence resonance energy transfer system for serum uric acid detection.

A covalent organic framework (COF) with aggregation-induced emission (AIE) property was successfully synthesized through in situ marriage of a commonly used AIE molecule tetraphenylethylene (TPE) with Schiff base network (SNW-1) through a simple one-pot method. The TPE@SNW-1 was characterized with different techniques of Fourier transform infrared spectroscopy, X-ray diffraction, transmission electron microscopy, scanning electron microscopy, and nitrogen adsorption/desorption experiments. The fluorescence of the TPE@SNW-1 strongly depends on the composition of tetrahydrofuran-water binary system. The AIE property of TPE@SNW-1 was directly supported with particle size distribution by dynamic light scattering technique. With the TPE@SNW-1 as an energy acceptor, a chemiluminescence resonance energy transfer (CRET) system was constructed with bis(2,4,6-trichlorophenyl) oxalate (TCPO)-hydrogen peroxide (H2O2) reaction as an energy donor. The chemiluminescence (CL) signal displays a good linear relationship with concentration of H2O2 in the 5.0-1000.0 μmol·L-1 range, and a detection limit of 2.34 μmol L-1. The system was further exploited to determine uric acid based on the fact that equal stoichiometric amount of H2O2 can be concurrently generated under the catalysis of uricase. The procedure exhibits a linear response to uric acid concentration in the range 10.0-150.0 μmol·L-1 and a detection limit of 4.94 μmol·L-1. The practicability of the method was demonstrated in the determination of uric acid in human serum samples.

Impact of iterative reconstruction algorithms on the applicability of Fourier-based detectability index for x-ray CT imaging.

The increasing application of iterative reconstruction algorithms in clinical computed tomography to improve image quality and reduce radiation dose, elicits strong interest, and needs model observers to optimize CT scanning protocols objectively and efficiently. The current paradigm for evaluating imaging system performance relies on Fourier methods, which presuppose a linear, wide-sense stationary system. Long-range correlations introduced by iterative reconstruction algorithms may narrow the applicability of Fourier techniques. Differences in the implementation of reconstruction algorithms between manufacturers add further complexity. The present work set out to quantify the errors entailed by the use of Fourier methods, which can lead to design decisions that do not correlate with detectability. To address this question, we evaluated the noise properties and the detectability index of the ideal linear observer using the spatial approach and the Fourier-based approach. For this purpose, a homogeneous phantom was imaged on two scanners: the Revolution CT (GE Healthcare) and the Somatom Definition AS+ (Siemens Healthcare) at different exposure levels. Images were reconstructed using different strength levels of IR algorithms available on the systems considered: Adaptative Statistical Iterative Reconstruction (ASIR-V) and Sinogram Affirmed Iterative Reconstruction (SAFIRE). Our findings highlight that the spatial domain estimate of the detectability index is higher than the Fourier domain estimate. This trend is found to be dependent on the specific regularization used by IR algorithms as well as the signal to be detected. The eigenanalysis of the noise covariance matrix and of its circulant approximation yields explanation about the evoked trends. In particular, this analysis suggests that the predictive power of the Fourier-based ideal linear observer depends on the ability of each basis analyzed to be relevant to the signal to be detected. The applicability of Fourier techniques is dependent on the specific regularization used by IR algorithms. These results argue for verifying the assumptions made when using Fourier methods since Fourier-task-based detectability index does not always correlate with signal detectability.

Fast Computation by MLFMM-FFT with NURBS in Large Volumetric Dielectric Structures

A refinement for the computation of the rigorous part of the multi-level fast multipole method (MLFMM) of analyzing volumetric objects is presented. A scheme based on the fast Fourier technique (FFT) is proposed with the objective of reducing the computational resources required to accurately analyze large homogeneous and non-homogeneous dielectric volumes. In order to reduce the memory requirements, the storage of the near-field terms of the method of moments (MoM) matrix is performed only for the positions corresponding to a parallelepiped with the size of the level 1 block of the MLFMM, computed with the vacuum permittivity, taking advantage of the Toeplitz symmetry present in regular hexahedral meshes. The FFT avoids applying the near-field MoM matrix in the iterative solution process. The application of this approach results in huge improvements in terms of memory usage, but also a speeds up the iterative solution process because the use of three-dimensional (3D) FFTs is very efficient for computing convolutions when the number of unknowns of the problems becomes very large as happens in volumetric problems. We also propose a new approach for the numerical treatment of the transition of the dielectric permittivity between different dielectrics or between a dielectric and a free space. To validate the computation technique, the radar cross section (RCS) of several dielectric bodies is computed using the classical MLFMM approach and it is compared with the presented FFT-based-MLFMM solution. The results demonstrate that the efficient memory and computation time usage of the proposed approach.

