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Fourier methods used in two‐ and three‐dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance‐type measure instead of information‐theoretic uncertainty, but the two measures are roughly collinear and the Fourier approach yields results close to that of standard RA. The Fourier method, however, does not require iterative calculations for models with loops. Moreover, the error in Fourier RA models can be assessed without actually generating the full probability distributions of the models; calculations scale with the size of the data rather than the state space. State‐based modeling using the Fourier approach is also readily implemented. Fourier methods may thus enhance the power of RA for data analysis and data mining.

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.

An interferogram is produced by modulating the difference between the extraordinary refractive index and the ordinary refractive index for photoelastic crystals in photoelastic-modulated Fourier transform spectrometers (PEM-FTs). Due to the influence of the refractive index dispersion characteristics on the maximum optical path difference of the interferogram, it is necessary to study wavelength calibration methods.

A wavelength calibration method for PEM-FTs was proposed based on the modulation principle of the photoelastic-modulated interferometer and the relationship between the maximum optical path difference and the refractive index difference. A 632.8 nm narrow-pulse laser was used as a reference source to measure the maximum optical path difference () of the interferogram, and the parameter was used to calculate the discrete frequency points in the frequency domain. To account for the influence of refractive index dispersion on the maximum optical path difference, the refractive index curve for the photoelastic crystal was used to adjust the discrete frequency coordinates.

The error in the reconstructed spectral frequency coordinates clearly decreased. The maximum relative error was 2.5%. A good solar absorption spectrum was obtained with a PEM-FT experimental platform and the wavelength calibration method.

The interferogram is produced by adjusting the difference between extraordinary refractive index and ordinary refractive index for the photoelastic crystal in the PEM-FTs. Given the wavelength dependence on the refractive indices, in view of the modulation principle of the photoelastic modulated interferometer, the relationship between the maximum optical path difference and the refractive index difference, the variation law of the refractive index of the photoelastic crystal and the process of spectral reconstruction is presented in this paper.

The purpose of this paper is to study the problem of fashion flat sketches classification and proposed an integrated approach. It aims to propose a fast, reliable method to handle multi-class fashion flat sketches classification problems and lay the foundation for the garment style query in the next step.

The proposed integrated approach adopts wavelet Fourier descriptor (WFD), linear discriminant analysis (LDA) and extreme learning machine (ELM). First, the discrete wavelet and Fourier transform are adopted to extract the shape features of fashion flat sketches. Then, LDA is employed for multi-class classification to reduce dimensionality. Finally, ELM is used as the classifier.

The experimental results show that the classification accuracy of the integrated approach is obtained at about 100 percent. Contrary to the traditional approaches, efficiency and accuracy are the advantages of the present approach.

Fashion concept is conveyed often in the form of the fashion illustration or sketch. This type of sketch is useful to imply the style and overall feel of the design. However, this sketch gives no clue about the parts or sections that make up each garment. For this reason, this paper only studies the classification of flat sketches.

A new shape descriptor named WFD is proposed. The WFD acquires high classification accuracy comparing with Fourier descriptor (FD) and multiscale Fourier descriptor (MFD) without dimensionality reduction and nearly the same classification accuracy comparing with FD while MFD easily causes small sample size problem with dimensionality reduction using LDA. In addition, ELM is first used as the classifier in the textiles field related to the classification problem.

Electric vehicles (EVs) require uninterrupted and safe conditions during operations. Therefore, the diagnostic of power devices and electric motor faults are needed to improve the availability of the system. Hence, fault-tolerant control (FTC), which combines switch fault detection, hardware redundancy and post-fault control, is used. This paper aims to propose an accurate open-phase fault detection and FTC of a direct torque control permanent magnet synchronous motor electrical vehicles by using discrete Fourier-transform phase method.

The main idea is to propose detection and identification of open-phase fault (faulty leg) among three phases voltage source invertor (VSI)-fed permanent magnet synchronous motor drives. Once the faulty leg is detected and isolated, a redundant phase leg insertion, shared by a three-phase VSI, is done by using independent bidirectional TRIAC switches to conduct FTC system. This accurate fault detection significantly improves system availability and reliability. The proposed method of open-phase fault detection and identification is based only on stator phase current measurement.

A novel method is proposed with experimental validation for fault detection, isolation and FTC for a three-phase VSI-fed permanent magnet synchronous motor.

