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This paper aims to explore a new way to extract the fault feature of a rolling bearing signal on the basis of a combinatorial method.

By combining local mean decomposition (LMD) with Teager energy operator, a new feature-extraction method of a rolling bearing fault signal was proposed, called the LMD–Teager transform method. The principles and steps of method are presented, and the physical meaning of the time–frequency power spectrum and marginal spectrum is discussed. On the basis of comparison with the fast Fourier transform method, a simulated non-stationary signal was processed to verify the effect of the new method. Meanwhile, an analysis was conducted by using the recorded vibration signals which include inner race, out race and bearing ball fault signal.

The results show that the proposed method is more suitable for the non-stationary fault signal because the LMD–Teager transform method breaks through the difficulty of the Fourier transform method that can process only the stationary signal. The new method can extract more useful information and can provide better analysis accuracy and resolution compared with the traditional Fourier method.

Combining the advantage of the local mean decomposition and the Teager energy operator, the LMD–Teager method suits the nature of the fault signal. A marginal spectrum obtained from the LMD–Teager method minimizes the estimation bias brought about by the non-stationarity of the fault signal. So, the LMD–Teager transform has better analysis accuracy and resolution than the traditional Fourier method, which provides a good alternative for fault diagnosis of the rolling bearing.

The spectral boundary element method for solving two‐dimensional transient heat conduction problems is developed. This method is combined with the fast Fourier transform (FFT) to convert the solution between the time and frequency domains. The fundamental solutions in the frequency domain, required for the present method, are discussed. The resulting line integrations in the frequency domain are discretized using constant boundary elements and used in a Fortran boundary element program. Three examples are used to illustrate the accuracy and effectiveness of the method in both the frequency and time domains. First, the frequency domain solution procedure is verified using the steady‐state example of a semi‐infinite half space with a heat flux applied to a patch of the surface. This spectral boundary element method is then applied to the problem of a circular hole in an infinite solid subjected to a time‐varying heat flux, and solutions in both the frequency and time domains are presented. Finally, the method is used to solve the circular hole problem with a convection boundary condition. The accurary of these results leads to the conclusion that the spectral boundary element method in conjunction with the FFT is a viable option for transient problems. In addition, this spectral approach naturally produces frequence domain information which is itself of interest.

The purpose of this paper is to present the method for efficient computation of risk measures using Fourier transform technique. Another objective is to demonstrate that this technique enables an efficient computation of risk measures beyond value-at-risk and expected shortfall. Finally, this paper highlights the importance of validating assumptions behind the risk model and describes its application in the affine model framework.

The method proposed is based on Fourier transform methods for computing risk measures. The authors obtain the loss distribution by fitting a cubic spline through the points where Fourier inversion of the characteristic function is applied. From the loss distribution, the authors calculate value-at-risk and expected shortfall. As for the calculation of the entropic value-at-risk, it involves the moment generating function which is closely related to the characteristic function. The expectile risk measure is calculated based on call and put option prices which are available in a semi-closed form by Fourier inversion of the characteristic function. We also consider mean loss, standard deviation and semivariance which are calculated in a similar manner.

The study offers practical insights into the efficient computation of risk measures as well as validation of the risk models. It also provides a detailed description of algorithms to compute each of the risk measures considered. While the main focus of the paper is on portfolio-level risk metrics, all algorithms are also applicable to single instruments.

The algorithms presented in this paper require little computational effort which makes them very suitable for real-world applications. In addition, the mathematical setup adopted in this paper provides a natural framework for risk model validation which makes the approach presented in this paper particularly appealing in practice.

This is the first study to consider the computation of entropic value-at-risk, semivariance as well as expectile risk measure using Fourier transform method.

In this paper, two transform methods, the Fourier transform (FT) and the wavelet transform (WT) methods, are utilized to process moiré fringes for the strain analysis of electronic packaging. With the introduction of fringe carriers, those transform techniques need only one fringe pattern for each deformation state. The strain modulation to the carrier frequency can be subtracted by filtering as the pattern is transformed into spectrum domain by the fast‐FT processing, and the deformation field can thus be restored by the inverse FT transform after spectral shifting. The WT method expands the pattern information involved in the fringe carrier in both spatial domain and spectral domain to analyze the deformation distribution in this combined space. By changing the transform scales in the processing, the wavelet transform offers multi‐resolution analysis for the deformation field with high gradients.

An introduction is given to the generation and use of new transform techniques which have important applications in binary control and processing methods. A comparison is made between the fast Fourier transform and the equivalent fast Walsh transform together with the steps required to produce a transform algorithm and computer program. Some applications of the transform are then discussed and which include spectral analysis, filtering, non‐linear control and communications uses. 18 references to current work in these applications areas are included.

