Testing the Reliability of Mathematical Models

The mathematical models are extensively used in the engineering fields. It is a very powerful tool to
design, analyze and test the systems without actually building them, which of course reduces time
spent on the designing. The question was raised, is it actually appropriate to use the mathematical
models for testing purposes, how precise is the outcome and what kind of information about the
system the mathematical model gives. In order to investigate this situation, testing the reliability of
the mathematical models was proposed. The purpose of this project is to scrutinize the mathematical
models, investigate the pros and cons, the criteria and limitations that a mathematical model have
and of course the errors introduces if those criteria and limitations are violated. The scope of the
project covers general mathematical models for sake of investigating how they are used and their
limitations. Also, models related to electrical and electronics field are studied to quantify the errors.
As this project is mostly research based, the theories behind mathematical models are investigated
and considered and then MATLABprogramming is used to illustrate how models are used and their
outcomes for given inputs for different situations. The results of the MATLAB simulations show the
quantity and percentage of the errors and are given in form of table later in the chapters. Considering
what has been studied and the results of the simulations, mathematical models do not ideally
represent real hfe models, although if carefully designed the errors could be reduced to acceptable
limits and a close approximation of the real life model could be obtained. As for educational
purposes the little percentage of the error does not carry any significance mathematical models can
be used to enhanceunderstanding of the student. If nature of the application requires high precision,
extra care must be taken while modelling and designing.