Selection of Important Parameters Using Uncertainty and Sensitivity Analysis

Models of systems often require parameter estimation in order to improve output predictions or to estimate a parameter value that cannot be measured directly. Fundamental constraints exist that limit the abilities of parameter estimation algorithms. Among these limitations are the data available, influence of the parameters on the available measurements, dependences of the parameters in the model, prior knowledge of the parameters, and nonlinear nature of the parameters. Knowledge of which parameters are most important for estimation can greatly increase the chance of finding a satisfactory model. For sufficiently small bounded uncertainties, this paper proposes a computationally efficient procedure that selects parameters based on the size of the uncertainty bounds, the sensitivities of the parameters, and the dependences among the parameters. The paper demonstrates the procedure with a quadruple pendulum vibration isolation system for the laser interferometer gravitational-wave observatory.

I. Introduction

Mathematical models are extremely important tools for predicting responses, engineering designs, and estimating attributes of systems from all fields of study. Consequently, it is critical to validate and fit models to measured data using a parameter estimation algorithm. These estimation algorithms, while powerful, have fundamental limitations. A necessary, though not sufficient, condition for unique parameter estimates is a number of measurements greater than or equal to the number of parameters. Even if there are more measurements than parameters, some of the parameters may couple weakly to the measurements. Further still, even the highly sensitive parameters may be indistinguishable from each other, i.e., one parameter can undo another's contribution.