Measurement history

As in the previous experiments, at each epoch we would like to select a waveform (or really the error covariance matrix associated with a measurement using this waveform) so that the measurement will minimize the uncertainty of the dynamic model of the target. We study two possible measures entropy of the a posteriori pdf of the models and mutual information between the dynamic model pdf and measurement history. Both of these involve making modifications to the LMIPDA-IMM approach that are described in [5]. Since we want to minimize the entropy before taking the measurement, we need to consider the expected value of the cost. To do this we replace the measurement z in the IMM equations by its expected value. In the case of the second measure, for a model we have... 

The HO2 disproportionation reaction has a rich measurement history beginning with the classic mass spectrometric study of Foner and Hudson in 1962 [14]. 

Model. The comparison of theory and experiment in Figure 9 indicates that the simplified model can be used to calculate transients which agree with experiment in gross trends. The model permits quantitative analysis of bulk and contact space-charge effects in PI transient current measurements. In particular, this model is sufficient to calculate measurement-history effects due to mobile ions and bulk electronic space-charge (9). The relaxation of space-charge upon removal of the bias is intrinsically slower than its accumulation. Thus, the sample history is stored in the space-charge distributions. These results will be demonstrated in a future publication. 

Without affecting unintended areas A measurable history... 

To gain an understanding of the composition of the reservoir rock, inter-reservoir seals and the reservoir pore system it is desirable to obtain an undisturbed and continuous reservoir core sample. Cores are also used to establish physical rock properties by direct measurements in a laboratory. They allow description of the depositional environment, sedimentary features and the diagenetic history of the sequence. 

A solid, by definition, is a portion of matter that is rigid and resists stress. Although the surface of a solid must, in principle, be characterized by surface free energy, it is evident that the usual methods of capillarity are not very useful since they depend on measurements of equilibrium surface properties given by Laplace s equation (Eq. II-7). Since a solid deforms in an elastic manner, its shape will be determined more by its past history than by surface tension forces. 

The strueture of quantum meehanies (QM) relates the wavefunetion E and operators F to the real world in whieh experimental measurements are performed through a set of rules (Dirae s text is an exeellent souree of reading eoneeming the historieal development of these fundamentals). Some of these rules have already been introdueed above. Here, they are presented in total as follows ... 

Level gauging has existed at least as long as written history markings on the walls of Egyptian temples show that as early as 3000 years ago humans tracked the level of water for hydrologic data. These nilometers are some of the first recorded uses of systems to measure level (1). 

In these cases what is usually measured is not the time of the original formation of the rocks, but the time at which the parent and daughter elements were last separated. That is, if the rocks were remelted at some point in their history in a manner that removed the daughter elements, this would be the age measured. For the measurements this is especially important. The daughter is a gas and thus could escape at any time when it was not sealed in. The decay sequences of Th, and all have gaseous members in their decay chains (see Tables 1 and 2), but the final members are solids. 

Results from measurements of time-dependent effects depend on the sample history and experimental conditions and should be considered approximate. For example, the state of an unsheared or undisturbed sample is a function of its previous shear history and the length of time since it underwent shear. The area of a thixotropic loop depends on the shear range covered, the rate of shear acceleration, and the length of time at the highest shear rate. However, measurements of time-dependent behavior can be usehil in evaluating and comparing a number of industrial products and in solving flow problems. 

Although vitreous siUca is a simple, single-component glass, its properties can vary significantly, depending on thermal history, the type and concentration of defects, and impurities. Vitreous siUca can, however, be one of the purest commercially available glassy materials. In synthetic vitreous sihcas, for example, total metal contamination is typically measured ia the 50—100 ppb range. Even at such a low level of impurities, differences ia properties, such as uv-transmission, are observed for various siUcas. 

The chemical and physical properties of cellulose depend ia large measure on the spatial arrangements of the molecules. Therefore, cellulose stmctures have been studied iatensively, and the resulting information has been important ia helping to understand many other polymers. Despite the extent of work, however, there are stiU many controversies on the most important details. The source of the cellulose and its history of treatment both affect the stmcture at several levels. Much of the iadustrial processiag to which cellulose is subjected is iatended to alter the stmcture at various levels ia order to obtain desired properties. 

Semiconducting Ceramics. Most oxide semiconductors are either doped to create extrinsic defects or annealed under conditions in which they become non stoichiometric. Although the resulting defects have been carefully studied in many oxides, the precise nature of the conduction is not well understood. Mobihty values associated with the various charge transport mechanisms are often low and difficult to measure. In consequence, reported conductivities are often at variance because the effects of variable impurities and past thermal history may overwhelm the dopant effects. 

The ductile-to-britde transition temperature (DBTT) is dependent on purity, history, grain size, etc. Furthermore, the potential utility of the metal is impaired by the fact that the ductility below this transition is essentially nil. To achieve measurable ductility, impurities should be below O, 2000 ppm N, 100 ppm C, 100 ppm H, 20 ppm Si, 1500 ppm S, 150 ppm. 

Seam correlations, measurements of rank and geologic history, interpretation of petroleum (qv) formation with coal deposits, prediction of coke properties, and detection of coal oxidation can be deterrnined from petrographic analysis. Constituents of seams can be observed over considerable distances, permitting the correlation of seam profiles in coal basins. Measurements of vitrinite reflectance within a seam permit mapping of variations in thermal and tectonic histories. Figure 2 indicates the relationship of vitrinite reflectance to maximum temperatures and effective heating time in the seam (11,15). 

Physical Properties. Most of the physical properties discussed herein depend on the direction of measurement as compared to the bedding plane of the coal. Additionally, these properties vary according to the history of the piece of coal. Properties also vary between pieces because of coal s britde nature and the crack and pore stmcture. One example concerns electrical conductivity. Absolute values of coal sample specific conductivity are not easy to determine. A more characteristic value is the energy gap for transfer of electrons between molecules, which is deterrnined by a series of measurements over a range of temperatures and is unaffected by the presence of cracks. The velocity of sound is also dependent on continuity in the coal. 

The SPE is defined as the ratio of the time required to produce a perceptible erythema on a site protected by a specified dose of the uv protectant product to the time required for minimal erythema development in the unprotected skin. An SPE of 8 indicates that the product allows a subject to expose the protected skin 8 times as long as the unprotected skin to produce the minimum erythema response. The measurement can be quite subjective unless skin color and the history of reactions to sun exposure of the test subjects are taken into account. The MED range for Caucasians at 300 nm averages 34 mj/cm. The range is 14—80 mj/cm. Perspiration or the use of artificial irradiation devices can create additional problems. 

History The histoiy of a plant forms the basis for fault detection. Fault detection is a monitoring activity to identify deteriorating operations, such as deteriorating instrument readings, catalyst usage, and energy performance. The plant data form a database of historical performance that can be used to identify problems as they form. Monitoring of the measurements and estimated model parameters are typic fault-detection activities. 

Known samples should also be run to verify the accuracy and precision of the routine methods to be used during the unit test. Poor quality will manifest itself as poor precision, measurements inconsistent with plant experience or laboratory history, and disagreement among methods. Plotting of laboratory analysis trends wiU help to determine whether calibrations are drifting with time or changing significantly. Repeated laboratory analyses will establish the confidence that can be placed in the results. 

Localized stagnation. Permeable deposits, crevices, preexisting cracks, and other conditions that result in physical shielding can lead to concentration of a corrodent in the stagnant solution, which can be 10-100 times or more greater than that measured in a bulk fluid (see Case History 9.1). 

---