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A novel frequency domain approach, which combines the pseudo excitation method modified by the authors and multi-domain Fourier transform (PEM-FT), is proposed for analyzing nonstationary random vibration in this paper.

For a structure subjected to a nonstationary random excitation, the closed-form solution of evolutionary power spectral density of the response is derived in frequency domain.

The deterministic process and random process in an evolutionary spectrum are separated effectively using this method during the analysis of nonstationary random vibration of a linear damped system, only modulation function of the system needs to be estimated, which brings about a large saving in computational time.

The method is general and highly flexible as it can deal with various damping types and nonstationary random excitations with different modulation functions.

The purpose of this paper is to develop an easy-to-implement and accurate fast boundary element method (BEM) for solving large-scale elastodynamic problems in frequency and time domains.

A newly developed kernel-independent fast multipole method (KIFMM) is applied to accelerating the evaluation of displacements, strains and stresses in frequency domain elastodynamic BEM analysis, in which the far-field interactions are evaluated efficiently utilizing equivalent densities and check potentials. Although there are six boundary integrals with unique kernel functions, by using the elastic theory, the authors managed to accelerate these six boundary integrals by KIFMM with the same kind of equivalent densities and check potentials. The boundary integral equations are discretized by Nyström method with curved quadratic elements. The method is further used to conduct the time-domain analysis by using the frequency-domain approach.

Numerical results show that by the fast BEM, high accuracy can be achieved and the computational complexity is brought down to linear. The performance of the present method is further demonstrated by large-scale simulations with more than two millions of unknowns in the frequency domain and one million of unknowns in the time domain. Besides, the method is applied to the topological derivatives for solving elastodynamic inverse problems.

An efficient KIFMM is implemented in the acceleration of the elastodynamic BEM. Combining with the Nyström discretization based on quadratic elements and the frequency-domain approach, an accurate and highly efficient fast BEM is achieved for large-scale elastodynamic frequency domain analysis and time-domain analysis.

The purpose of this paper is to analyze the mechanism and filter efficacy of accumulation generation operator (AGO)/inverse accumulation generation operator (IAGO) in the frequency domain.

The AGO/IAGO in time domain will be transferred to the frequency domain by the Fourier transform. Based on the consistency of the mathematical expressions of the AGO/IAGO in the gray system and the digital filter in digital signal processing, the equivalent filter model of the AGO/IAGO is established. The unique methods in digital signal processing systems “spectrum analysis” of AGO/IAGO are carried out in the frequency domain.

Through the theoretical study and practical example, benefit of spectrum analysis is explained, and the mechanism and filter efficacy of AGO/IAGO are quantitatively analyzed. The study indicated that the AGO is particularly suitable to act on the system's behavior time series in which the long period parts is the main factor. The acted sequence has good effect of noise immunity.

The AGO/IAGO has a wonderful effect on the processing of some statistical data, e.g. most of the statistical data related to economic growth, crop production, climate and atmospheric changes are mainly affected by long period factors (i.e. low-frequency data), and most of the disturbances are short-period factors (high-frequency data). After processing by the 1-AGO, its high frequency content is suppressed, and its low frequency content is amplified. In terms of information theory, this two-way effect improves the signal-to-noise ratio greatly and reduces the proportion of noise/interference in the new sequence. Based on 1-AGO acting, the information mining and extrapolation prediction will have a good effect.

The authors find that 1-AGO has a wonderful effect on the processing of data sequence. When the 1-AGO acts on a data sequence X, its low-pass filtering effect will benefit the information fluctuations removing and high-frequency noise/interference reduction, so the data shows a clear exponential change trends. However, it is not suitable for excessive use because its equivalent filter has poles at the non-periodic content. But, because of pol effect at zero frequency, the 1-AGO will greatly amplify the low-frequency information parts and suppress the high-frequency parts in the information at the same time.

To identify the dynamic feature of the aerostatic slider caused by gas film, an evaluation system by a piezoelectric acceleration sensor is presented in time and frequency domain.

