An exemplified semi-analytical approach to the transient sensitivity of nonlinear systems

The internal logic of a model formulated as coupled differential equations is severely challenged in cases where the value of a poorly determined parameter greatly affects the solution of the model. Thus, the sensitivity to parameter changes is essential in the verification stage of the modelling process. Since a sensitivity analysis points out where the influence of flaws in present knowledge has important consequences, a sensitivity analysis will also act as a guideline for future research.In the literature known to the author, the approach to sensitivity has been either by parameter changes or local linearization. However, neither of these approaches will indicate the role played by parameter interactions in sensitivity unless a prohibitively large number of simulations are carried out.The present paper shows a known analytical expression for the sensitivity to parameter changes in nonlinear systems. A simplified version of the expression is solved for a model of the biological processes in activated sludge with 10 state-variables and 31 parameters leading to the presentation of simulated sensitivity of sensitivity, i.e. to an estimate of parameter interactions in sensitivity. The result of the approach is demonstrated through a comparison of actual and predicted changes in solution. Finally, a proposal of the extent of a complete sensitivity analysis is given.