Sensitivity Analysis Using Interval Arithmetic

Sensitivity analysis is the qualitative or quantitative study of how the model output varies with changes of model inputs. In this paper, we present an approach to sensitivity analysis using interval arithmetic. The study of the effect of slightly changes in the investigated parameters is important for theoretical as well as for practical reasons. Presently, most of the numerical approaches to sensitivity analysis have characterized the solution in terms of changes in the parameters. In our work we use interval arithmetic to generate a list of intervals as the solution set, which represents the corresponding parameter values. Since the measurement values include errors, traditional parameter estimation may fail, because small changes of the measurements can cause significant changes of the parameter vector values. In general, common sensitivity analysis cannot compute the whole set of possible parameter vector values. The presented new approach using interval arithmetic compute an inner and outer approximation for the desired set of all possible parameter vector values. An example of a microelectromechanical system is discussed in this paper to illustrate the new method to sensitivity analysis and display the set of possible parameter vector values.