The dynamic pressure fluctuation is evaluated by the wavelet transform, cross correlation analysis and power spectral density (PSD). Wavelet transform is used to process the measured result of the aerostatic slider and the signal is decomposed into high-frequency and low-frequency signal. Correlation analysis method is used to evaluate the impact of the initial gas gap on the fluctuation in time domain.

According to the PSD analysis of the processed signal in the frequency domain, the natural frequency of the aerostatic slider is identified from the measured signal in frequency domain; this method provides a basis for the identification of guideway errors.

The method can also be applied to the error identification of other components of the machine tool.

Wavelet transform is used to process the measured result of the aerostatic slider by acceleration sensor, and the signal is decomposed into high-frequency and low-frequency signal. Correlation analysis method is used to evaluate the impact of the initial gas gap on the fluctuation in time domain. According to the PSD analysis of the processed signal in the frequency domain, the natural frequency of the aerostatic slider is identified from the measured signal in frequency domain; this method provides a basis for the identification of slider errors.

Analytical determination of harmonic components of current in electric circuits containing semiconductor converters with the use of a small parameter method (SPM) in frequency domain. The paper aims to discuss these issues.

A SPM realized in frequency domain was used in the analytical analysis of electric circuits with semiconductor converters. An automated method of formation of orthogonal harmonic components of electrical values on the basis of discrete convolution algorithm was used to provide the possibility of realization of calculation in frequency domain. A nonlinear characteristic of a semiconductor converter was presented by the method of numerical approximation. A numerical structured simulation method was applied to determination of the reference values of current in the analyzed circuit. Laws of theoretical electrical engineering were used for formation of the equations of voltage balance in the circuit with a nonlinear element.

It is shown that application of a SPM with its realization in frequency domain enables significant simplification of the process of the analysis of electric circuits with semiconductor converters in an analytical form and facilitation of calculation automation. Analytical and numerical calculation of a circuit with a diode under active-inductive load demonstrated efficiency and sufficient accuracy of the proposed method. It is shown that increase of the order of approximating polynomial and of the number of the analyzed harmonics provides the improvement of the accuracy of numerical calculations.

The results of the work can be used in calculation of electrotechnical devices containing semiconductor appliances and electric devices with nonlinear characteristics. Moreover, the obtained results enable studying the processes of compensation of current higher harmonics in electric networks with a nonlinear load containing semiconductor converters.

For the first time it was proposed to apply a SPM with its realization in frequency domain to the analysis of nonlinear electric circuits. The significance of the paper consists in the fact that the offered method makes it possible to carry out both circuit analytical and numerical analysis with the possibility of its automation.

The chapter considers parameter identification, estimation, and model diagnostics in medium scale DSGE models from a frequency domain perspective using the framework developed in Qu and Tkachenko (2012). The analysis uses Smets and Wouters (2007) as an illustrative example, motivated by the fact that it has become a workhorse model in the DSGE literature. For identification, in addition to checking parameter identifiability, we derive the non-identification curve to depict parameter values that yield observational equivalence, revealing which and how many parameters need to be fixed to achieve local identification. For estimation and inference, we contrast estimates obtained using the full spectrum with those using only the business cycle frequencies to find notably different parameter values and impulse response functions. A further comparison between the nonparametrically estimated and model implied spectra suggests that the business cycle based method delivers better estimates of the features that the model is intended to capture. Overall, the results suggest that the frequency domain based approach, in part due to its ability to handle subsets of frequencies, constitutes a flexible framework for studying medium scale DSGE models.

The purpose of this paper is to investigate the volatility spectral of five major public real estate markets, namely, the USA, the UK, Japan (JP), Hong Kong (HK), and Singapore (SG), during the pre- and post-global financial crisis (GFC) periods.

First, univariate spectral analysis is concerned with discovering price cycles for the respective real estate markets. Second, bivariate cross-spectral analysis seeks to uncover whether any two real estate price series share common cycles with regard to their relative magnitudes and lead-lag patterns of the cyclical variations. Finally, to test the contagion effects, the authors estimate the exact percentage change in co-spectral density (cyclical covariance) due to high frequencies (short run) after the GFC.

