Data analysis discriminant uncertainty

Several significant challenges exist in applying data analysis and interpretation techniques to industrial situations. These challenges include (1) the scale (amount of input data) and scope (number of interpretations) of the problem, (2) the scarcity of abnormal situation exemplars, (3) uncertainty in process measurements, (4) uncertainty in process discriminants, and (5) the dynamic nature of process conditions. 

Uncertainty in Process Discriminants. Because processes operate over a continuum, data analysis generally produces distinguishing features that exist over a continuum. This is further compounded by noise and errors in the sensor measurements. Therefore, the discriminants developed to distinguish various process labels may overlap, resulting in uncertainty between data classes. As a result, it is impossible to define completely distinguishing criteria for the patterns. Thus, uncertainty must be addressed inherently. 

Regression analysis is often employed to fit experimental data to a mathematical model. The purpose may be to determine physical properties or constants (e.g., rate constants, transport coefficients), to discriminate between proposed models, to interpolate or extrapolate data, etc. The model should provide estimates of the uncertainty in calculations from the resulting model and, if possible, make use of available error in the data. An initial model (or models) may be empirical, but with advanced knowledge of reactors, distillation columns, other separation devices, heat exchangers, etc., more sophisticated and fundamental models can be employed. As a starting point, a linear equation with a single independent variable may be initially chosen. Of importance, is the mathematical model linear In general, a function,/, of a set of adjustable parameters, 3y, is linear if a derivative of that function with respect to any adjustable parameter is not itself a function of any other adjustable parameter, that is. 

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