Physical parameter sensitivity of system eigenvalues and physical model reduction

The identification of subsystems and/or components that is related to a given eigenvalue of the overall system is a challenging and important topic. The use of special structure of the system matrices obtained busing bond graphs can result in identifying subsystems and/or components that affect a given eigenvalue of an overall system. This paper, by making use of a set of theorems and definitions proposes an efficient procedure for this purpose. The basic procedure is based upon the calculation of sensitivity of eigenvalues. The so-called "effect" matrices are produced that indicates the relative importance of physical parameters on a selected eigenvalue. In addition to the relative importance, the effect matrix is used for an efficient physical model reduction procedure. Furthermore, reasons of different dynamic behavior of a system can be explained. Use of effect matrices also improves the physical model reduction method based on decomposition procedures. Three examples are given to illustrate the approach and its consequences

Discovering an active subspace in a single-diode solar cell model

Predictions from science and engineering models depend on the values of the model's input parameters. As the number of parameters increases, algorithmic parameter studies like optimization or uncertainty quantification require many more model evaluations. One way to combat this curse of dimensionality is to seek an alternative parameterization with fewer variables that produces comparable predictions. The active subspace is a low-dimensional linear subspace defined by important directions in the model's input space; input perturbations along these directions change the model's prediction more, on average, than perturbations orthogonal to the important directions. We describe a method for checking if a model admits an exploitable active subspace, and we apply this method to a single-diode solar cell model with five input parameters. We find that the maximum power of the solar cell has a dominant one-dimensional active subspace, which enables us to perform thorough parameter studies in one dimension instead of five