Interpretation of parameter estimates

54] constitutes the basis for the resolution of the logical problem, described earlier, in which different cosolvents, with a given solute, yield different gA values, although gA had been assumed to be independent of composition. As eq. [5.5.54] shows, gA is determined by a difference of two fixed quantities, thus guaranteeing its composition independence, and at the same time permitting gA to vary with cosolvent identity. 

53] is therefore conceptually sounder and physically more detailed than is eq. [5.5.23]. Eq. [5.5.53] shows, however, that in the absence of independent additional information (that is, information beyond that available from the solubility study alone) it is not possible to dissect the quantity (g2Y2A2 - giYiAj) into its separate terms. In some cases such additional information may be available, and here we discuss the example of naphthalene solubility in mixed aqueous-organic binary mixtures. Table 5.5.8 lists the values of gA(Y2-Yi) obtained by applying eq. [5.5.23] to solubility data in numerous mixed solvent systems. In an independent calculation, the solubility of naphthalene in water was written as eq. [5.5.55], 

Observe that giA,Yi and g2A2Y2 are positive quantities, as expeeted gA(Y2-Yi) is negative because of the surface tension difference. It is tempting to divide each of feese quantities by its surface tension factor in order to obtain estimates of gA, giA, and g2A2, but this procedure may be unsound, as proposed subsequently. 

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Hood DC, Birch DG. Rod phototransduction in retinitis pigmentosa estimation and interpretation of parameters derived from the rod a-wave. Invest Ophthalmol Vis Sci 1994 35 2948-2961. 

Interpretation of data was also based on multiple comparisons of parameter estimates by calculating F-statistics for contrasts. For the factor "time of day" a family of contrasts between the mean obtained for one time point and the average of the means for the other times was calculated. With six contrasts, the probability of one or more type I errors is 0.26 for an error probability of 0.05,... 

The vertices are connected with hues indicating information flow. Measurements from the plant flow to plant data, where raw measurements are converted to typical engineering units. The plant data information flows via reconciliation, rec tification, and interpretation to the plant model. The results of the model (i.e., troubleshooting, model building, or parameter estimation) are then used to improve plant operation through remedial action, control, and design. 

Overview Interpretation is the process for using the raw or adjusted unit measurements to troubleshoot, estimate parameters, detect faults, or develop a plant model. The interpretation of plant performance is defined as a discreet step but is often done simultaneously with the identification of hypotheses and suitable measurements and the treatment of those measurements. It is isolated here as a separate process for convenience of discussion. 

Parameter estimation is a procedure for taking the unit measurements and reducing them to a set of parameters for a physical (or, in some cases, relational) mathematical model of the unit. Statistical interpretation tempered with engineering judgment is required to arrive at realistic parameter estimates. Parameter estimation can be an integral part of fault detection and model discrimination. 

Parameter Estimation Relational and physical models require adjustable parameters to match the predicted output (e.g., distillate composition, tower profiles, and reactor conversions) to the operating specifications (e.g., distillation material and energy balance) and the unit input, feed compositions, conditions, and flows. The physical-model adjustable parameters bear a loose tie to theory with the limitations discussed in previous sections. The relational models have no tie to theory or the internal equipment processes. The purpose of this interpretation procedure is to develop estimates for these parameters. It is these parameters hnked with the model that provide a mathematical representation of the unit that can be used in fault detection, control, and design. 

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