The authors find that whilst none of the public real estate markets examined are spared from the crisis, the three Asian markets were less severely affected by the GFC and were accompanied by a reversal in volatility increase three years post-global financial crisis. Additionally, the public real estate markets studied have become more cyclically linked in recent years. This is particularly true at longer frequencies. Finally, these increased cyclical co-movements measure the outcomes of contagion and indicate fairly strong contagious effects between the public real estate markets examined due to the crisis.

The implication of this research is that benefits to investors from international real estate diversification may not be as great during the present time compared to previous periods because national public real estate markets have become more correlated. Nevertheless, the findings do not imply the complete absence of diversification benefits. This is because although cyclical correlations increase in the short run, many of the correlation values are still between low and moderate range, indicating that some diversification benefits may still be realized.

Given the significant market share and the highest levels of securitization in Asia-Pacific markets including JP, HK/China, and SG, this cyclical research including major public real estate markets has practical implications for ongoing international real estate investment strategies, particularly for the USA/UK and Asian portfolio managers.

This paper contributes to the limited research on the cyclical return and co-movement dynamics among major public real estate markets during financial/economic crisis in international finance. Moreover, the frequency-domain analysis conducted in this paper adds to better understanding regarding the impact of GFC on the cyclical return volatility and co-movement dynamics of major developed public real estate markets in international investing.

The purpose of this paper is to highlight that the need for improved system identification methods within the domain of modal analysis increases under the impulse of the broadening field of applications, e.g., damage detection and vibro-acoustics, and the increased complexity of today’s structures. Although significant research efforts during the last two decades have resulted in an extensive number of parametric identification algorithms, most of them are certainly not directly applicable for modal parameter extraction. So, based on this, the aim of the present work is to develop a technique for modal parameter extraction from the measured signal.

A survey and classification of the different modal analysis methods are made; however, the focus of this thesis is placed on modal parameter extraction from measured time signal. Some of the methods are examined in detail, including both single-degree-of-freedom and multi-degree-of-freedom approaches using single and global frequency-response analysis concepts. The theory behind each of these various analysis methods is presented in depth, together with the development of computer programs, theoretical and experimental examples and discussion, in order to evaluate the capabilities of those methods. The problem of identifying properties of structures that possess close modes is treated in particular detail, as this is a difficult situation to handle and yet a very common one in many structures. It is essential to obtain a good model for the behavior of the structure in order to pursue various applications of experimental modal analysis (EMA), namely: updating of finite element models, structural modification, subsystem-coupling and calculation of real modes from complex modes, to name a few. This last topic is particularly important for the validation of finite element models, and for this reason, a number of different methods to calculate real modes from complex modes are presented and discussed in this paper.

In this paper, Modal parameters like mode shapes and natural frequencies are extracted using an FFT analyzer and with the help of ARTeMiS, and subsequently, an algorithm has been developed based on frequency domain decomposition (FDD) technique to check the accuracy of the results as obtained from ARTeMiS. It is observed that the frequency domain-based algorithm shows good agreement with the extracted results. Hence the following conclusion may be drawn: among several frequency domain-based algorithms for modal parameter extraction, the FDD technique is more reliable and it shows a very good agreement with the experimental results.

In the case of extraction techniques using measured data in the frequency domain, it is reported that the model using derivatives of modal parameters performed better in many situations. Lack of accurate and repeatable dynamic response measurements on complex structures in a real-life situation is a challenging problem to analyze exact modal parameters.

During the last two decades, there has been a growing interest in the domain of modal analysis. Evolved from a simple technique for troubleshooting, modal analysis has become an established technique to analyze the dynamical behavior of complex mechanical structures. Important examples are found in the automotive (cars, trucks, motorcycles), railway, maritime, aerospace (aircrafts, satellites, space shuttle), civil (bridges, buildings, offshore platforms) and heavy equipment industry.