Combines the techniques of fast Fourier transforms, Buneman cyclic reduction and the capacity matrix in a finite difference Poisson solver specifically designed for modelling realistic electronic device structures. A solution may be determined on a number of connected rectangular regions which correctly accounts for continuity of the electric displacement at dielectric interfaces. Suggests the method is particularly well suited to problems requiring repeated solution with the same device structure and provides a self‐consistent Monte Carlo simulation as an example of such an application.

The purpose of this paper is to introduce a spectral model capable of simulating fully transient conductive‐convective heat transfer processes in an axially‐symmetric shallow geothermal system consisting of a borehole heat exchanger embedded in a soil mass.

The proposed model combines the exactness of the analytical methods with important extent of generality in describing the geometry and boundary conditions of the numerical methods. It calculates the temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass using the discrete Fourier transform, for the time domain, and the Fourier‐Bessel series, for the spatial domain.

The paper calculates the temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass in a robust and computationally very efficient procedures. Analysis which might take long time in a work station, if use is made of standard numerical procedures, takes only 1 second in an Intel PC with the proposed model.

The model is capable of simulating fully transient heat transfer in a shallow geothermal system subjected to short and long‐term time varying boundary conditions. The CPU time for calculating temperature distributions in all involved components; pipe‐in, pipe‐out, grout, and soil, using 2048 FFT samples, for the time domain, and 100 Fourier‐Bessel series samples, for the spatial domain, was in the order of 1 second in an Intel PC. The accuracy and computational efficiency of the model makes it, if elaborated, vital for engineering practice.

The proposed model is original and generic. The idea behind it is new and has not been utilized in this field of application. The model can be extended easily to include other types of borehole heat exchangers embedded in multi‐layer systems.

The purpose of this paper is to solve the local problem involving strong contrast heterogeneous conductive material, with application to gas-filled porous media with both perfect and imperfect Kapitza boundary conditions at the bi-material interface. The effective parameters like the dynamic conductivity and the thermal permeability in the acoustics of porous media are also derived from the cell solution.

The Fourier transform method is used to solve frequency-dependent heat transfer problems. The periodic Lippmann–Schwinger integral equation in Fourier space with source term is first formulated using discrete Green operators and modified wavevectors, which can then be solved by iteration schemes.

Numerical examples show that the schemes converge fast and yield accurate results when compared with analytical solution for benchmark problems.

The formulation of the method is constructed using static and dynamic Green operators and can be applied to pixelized microstructure issued from tomography images.

The purpose of this paper is to exploit a new and robust method to forecast the long-term extreme dynamic responses for wave energy converters (WECs).

A new adaptive binned kernel density estimation (KDE) methodology is first proposed in this paper.

By examining the calculation results the authors has found that in the tail region the proposed new adaptive binned KDE distribution curve becomes very smooth and fits quite well with the histogram of the measured ocean wave dataset at the National Data Buoy Center (NDBC) station 46,059. Carefully studying the calculation results also reveals that the 50-year extreme power-take-off heaving force value forecasted based on the environmental contour derived using the new method is 3572600N, which is much larger than the value 2709100N forecasted via the Rosenblatt-inverse second-order reliability method (ISORM) contour method.

The proposed method overcomes the disadvantages of all the existing nonparametric and parametric methods for predicting the tail region probability density values of the sea state parameters.

It is concluded that the proposed new adaptive binned KDE method is robust and can forecast well the 50-year extreme dynamic responses for WECs.

This paper describes fabric inspection system aided by computer vision to detect and classify defects in circular knitted fabrics using different common texture-recognition methods, including co-occurrence matrices, the discrete Fourier transform, wavelets, Gabor, and clustering. The images of the fabrics were broadly classified into six classes: cracks, holes, vertical stripes, horizontal stripes, soil freckles, and defect-free. One hundred and twenty images (256 gray level and 100 dpi) containing 20 images of defect-free fabrics (rib 1x1) as well as 100 images corresponding to five different categories were used. In general, one-half of the images in each category were employed for training and the remaining images were used for testing.

The application of the clustering method applied in this work was found to be highly promising at identifying defects in knitted fabrics. With an overall success rate of 91.6%, the clustering method has a higher efficiency value than all of the other methods. In the case of the wavelet and Gabor methods, the results are acceptable. However, the overall success rates of the co-occurrence matrix and Fourier transform methods in recognizing defects in knitted fabrics are not acceptable.