Effects of doping concentration on thermoluminescence parameters of CaAl2O4:Re3+ (Re3+ = Dy3+, Sm3+, Tm3+) prepared by combustion method

In this study, we investigate thermoluminescence (TL) of calcium aluminate undoped and doped with three rare earth elements at five different concentrations, synthesized by the combustion method, which can be designed for relevant applications with suitable doping of activators. From the XRD data, we determine the phase, structure and particle size, using Scherrer's equation. Investigations on the morphology and functional groups of the prepared samples are carried out by using the techniques of field emission scanning electron microscope (FE-SEM) and Fourier transform infrared (FTIR) spectroscopy. The samples are exposed to γ-ray doses of 10 Gy to investigate their optimum concentrations, the effects of doping with different rare earth elements and kinetic parameters. The TL glow curves are deconvoluted using the TLanal program, and TL trapping parameters, viz. activation energy (E), frequency factor (s) and order of kinetics (b) of trapped charges, are obtained. We theoretically evaluate lifetimes (τ) of the charges in the traps present in these phosphors using kinetic parameters. The phosphor CaAl2O4:Sm3+ has the most intense stable TL peaks and the trap charge-lifetime in the range of years, which make it an eligible candidate for dosimetric applications. We also observe photoluminescence spectra of doped calcium aluminate at the optimum concentration exhibiting maximum TL intensity.

Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach

In recent years, different experimental works with molecular simulation techniques have been developed to study the transport of plasma-generated reactive species in liquid layers. Here, we improve the classical transport model that describes the molecular species movement in liquid layers via considering the fractional reaction–telegraph equation. We have considered the fractional equation to describe a non-Brownian motion of molecular species in a liquid layer, which have different diffusivities. The analytical solution of the fractional reaction–telegraph equation, which is defined in terms of the Caputo fractional derivative, is obtained by using the Laplace–Fourier technique. The profiles of species density with the mean square displacement are discussed in each case for different values of the time-fractional order and relaxation time.

Experimental investigation of diesel soot oxidation reactivity along the exhaust after-treatment system components

The primary objective of the present study is to investigate the variations of soot particles’ oxidation reactivity along the components of the exhaust after-treatment system in a diesel engine and analyze its quantitative correlation with surface functional groups (SFGs) and graphitization degree. Soot particles generated from a 16-cylinder turbocharged diesel engine were sampled thoroughly before and after the diesel oxidation catalyst (DOC), as well as after a catalyzed diesel particulate filter (CDPF). Using a set of characterization techniques of Fourier transform infrared (FTIR), Raman spectroscopy and Thermal gravimetric analyzer (TGA), the surface functional groups (SFGs), graphitization degree and oxidation reactivity of soot particle samples along the exhaust after-treatment system components were examined. Results showed that, for all conditions, soot oxidation activation energies increased almost linearly along the after-treatment system, indicating that soot particles became more and more stable, with the inherent graphitization degree achieved the highest right after the CDPF. Meanwhile, the combined characterization results also indicated that amorphous carbon and reactive light volatile fractions have been removed or oxidized via passing through the DOC and CDPF monolith. It was thus concluded that the higher oxidation activity of soot particles was characterized by lower graphitization degree and higher aliphatic C-H group concentration. The catalyst components in the after-treatment systems (DOC and CDPF) effectively increases the graphitization of the exhaust particles, leaving more stable particles that would require much higher energies from active regeneration or more powerful catalysts on the CDPF wall surface to clean them up.

The half-order energy balance equation – Part 2: The inhomogeneous HEBE and 2D energy balance models

Abstract. In Part 1, I considered the zero-dimensional heat equation, showing quite generally that conductive–radiative surface boundary conditions lead to half-ordered derivative relationships between surface heat fluxes and temperatures: the half-ordered energy balance equation (HEBE). The real Earth, even when averaged in time over the weather scales (up to ≈ 10 d), is highly heterogeneous. In this Part 2, the treatment is extended to the horizontal direction. I first consider a homogeneous Earth but with spatially varying forcing on both a plane and on the sphere: the new equations are compared with the canonical 1D Budyko–Sellers equations. Using Laplace and Fourier techniques, I derive the generalized HEBE (the GHEBE) based on half-ordered space–time operators. I analytically solve the homogeneous GHEBE and show how these operators can be given precise interpretations. I then consider the full inhomogeneous problem with horizontally varying diffusivities, thermal capacities, climate sensitivities, and forcings. For this I use Babenko's operator method, which generalizes Laplace and Fourier methods. By expanding the inhomogeneous space–time operator at both high and low frequencies, I derive 2D energy balance equations that can be used for macroweather forecasting, climate projections, and studying the approach to new (equilibrium) climate states when the forcings are all increased and held constant.

