Histograms

The procedure for the development of histograms is described in detail in statistics books as well as books that specifically deal with the basic quality tools. 

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The mean (m) and the standard deviation (a) of the population of localized AE sources over each cell of the (ATi,AT2) histogram are calculated. 

Finally, the concentrated localized AE events are represented on the monitor in the form of a histogram "number of localized AE events vs axial coordinate", which is automatically updated at user-defined time intervals. 

Off-line analysis of stored data review of the stored data, organize data in different presentation windows, plot AE and plant parameters data so as to enable comparison and coirelation with the possibility to present data (histogram of AE events vs position, plant parameters and/or AE parameters vs time) conditioned in terms of time interval (initial time, final time) and/or position interval (defined portion of the component = initial coordinate, final coordinate) and/or plant parameters intervals (one or more plant parameters = initial value, final value). 

SCREENINGOPSOURCES CALCULATE MEAN(in) AND STANDARD DEVUTION(< FOR ALL THE CELLSOF THE (AT1,AT2) HISTOGRAM... 

Fig.5 Example of histogram presentatioa The lower picture is a schematic representation of the monitored component with Uie position of the transducers (1-4). The higher window is the total AE counts vs linear location representation of the located AE sources...

Current histogram of cumulated AE events vs axial position, for each monitored component. 

Figure 6 shows the histogram of localized AE events vs axial position for the same time period as in fig.5. The location of the AE source corresponds, within source location errors (< 10-15 cm), to one of the welds under surveillance. The weld was known by ultrasonic examination to be affected by internal discontinuities. However, the position of the source could also correspond to one of the hangers. The steps observed in EA event accumulation have taken place during steady load operation, which normally corresponds to very low background noise conditions. This type of event, however, has not been observed afterwards. 

Localized AE sources appear during load variations, startups or shutdowns, but their positions are uniformly spread over the length of the two bodies of the header this can be seen from the histogram of the localized AE events for the front body (fig.S) and for the rear body (fig.9). 

Examination of the cumulated histogram of localized AE sources for all monitoring intervals, in different operating conditions, suggests the conclusion that no structurally significant sources have been active in the monitored area of the SH header. 

Fig.6 600 MW ENEL power plant, unit 4. Monitoring period from 22-01-1997 to 03-03-1997. Histogram of the localized AE events on the front body of the SH header...

In the experiments, the probabilities were estimated from the processed signal by means of a histogram. It is well known that the entropy is large for nearly uniform distributions and small for distributions with few peaks. Thus it is an interesting candidate as a performance measure when the goal is to process a signal to become more easily interpreted. 

Figure 8 VIGRAL process results top left - amplitude tuid ToF vs. position plot top right - source histogram lower right the V-scan image lower left -specimen location and dimensions.

From an analysis of the defects reflecting point distribution histograms it was established that for SDH with R > 1 mm, more than 80 % of reflecting points lie within the zone of local reflection. 

It is possible to perform volume visualization with different color and opacity tables, which can be designed by the user out of the samples intensity histogram. 

When the grey level dynamic range in the image processed is small, usually because of a poor illumination or a non uniform lighting, it s possible to increase this dynamic range by a histogram transformation. This transformation affect the intensity distributions and increase the contrast. 

The region segmentation can be processed by automatic classification or using histogram. Two automatic classification are commonly used ... 

Intensity classification is often based on image histogram which shows different peaks, each corresponding to one region and adjacent peaks are likely to be separated by a valley. The problem posed is to determine thresholds corresponding to these valleys [Fig 04]. 

Figure Bl.10.4. Time-of-flight histogram for ions resulting from the ionization of a sample of air with added hydrogen. The ions have all been aeeelerated to the same energy (2 keV) so that their time of flight is direetly proportional to the reeiproeal of the square root of tiieir mass.

Figure Bl.10.12. Schematic diagram of a two-dimensional histogram resulting from the triple coincidence experiment shown in figure BLIP. 10. True triple coincidences are superimposed on a imifomi background and tliree walls corresponding to two electron correlated events with a randomly occurring third electron.

Recently, Orkoulas and Panagiotopoulos [161] have shown that it is possible to use histogram reweighting and multicanonical simulations, starting with individual simulations near the critical point, to map out the liquid-vapour coexistence curve in a very efficient way. 

Ferrenberg A M, Landau D P and Swendsen R H 1995 Statistical errors in histogram reweighting Phys. Rev. E 51 5092-100... 

Figure C2.5.3. Histogram of the number of stmctures with a given number of associated sequences for the 3D 3 X 3 X 3 case, in a log-log plot.

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