Frequency-estimating methods

The frequency analysis step involves estimating the likelihood of occurrence of each of the undesired situations defined in the hazard identification step. Sometimes you can do this through direct comparison with experience or extrapolation from historical accident data. While this method may be of great assistance in determining accident frequencies, most accidents analyzed by QRA are so rare that the frequencies must be synthesized using frequency estimation methods and models. 

The estimation method requires simply the addition of the appropriate number of molecular descriptors (bj) based on their frequency of occurrence in the compound (rq) ... 

This method of estimating Rc is useful when it can be applied, since the determination is not based on any presumed model of the corrosion damage process or any of the assumptions that come with assignment of an equivalent circuit model. This method is particularly helpful when there is more than one time constant in the spectrum, or the impedance spectrum is particularly complicated. Caution is warranted however. This method of estimation can be in serious error for samples with large capacitance-dominated low-frequency impedances. As a general rule, for this estimation method to be reasonably accurate, the impedance function must exhibit a clear DC limit, or a diffusional response that can be modeled by a constant phase element in equivalent circuit analysis (75). 

Clements also estimated the frequency response from the pulse response. A frequency-response method is also suggested by Kramers and Alberda.52 Schwartz et al.9S suggested a new, two-tracer technique for simultaneous determination of liquid holdup and Peclet number. 

With the advent of rapid-scan and high-frequency pulse methods, more direct approaches for evaluating annihilation mechanisms and dynamics have been developed. Early work of van Duyne, using triple potential steps with very short step times, allowed estimation of the annihilation rate constant for DPA anion and cation radicals [29]. More recently, Wightman and coworkers have used multicycle generation of ECL at microelectrodes to determine annihilation rate constants and ECL efficiencies [41, 42]. Figure 7 shows the normalized ECL intensity from DPA at a 1-pm Pt disk as a function of time (t/tf) at different oscillation frequencies. The intensity increases rapidly after the potential is switched, and then decays as the reactants are depleted. As the oscillation frequency is increased, the annihilation occurs closer to the electrode surface, the intensity-time profile broadens and... 

Gas chromatography-olfactometery (GC-O) provides a sensory profile of odor active compounds present in an aroma extract by sniffing the GC effluent. Several techniques have been developed to collect and process GC-O data and to estimate the sensory contribution of individual odor active compounds, including dilution analysis (29, 30), time intensity (31), and detection frequency (32) methods. GC-O has successfully been used to evaluate the odor active compounds of olive oil (33), soybean oil (34), and fish oil enriched mayonnaise (35). 

The bimetallic catalysts exhibit higher catalytic activity at lower temperatures in comparison with pure Pt and Rh ones, as shown in Fig. 2. Otherf workers have also observed this synergism for Pt-Rl bimetallic catalysts.s The rate constants found by the RF-GC technique such as those in Table 1, are very close to thosm determined experimentally by the frequency response method " for the adsorption of CO on Pt/Si02. The values of the estimated activation energies for CC dissociative adsorption, given in Table 2, are low. ... 

By applying an appropriate perturbation to a relevant parameter of a system under equilibrium, various frequency modulation methods have been used to obtain kinetic parameters of chemical reactions, adsorption-desorption constants on surfaces, effective diffusivities and heat transfer within porous solid materials, etc., in continuous flow or batch systems [1-24]. In principle, it is possible to use the FR technique to discriminate between all of the kinetic mechanisms and to estimate the kinetic parameters of the dynamic processes occurring concurrently in heterogeneous catalytic systems as long as a wide enough frequency range of the perturbation can be accessed experimentally and the theoretical descriptions which properly account for the coupling of all of the dynamic processes can be derived. 

A comparison between Bayesian and Fourier analysis is provided by Kotyk et and Evilia et They both show that the Bayesian methods provide more precise frequency estimates and far more precise amplitude estimates than DFT and explain the difference. However, it should be said that the methods are so different in nature that comparison is more difficult than for other methods discussed in this paper. For example, by known Ti the Kotyk etal. mean that T2 has been included in the calculation as a matched exponential apodiza-tion. Vines et demonstrated the ability to mea.sure scalar couplings that are much smaller than linewidth in the case of spectra with favorable S/N ratio. The same authors took advantage of the ability of BPT to accurately measure linewidth to improve exchange parameters and gain in the precision and accuracy of thermodynamic properties.- ... 

The Bayesian spectral density approach, which is a frequency-domain method, transforms the response time history to the spectral density estimator by discrete Fourier transform. 

For the plant having been analyzed, the PSA provided some recommendations for improving the fire protection In a few cable channels in the auxihary building and the independent emergency building no fire detectors are installed. An early fire detection and suppression cannot be ensured. The frequency of an incipient fire for these channels is the same as the fire induced damage frequency. On the other hand, the fire occurrence frequencies estimated by the method of Berry (1979) are too pessimistic. In conclusion, the installation of automatic fire detectors in these compartments will reduce the compartment specific... 

Engineering Sciences Data Unit (ESDU), Estimation of rms strain in laminated face plates of simply-supported sandwich panels subjected to random acoustic loading. Including a simplified natural frequency prediction method. Item No. 86024, V3, 1990. 

Estimation methods for the vapor pressure are still not reliable enough to apply them in process simulations for components whose behavior is decisive. Vapor pressure estimations can be used for components where the order of magnitude of the vapor pressure is sufficient (e.g., to decide whether the component occurs at the top or at the bottom of a column). Even in this case, it depends on the frequency it is used. For the simulation and optimization of a process for basic chemicals it is strongly recommended to have vapor pressure curves based on data points for all the components involved, whereas for the batch production of fine chemicals with a tight timef rame or during process evaluation an estimation might be acceptable. 

The direction data mainly come from the scan lines, which are divided into three groups, (SLOl-17, SL17-30 and SL31- 0) for the three discontinuity sets, respectively. The mean and variance of the discontinuity dip directions and dip angles are evaluated by the maximum likelihood estimation method (Table 1). Then, the frequency histograms of the orientation data are drawn out and combined with the x test the probability distribution functions of the... 

In choosing the method for delivering frequency estimates, while the use of fault/event logic trees is superior to deriving hazardous event frequency from generic historical data, it is also more costly. 

Peeters, B., Van der Auweraei H., Guillaume, P. Leuridan, J. 2004. The Polymax frequency-domain method a new standard for modal parameter estimation Shock and Vibration 11(3-4) 395-409. 

The benzylic couplings, " Vh,ch3. in toluene, in a series of 4-mono- and 3,5-disubstituted toluene derivatives as well as in 4-picoline have been determined by Perez-Hernandez et al by the use of the recently modified J doubling in the frequency domain method. All these experimental benzylic couplings have been correctly estimated by DFT calculations at the B3LYP/ aug-cc-pVTZ level of theory. 

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