The half-order energy balance equation – Part 1: The homogeneous HEBE and long memories

Abstract. The original Budyko–Sellers type of 1D energy balance models (EBMs) consider the Earth system averaged over long times and apply the continuum mechanics heat equation. When these and the more phenomenological box models are extended to include time-varying anomalies, they have a key weakness: neither model explicitly nor realistically treats the conductive–radiative surface boundary condition that is necessary for a correct treatment of energy storage. In this first of a two-part series, I apply standard Laplace and Fourier techniques to the continuum mechanics heat equation, solving it with the correct radiative–conductive boundary conditions and obtaining an equation directly for the surface temperature anomalies in terms of the anomalous forcing. Although classical, this equation is half-ordered and not integer-ordered: the half-order energy balance equation (HEBE). A quite general consequence is that although Newton's law of cooling holds, the heat flux across surfaces is proportional to a half-ordered (not first-ordered) time derivative of the surface temperature. This implies that the surface heat flux has a long memory, that it depends on the entire previous history of the forcing, and that the temperature–heat flux relationship is no longer instantaneous. I then consider the case in which the Earth is periodically forced. The classical case is diurnal heat forcing; I extend this to annual conductive–radiative forcing and show that the surface thermal impedance is a complex valued quantity equal to the (complex) climate sensitivity. Using a simple semi-empirical model of the forcing, I show how the HEBE can account for the phase lag between the summer maximum forcing and maximum surface temperature Earth response. In Part 2, I extend all these results to spatially inhomogeneous forcing and to the full horizontally inhomogeneous problem with spatially varying specific heats, diffusivities, advection velocities, and climate sensitivities. I consider the consequences for macroweather (monthly, seasonal, interannual) forecasting and climate projections.

Effective Single-Frequency Source Spectra in Broadband Time-Domain Electromagnetic Simulation of Time-Varying Materials

An advantage of time-domain electromagnetic simulation tools is that an entire spectrum can be obtained in a single simulation run by using a broadband initial condition and Fourier transformation of the ensuing time sequences. However, when the simulation involves time-varying materials, the system is no longer time-invariant, and Fourier techniques must be reconsidered to obtain desired results. Most theoretical and many experimental conditions assume a single-frequency or narrowband source excitation, which minimizes the unintended effects of frequency mixing. However, performing many single-frequency time-domain simulations would be needed to construct an entire spectrum in this way, which would become computationally impractical. This work shows how a few finite-difference time-domain (FDTD) simulations can be used with broadband initial conditions to obtain scattering spectra in time-modulated resonator systems that effectively correspond to a single-frequency source spectrum. The approach involves running FDTD simulations in which the phase between the modulating signal and the source signal is deliberately changed and then averaging the spectra from the simulations. Using only six simulations, the source frequencies up to (plus or minus) five times the modulating frequency can be canceled out, which provides good agreement with theoretical predictions over a broad range of parameter values.

Large time behaviour for the heat equation on [formula omitted], moments and decay rates

The paper is devoted to understand the large time behaviour and decay of the solution of the discrete heat equation in the one dimensional mesh Z on ℓp spaces, and its analogies with the continuous-space case. We do a deep study of the moments of the discrete gaussian kernel (which is given in terms of Bessel functions), in particular the mass conservation principle; that is reflected on the large time behaviour of solutions. We prove asymptotic pointwise and ℓp decay results for the fundamental solution. We use that estimates to get rates on the ℓp decay and large time behaviour of solutions. For the ℓ2 case, we get optimal decay by use of Fourier techniques.

