Frequency index set

Furthermore, simulation shows that the random variables Sy icok) and Sy kf ojk ) are un-correlated in the same range of frequencies for the Chi-square distribution, for k k and k, k 6 K.. According to Yaglom [277], uncorrelated Chi-square random variables are independent. Use K to denote the, frequency index set that contains the frequency indices for these approximations to be accurate. Given the observed data V, the spectral set can be computed by using Equation (3.25) ... 

Here the frequency index set K. represents a range over which Equations (3.56) and (3.58) give a satisfactory approximation and this will be further discussed in Section 3.3.3. Using the Bayes theorem, the updated PDF of the model parameter vector 0, given the averaged spectral set [Pg.114]

Another case is investigated with a very short duration of measurement, namely T = 60 s, so it contains roughly 38 fundamental periods of the oscillator. The Bayesian spectral density approach is used for its identification with the frequency index set /C = 1,2,..., 45. Figure 3.13 shows the conditional updated PDFs of and with all other parameters fixed at their optimal values. It is obvious that the conditional PDFs are non-Gaussian so the Gaussian... 

Even though the spectral density approach requires computation of the inverse and determinant of a number of matrices, the size of these matrices is only No y. No. They are significantly smaller than the NgNp x NgNp matrix Eyj j (= E22) required in the time-domain approach. Comparison of the computational efficiency between the two methods depends on the number of the elements in the frequency index set and the number of data points in a fundamental period. The ratio of the computations required by the Bayesian spectral density approach and the Bayesian time-domain approach can be approximated by ... 

With all A = 3 factors listed in the index set I = 1,2,3 all effects in the output should be ascribed to a specific input factor or an interaction of input factors. However, the total effect of / is estimated by Sfi = 0.91 in contrast to theoretically iS y = 1.0. Thus, the absolute values derived from the frequency decomposition of n y) are not rehable. Moreover, it also shows that the sample size can also be too large From the 10,000 samples available, only M(1 4- P 4- P ) = 665 Fourier coefficients (not all of them are shown in the plot) are used for spectral analysis, all others contribute to sporadic errors which only form part of the overall variance, but not part of input-factor relate effects. 

Here it should be remarked that the symbol scalar product in J/ and that A q symbolizes the index set of the labels which characterize the irreducible G-representations, and that the index s = 1, 2,... nta indicates the frequency of the irreducible representations G in 31, respectively. 

Fire and Explosion Index (Ffrom fires and explosions. frequency The rate at which observed or predicted events occur. HAZOP HAZOP stands for hazard and operabihty studies. This is a set of formal hazard identification and ehmination procedures designed to identify hazards to people, process plants, and the environment. See subsequent sections for a more complete description. 

The Gini index and the cross entropy measure are differentiable which is of advantage for optimization. Moreover, the Gini index and the deviance are more sensitive to changes in the relative frequencies than the misclassification error. Which criterion is better depends on the data set, some authors prefer Gini which favors a split into a small pure region and a large impure one. 

Number densities of the set of ions of valence v in region i (with v subscript to distinguish from index in frequency summation and index of refraction). Number densities of suspended particles, molecules, atoms, polarizable units. 

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