Presently structural health monitoring has become a significantly important issue in the area of structural engineering particularly in the context of safety and future usefulness of a structure. A lot of research is being carried out in this area incorporating the modern sophisticated instrumentations and efficient numerical techniques. The dynamic approach is mostly employed to detect structural damage, due to its inherent advantage of having global and location-independent responses. EMA has been attempted by many researchers in a controlled laboratory environment. However, measuring input excitation force(s) seems to be very expensive and difficult for the health assessment of an existing real-life structure. So Ambient Vibration Analysis is a good alternative to overcome those difficulties associated with the measurement of input excitation force.

Three single bay two storey frame structure has been chosen for the experiment. The frame has been divided into six small elements. An algorithm has been developed to determine the natural frequency of those frame structures of which one is undamaged and the rest two damages in single element and double element, respectively. The experimental results from ARTeMIS and from developed algorithm have been compared to verify the effectiveness of the developed algorithm. Modal parameters like mode shapes and natural frequencies are extracted using an FFT analyzer and with the help of ARTeMiS, and subsequently, an algorithm has been programmed in MATLAB based on the FDD technique to check the accuracy of the results as obtained from ARTeMiS. Using singular value decomposition, the power Spectral density function matrix is decomposed using the MATLAB program. It is observed that the frequency domain-based algorithm shows good consistency with the extracted results.

A number of works have been published in the scientific literature proposing the solution of heat diffusion problems by first transforming the relevant partial differential equation to the frequency domain. The purpose of this paper is to present a mesh-free strategy to assess transient heat propagation in the frequency domain, also allowing incorporating initial non-zero conditions.

The strategy followed here is based in Kansa's method, using the MQ RBF as a basis function. The resulting method is truly mesh-free, and does not require any domain or boundary integrals to be evaluated. The definition of good values for the free parameter of the MQ RBF is also addressed.

The strategy was found to be accurate in the calculation of both frequency and time-domain responses. The time evolution of the temperature considering an initial non-uniform distribution of temperatures compared well with a standard time-marching algorithm, based on an implicit Crank-Nicholson implementation. It was possible to calculate frequency-dependent values for the free parameter of the radial basis function.

As far as the authors are aware, previous implementations of the frequency domain heat transfer approach required domain integrals to be evaluated in order to implement non-zero initial conditions. This is totally avoided with the present formulation. Additionally, the method is truly mesh-free, accurate and does not require any element or background mesh to be defined.

The purpose of this paper is to identify the flexible aircraft model accurately from the frequency responses.

The frequency domain output error method is used to estimate the aerodynamic (rigid body and elastic body) derivatives, and mode shape parameters in the process of identification of flexible aircraft model. The accurate identification of lightly damped low frequency rigid-body response modes requires a careful selection of the frequency sweep length and the fast Fourier transform (FFT) window size, as the FFT window length cannot be longer than any individual sweep records. To address this issue, an effort is made to derive the FFT window length for the application of frequency domain estimation approach.

The investigations are initially made to select a suitable FFT window size for the accurate identification of the lightly damped low frequency rigid-body response modes of the flexible aircraft. Subsequently, frequency domain estimation approach is applied to simulated data of flexible aircraft. Besides the stability and control derivatives, the structural modes of the flexible aircraft are also estimated as part of state space model identification, and it is shown that all the model parameter estimates are accurate. Identification of such flexible aircraft aerodynamic (rigid body and elastic body) derivatives and structural mode shape parameters will lead to mathematical models of flexible aircraft that are accurate over a wide frequency range. The identified models are validated using the time response of frequency sweep data.

Aircraft system identification is an integral part of aerospace system design and life cycle process. This becomes a complex process when the aircraft has significant effects of flexibility on the flight dynamics, especially as the frequencies of the elastic modes become lower and approach those of the rigid body modes. Thus, an integrated mathematical model of flexible aircraft is required to develop, and it should be valid for a wide frequency range and relevant for the design of flight control system.

This paper focuses on the application of frequency domain approach to identify the valid model of flexible aircraft by estimating the aerodynamic (rigid body and elastic body) derivatives and structural mode shape parameters of flexible aircraft. The unknown frequencies of structural modes are also able to identify accurately in frequency domain. This gives more value addition to analyze the flight data of flexible aircraft, as it is challenging problem in parameter estimation of flexible aircraft.