A Bivariate Normal Inverse Gaussian Process with Stochastic Delay: Efficient Simulations and Applications to Energy Markets

ABSTRACT Using the concept of self-decomposable subordinators introduced by Gardini, Sabino, and Sasso, we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme that relies on the mathematical connection between self-decomposable Inverse Gaussian laws and Lévy-driven Ornstein–Uhlenbeck processes with Inverse Gaussian stationary distribution. We show that our approach provides an improvement to the existing simulation scheme detailed in Zhang and Zhang, because it does not rely on an acceptance–rejection method. Eventually, these results are applied to the modelling of energy markets and to the pricing of spread options using the proposed Monte Carlo scheme and Fourier techniques.

Harmonic analysis of annual global irradiation in the cities of India

Intermittent renewable energy sources, installation and maintenance of sophisticated instruments to measure irradiation in remote locations has become a serious concern, so this study model the irradiation by harmonic analysis. The evaluated analysis recognises the suitable harmonic equation for the cities, which would sustainably enhance energy usage. Time series analysis involves the correlation of Fourier technique to meteorological parameters such as irradiation and precipitation. This process’s application highlighted the predominant contribution of yearly harmonic in a productive way rather than the subsequent harmonics. This idea allows obtaining a time series function that estimates irradiation’s possible value for any day of the year in a geographical location. The interpretation of global irradiation’s spatial characteristics over twelve sites in India includes the estimation of amplitude, percentage variance, and phase angle of the harmonics. The first and second harmonic components contribute larger than 91% of the irradiation variance in studied locations. Statistical error metrics evaluate the developed harmonic equations’ performance based on ranking technique. Global Performance Indicator identifies the appropriate harmonic equation using scaled statistical metrics. The study found a mean bias error closer to zero, and a lower value of root mean square error indicate a close estimation to measured values. However, the mean absolute percentage error varies between 1.9491% (Chennai) and 22.2184% (Goa) specifies overestimation due to overcast and cloudy conditions.

Estimating blood flow velocity using time-resolved 3D angiography and a derived physical law of contrast media

Objective. Four-dimensional (4D) digital subtraction angiography (DSA) offers a method for evaluating hemodynamics. It is, however, unclear how the delivered contrast medium interacts with the physiological blood flow, and how hemodynamic information may be inferred from the mixture of the contrast medium and blood. In this study, we present a theoretical explanation of contrast dynamics, and an accompanying algorithm for estimating blood flow velocity. Approach. We retrospectively recruited 23 patients who underwent both 4D DSA and magnetic resonance (MR) phase-contrast imaging. The 4D DSA-reconstructed contrast dynamics were first studied for the internal carotid arteries. Using physical laws governing fluid motion within a curved tube, we showed that the reconstructed contrast dynamics obeyed a simple advection equation. We then proposed an algorithm for estimating the contrast dynamics using angiographic data, and subsequently estimated the axial blood flow velocity using an advection equation. Main results. The estimated velocities were compared using three techniques: the Fourier technique, Lin’s method, and MR phase contrast. Testing with noise-corrupted artificial data showed that the proposed algorithm was noise resistant. The velocities of 23 patients computed by 4D DSA using the proposed algorithm showed a moderate correlation with the MR phase contrast (r = 0.61), and good correlations with the other two techniques (r = 0.75 and r = 0.72). Significance. The proposed algorithm and has been applied to blood vessel segments with poor signal-to-noise ratios and axial lengths of less than 3 cm, and has a physical basis for computing axial flow velocities using an advection equation. The results of the proposed algorithm are consistent with existing methods.

Roller Element Bearing Fault Size Estimation Using Adaptive Neurofuzzy Inference System

Abstract The vibration level is a function of the defects in the bearing. By identifying a change in vibration level, one can predict the dynamic behavior and fault in the rotor-bearing system. An imminent bearing fault detection can reduce downtime or avoid the failure of rotating machinery. The condition monitoring or maintenance schedule can be set well if the diagnosis estimate bearing fault size accurately. In view of this, the adaptive neurofuzzy inference system (ANFIS) and dimension analysis (DA) were utilized to detect the bearing fault size. Several experiments were performed at different rotating speeds on the rotor-bearing system. Localized defects were simulated on bearing races artificially using electrode discharge machining (EDM) and the vibration responses are acquainted by accelerometer and fast Fourier techniques (FFT). With a 0.1 mm error band to fix minor bugs, a two-performance indicator evaluated the model accuracy. A comparison of the performance of models with experimental results and artificial neural network (ANN) validated the potential of the present approach. The results showed that an ANFIS performs better over DA and ANN. This contributes to detecting bearing fault effectively and accuracy improvement in the estimation of the bearing fault size.