15 Incremental Model Adjustment

Customarily in regression, the user collects many data sets and then uses optimization to adjust the model coefficients to make the model best fit the entire batch of data. It is a batch operation. However, it is not uncommon to update a model as new data are acquired, to incrementally adjust the model coefficient values. This practice is common in continuously operating processes in which attributes progressively change in time. Examples of some time-dependent attributes include:

• catalyst reactivity,

• heat exchanger fouling,

• feed raw material composition,

• air density and humidity,

• accumulation of poisons or pathogens in a batch reaction,

• viscosity impacted mixing in a batch polymerization,

• human attitude,

• group morale or preferences,

• process gain change with operating conditions,

• viable cell growth factor,

• reaction yield,

• average distillation tray efficiency,

• insulation effectiveness, and

• piping assembly friction factor response to screen blockage or piping rearrangements.