ABSTRACT
One of the goals of engineering research is to invent, design, or develop new technology for practical applications (Petroski, 2010). To achieve this goal, there are two distinct activities in engineering research: the first is simulation and the second is data collection. Simulation requires some type of model, typically a mathematical one. Data collection requires instrumentation and the building of prototypes,
5.1 Introduction .................................................................................................. 111 5.1.1 Forward Problem versus Inverse Problem ........................................ 112
5.1.1.1 Forward Problem ............................................................... 112 5.1.1.2 Inverse Problem ................................................................. 113
5.1.2 Importance of the Inverse Problem and Parameter Estimation ........ 114 5.2 Theory of Parameter Estimation .................................................................. 115
5.2.1 Standard Statistical Assumptions ..................................................... 115 5.2.2 Scaled Sensitivity Coefficients ......................................................... 116 5.2.3 Ordinary Least Squares .................................................................... 117 5.2.4 Confidence Intervals of the Parameters ............................................ 118 5.2.5 Residual Analysis ............................................................................. 118 5.2.6 Sequential Estimation ....................................................................... 119
5.3 Case Study .................................................................................................... 120 5.3.1 Choice of the Model ......................................................................... 121 5.3.2 Data Transformation and Weighting Method ................................... 122 5.3.3 Scaled Sensitivity Coefficients ......................................................... 123 5.3.4 Estimation of the Parameters ............................................................ 125 5.3.5 Statistical Results for the Optical Parameters
and the Dependent Variable .............................................................. 126 5.4 Summary ...................................................................................................... 129 References .............................................................................................................. 130
whether they are software or hardware. In today’s competitive world, neither area alone is sufficient. Simulation alone lacks experimental verification that could show deficiencies in the model. Data collection alone cannot determine the results of other experimental conditions that are not tested. Combining the two areas gives the most insight into how to efficiently advance the technology.
