Parametric Estimation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 281

CHAPTER
7

Pa rametric Estimati on

OUTLINE

7.1. Regression Models 282 7.8.1. Integral Methods 300

7.8.2. Differential Methods 302

7.2. Classification of Regression Models 286

7.8.3. Which Methods to Use:
Differential or Integral? 7.3. Criteria for “Best” Fit and Simple

Linear Regressions

304

287 7.8.4. A General Approach of

Parametric Estimation for
Differential Models

7.4. Correlation Coefficient 291

306

7.5. Common Abuses of Regression 293

7.9. Summary 317

7.6. General Regression Analysis 294

Problems 318

7.7. Quality of Fit and Accuracy of Data 295

7.8. Batch Kinetic Data Interpretation:
Differential Regression Model

297

In many engineering problems, two or more variables are inherently related. Ideally, if one
who is attempting to model the problem also knows the problem well, the relationship
between the variables can be established using biological, engineering, physical, and/or
chemical principles. To avoid complexity and/or uncertainties, one usually starts with
heuristic arguments based on engineering and/or physical principles to derive at a mathemat-
ical model to relate these variables qualitatively. Undetermined parameters or coefficients are
left in the mathematical model/relationship to guard against any uncertainty and/or unac-
counted complexity. The kinetic modeling as discussed in Chapter 6 is a means to achieve
the fundamental understanding and accurate models. Field (or experimental) data must be
collected to estimate these unknown parameters before any actual use of this model. This
leads to the classic problem of parametric estimation . While the model is known to be correct
(if the parameters are determined accurately), the data contain error due to observation and
instrumentation limitations. This situation is in contrary to functional approximation where
the data are error-free while the model is not exact. Parametric estimation is commonly