Frequency data analysis definitions

In summary, the quantitative information on the frequencies, amplitudes, and directions of Fe motion from NIS measurements provides a definitive test of the detailed normal-mode predictions provided by modem quantum chemical calculations. However, first-principles calculations greatly assist in the analysis and interpretation of experimental NIS data, thus revealing a consistent picture of the vibrational dynamics of iron in molecules. 

In arriving at a satisfactory analysis of the spectrum we must make use not only of the polarization data, but also of the results of deuteration studies, full [Narita, Ichinohe, and Enomoto (145)] and partial [Folt, Shipman, and Berens (55)], and studies of C—Cl frequencies in small molecules. [Mizushima, Shimanouchi, Nakamura, Hayashi, and Tsuchiya (139) Shimanouchi, Tsuchiya, and Mizushima (196)]. The lack of the Raman spectrum is a definite handicap, but is in part mitigated by the expectation that many of the Raman active fundamentals should be close to the frequencies of infrared active fundamentals. 

QA splits are particularly valuable for field screening with definitive analysis confirmation and for the verification of field laboratory analysis. The frequency of the QA sample collection is best determined based on the project duration and the total numbers of samples to be collected. Typically, they are collected at a 10 percent frequency (one QA sample for every 10 field samples). It is beneficial to establish data comparability in the early phase of field implementation. If data are comparable, the frequency of QA sampling may be reduced as the confidence in field screening or field laboratory results has been established. But if the data are not comparable, the project team needs to identify the cause of the differences and resolve them as soon as possible in order to avoid making decisions on inaccurate or unrepresentative data. 

A working understanding of statistics is essential for the analysis of experiments conducted in the frequency domain, such as impedamce spectroscopy. The objective of this chapter is to provide an overview of concepts and definitions used in statistics at a level sufficient to understand the interpretation of frequency domain data. 

Based on the rupture definition mentioned in Paragraph 2.1.1, a failure frequency has been derived for Dutch oil transmission pipelines. For the derivations the complete data pool from 1971 to 2004 has been used, as there were no evident technical or organizational grounds to use a shorter time period. To have a statistically solid derivation, a Gaussian distribution is used with 95% confidence that the frequency will be below the upper bound. The result of the analysis is a failure frequency of 1.8 x 10 per kilometer per year for a rupture. 

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