The novel discrete Fourier-transform phase method is proposed to detect an open phase based on the measurement in real time of the instantaneous phase of stator current components in the stationary frame. The experimental implementation is carried out on powerful dSpace DS1104 controller board based on the digital signal processor TMS320F240. The validity of the proposed method has been experimentally verified.

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.

Watermarking technique is one of the significant methods in which carrier signal hides digital information in the form of watermark to prevent the authenticity of the stakeholders by manipulating different coefficients as watermark in time and frequency domain to sustain trade-off in performance parameters. One challenging component among others is to maintain the robustness, to limit perceptibility with embedding information. Transform domain is more popular to achieve the required results in color image watermarking. Variants of complex Hadamard transform (CHT) have been applied for gray image watermarking, and it has been proved that it has better performance than other orthogonal transforms. This paper is aimed at analyzing the performance of spatio-chromatic complex Hadamard transform (Sp-CHT) that is proposed as an application of color image watermarking in sequency domain (SD).

In this paper, color image watermarking technique is designed and implemented in SD using spatio-chromatic – conjugate symmetric sequency – ordered CHT. The color of a pixel is represented as complex number a*+jb*, where a* and b* are chromatic components of International Commission on Illumination (CIE) La*b* color space. The embedded watermark is almost transparent to human eye although robust against common signal processing attacks.

Based on the results, bit error rate (BER) and peak signal to noise ratio are measured and discussed in comparison of CIE La*b* and hue, saturation and value color model with spatio-chromatic discrete Fourier transform (Sp-DFT), and results are also analyzed with other discrete orthogonal transforms. It is observed from BER that Sp-CHT has 8%–12% better performance than Sp-DFT. Structural similarity index has been measured at different watermark strength and it is observed that presented transform performs better than other transforms.

This work presents the details and comparative analysis of two orthogonal transforms as color image watermarking application using MATLAB software. A finding from this study demonstrates that the Complex Hadamard transform is the competent candidate that can be replaced with DFT in many signal processing applications.

The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length and withstand tension and bending. The constitutive equations of the lattice in discrete and differential formulations are derived. Two complementary systems of loads, which cause different deformation two orthogonal families of fibers, occur in the lattice. The fracture behavior of the material containing a semi-infinite crack is investigated. The crack problem reduces to the exactly solvable Riemann-Hilbert problem. The solution demonstrates that the behavior of material cardinally depends upon the tension in the orthogonal family of fibers. If tension in fibers exists, opening of the crack under action of loads in two-dimensional lattice is similar to those in elastic solid. In the absence of tension, contrarily, there is a finite angle between edges at the crack tip.

The description of stress state in the crack vicinity is reduced to the solution of mixed boundary value problem for simultaneous difference equations. In terms of Fourier images for unknown functions the problem is equivalent to a certain Riemann-Hilbert problem.

The analytical solution of the problem shows that fracture behavior of the material depends upon the presence of stabilizing tension in fibers, parallel to crack direction. In the presence of tension in parallel fibers fracture character of two-dimensional lattice is similar to behavior of elastic solid. In this case the condition of crack grows can be formulated in terms of critical stress intensity factor. Otherwise, in the absence of stabilizing tension, the crack surfaces form a finite angle at the tip.

Linear behavior of fibers until rupture. Small deflections. Perfect two-dimensional lattice.

The model provides exact analytical estimation of stresses on the crack tip as the function of fibers’ stiffness.

The model is the extension of known lattice models, taking into account the semi-infinite crack in the lattice. This is the first known closed form solution for an infinite lattice model with the crack.

The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested for nonstationary cases.

This paper aims to present a framework for deriving analytical and semi‐numerical models for coupled conductive‐convective heat transfer processes in a borehole heat exchanger subjected to general initial and boundary conditions.

The discrete Fourier transform and the spectral element method have been utilized for deriving two spectral models for a single U‐tube borehole heat exchanger in contact with a soil mass.

Verification and numerical examples have shown that the developed models are accurate and computationally very efficient. It is illustrated that one spectral element is capable of producing results which are more accurate than those produced by 200 finite elements.

The gained computational efficiency and accuracy will boost considerably the possibilities for more insight into geothermal analysis, which will improve the procedure for designing competitive energy extraction systems.

The models are capable of calculating exactly the temperature distribution in all involved borehole heat exchanger components and their thermal interactions.