Sensitivity Analysis of Distributed Parameter Systems

A wide variety of phenomena are described by partial differential equations, so-called distributed parameter systems. In such partial differential equation models it is often desirable to determine the effect of uncertainties in parameters appearing in the equations on their solutions and also, if more than one .parameter may vary, which parameters arc most influential. The sensitivity analysis of distributed parameter systems poses several problems that do not arise in the lumped parameter case. First, parameters may occur in the boundary conditions as well as in the differential . equations. Second, parameters may vary spatially andj or temporally. Comparatively little work has been done on the distributed parameter sensitivity analysis problem as opposed to the corresponding lumped parameter case. Koda eta/. [I] developed methods for the local sensitivity analysis of constant, spatially varying, and temporally varying parameters in parabolic partial differential equations characteristic of reaction and diffusion processes. In the present work we extend that analysis to a general class of distributed systems and apply the results to a problem in one-dimensional heat conduction.