Time-domain approach for

Majumder, L. and Manohar, C. S. A time-domain approach for damage detection in beam structures using vibration data with a moving oscillator as an excitation source. Journal of Sound and Vibration 268(4) (2003), 699-716. 

Yuen, K.-V. and Katafygiotis, L. S. Bayesian time-domain approach for modal updating using ambient data. Probabilistic Engineering Mechanics 16(3) (2001), 219-231. 

Nonstationary power spectral density functions for the displacement response of a dam reservoir system subjected to a simple but nonstationary random acceleration excitation are obtained by a frequency domain approach due to Shinozuka. These spectral response solutions are new and are checked satisfactorily in the limiting stationary case and against the corresponding solution obtained previously by a time domain approach. For the range of frequency ratio Oj- representing dam reservoir interaction effect, it is found that the displacement spectral peak value increases with increasing dam flexibility. The location of the spectral peak is at a nearly constant value of f2Qj- (w/o) ) (c x/ s) 0.6, which means that the peak spectral response is at... 

Binsch [6] provided the standard way of calculating these lineshapes in the frequency domain, and implemented it in the program DNMR3 [7], Fonnally, it is the same as the matrix description given in section (B2.4.2.3). The calculation of the matrices L, R and K is more complex for a coupled spin system, but that should not interfere witii the understanding of how the method works. This work will be discussed later, but first the time-domain approach will be developed. 

The state-space approach is a generalized time-domain method for modelling, analysing and designing a wide range of control systems and is particularly well suited to digital computational techniques. The approach can deal with... 

The noise can be described by means of two approaches, namely, in the time domain and in the frequency domain. For the time domain approach the characteristic value is the well-known mean square deviation from the value over the time T,... 

In this chapter I have presented the basics of SD and described several approaches that can be used to uncover the molecular mechanisms contributing to SD both within the LRA and when the response is nonlinear. Within the LRA, I discussed INM and time-domain methods for analyzing the solvation TCP and the related solvation velocity time correlation, G(f). The methods were illustrated by showing how they can determine the relative contributions to SD from different molecules, types of molecular motion, and correlations among solvent molecules. I also discussed how they can be used relate SD to other observable dynamics in liquids and to explore the similarities and differences between SD in... 

As can be deduced, for m > 2, expression (2.67) leads to cross derivatives by x and y, whose evaluation is rather cumbersome. To alleviate this difficulty, only one fictitious point can be considered at each side of the interface and hence only the zero- and first-order jump conditions are implemented. While this notion gives reliable solutions, an alternative quasi-fourth-order strategy has been presented in [28] for the consideration of higher order conditions and crossderivative computation. A fairly interesting feature of the derivative matching method is that it encompasses various schemes with different orders that permit its hybridization with other high-accuracy time-domain approaches. 

The Bayesian time-domain approach presented in this chapter addresses this problem of parametric identification of linear dynamical models using a measured nonstationary response time history. This method has an explicit treatment on the nonstationarity of the response measurements and is based on an approximated probability density function (PDF) expansion of the response measurements. It allows for the direct calculation of the updated PDF of the model parameters. Therefore, the method provides not only the most probable values of the model parameters but also their associated uncertainty using one set of response data only. It is found that the updated PDF can be well approximated by an appropriately selected multi-variate Gaussian distribution centered at the most probable values of the parameters if the problem is... 

The additional measurement of y3 improves only slightly the prediction for y but the additional measurement of y4 has virtually no effect on the prediction. This example is useful to demonstrate the approximation used in the Bayesian time-domain approach. The random variable yi is predicted by the measurements of y2. y3 and 4, which are 0.5,1 and 1.5 periods apart from yi, respectively. It turns out that including the data points within one period is sufficient. Furthermore, in a usual situation, the sampling time step is much less than half of... 

Figure 4.4 shows the conditional PDF of the natural frequency and the damping ratio C with the spectral intensity and the prediction-error variance fixed at their optimal values. The conditional PDFs by the Bayesian time-domain approach and the Gaussian approximation are plotted with solid lines and dashed lines, respectively. The two groups of curves are on top on each other, indicating that the Gaussian approximation is accurate when the number of data points is sufficiently large. This can be used to represent the posterior PDF, e.g., for statistical moments computation. 

Another case is investigated with a very short period of measurement, namely T = 5 s, so it contains less than four fundamental periods of the oscillator. The Bayesian time-domain method is used for the identification and Figure 4.5 shows the conditional PDF of and f with all other parameters fixed at their optimal values. The solid lines show the conditional posterior PDF obtained by the Bayesian method and the dashed lines show the Gaussian approximation. It is clear that the posterior PDF is non-Gaussian. This confirms that the Bayesian time-domain approach is capable to offer the correct inference without assuming the type of the posterior PDF. In the case of a non-Gaussian posterior PDF, statistical moments, such as the variances of the estimates, can be computed by direct Monte Carlo simulation. The results are shown in Table 4.2 in the same fashion as Table 4.1. The computed uncertainty obtained here is reasonable by judging the normalized distance of the estimates. 

In this chapter, the Bayesian time-domain approach was introduced for identification of the model parameters and stochastic excitation parameters of linear multi-degree-of-freedom systems using noisy stationary or nonstationary response measurements. The direct exact formulation was presented but it turned out to be computationally prohibited for a large number of data points. Then, an approximated likelihood function expansion was proposed to resolve this obstacle. For a globally identifiable case with a large number of data points, the updated PDF... 

Different from conventional Mossbauer spectroscopy, which is an ener gy-domain technique, NFS is a time-domain technique—it monitors the change of the nuclear decay signal from the nuclear excited states as a function of time. The use of SR in a time-domain approach eliminates the source contribution to the spectral linewidth, making the spectral resolution of NFS higher than the conventional Mossbauer. NFS has been applied to many different Mossbauer isotopes, and has been demonstrated as a promising new technique for studies in solid-state physics, materials science, geosciences, thin film, and bioinorganic chemistry [13-16]. 

Two widely used approaches are used for lifetime measurements, the time-domain approach and the frequency-domain approach. In time-domain measurements, a pulsed source is employed and the time-dependent decay of fluorescence is measured. In the frequency-domain method, a sinusoidally modulated source is used to excite the sample. The phase shift and demodulation of the fluorescence emission relative to the excitation waveform provide the lifetime information. Commercial instrumentation is available to implement both techniques. "... 

A gravity dam-reservoir system is selected for studying the interaction of structure-fluid systems under nonstationary random excitation. For an idealized random excitation with a zero start and a white power spectrxjun, the nonstationary power spectral density for the structural displacement is obtained by a frequency domain approach due to Shinozuka. The spectral density functions are then integrated to check the transient variance solution obtained previously by a time domain approach. Using this power spectral solution the random interaction effect is examined for the entire frequency range in detail. This interaction problem of the structure-fluid system is important because it simulates random and time dependent structural response to earthquake ground accelerations. 

Comparing the frequency-domain and the time-domain approach, it was found that one is not fundamentally better than the other in terms of signal to noise ratio, when measuring the fluorescence lifetime of a mono-exponentially decaying fluorochrome [33]. In both systems, it is crucial, however, to use the optimal settings for each particular measurement. In frequency-domain FLIM, the... 

One of the classical approaches to analyze the performance of the inertial sensors is to calculate a so-called Allan Variance (AV) for each of the sensor axes. This analysis technique is able to take into account the long-term noises in the sensor outputs and is a time domain approach which was originally developed to study the frequency stability of the oscillators (clocks) [10]. The AV curve is extremely helpful in identifying the noise terms which affect... 

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