A finite element based formulation for sensitivity studies of piezoelectric systems

Sensitivity Analysis is a branch of numerical analysis which aims to quantify the affects that variability in the parameters of a numerical model have on the model output. A finite element based sensitivity analysis formulation for piezoelectric media is developed here and implemented to simulate the operational and sensitivity characteristics of a piezoelectric based distributed mode actuator (DMA). The work acts as a starting point for robustness analysis in the DMA technology

An optimal experimental design criterion for discriminating between non-normal models

Typically "T"-optimality is used to obtain optimal designs to discriminate between homoscedastic models with normally distributed observations. Some extensions of this criterion have been made for the heteroscedastic case and binary response models in the literature. In this paper, a new criterion based on the Kullback-Leibler distance is proposed to discriminate between rival models with non-normally distributed observations. The criterion is coherent with the approaches mentioned above. An equivalence theorem is provided for this criterion and an algorithm to compute optimal designs is developed. The criterion is applied to discriminate between the popular Michaelis-Menten model and a typical extension of it under the log-normal and the gamma distributions. Copyright 2007 Royal Statistical Society.

Horwitz's rule, transforming both sides and the design of experiments for mechanistic models

The paper develops methods for the design of experiments for mechanistic models when the response must be transformed to achieve symmetry and constant variance. The power transformation that is used is partially justified by a rule in analytical chemistry. Because of the nature of the relationship between the response and the mechanistic model, it is necessary to transform both sides of the model. Expressions are given for the parameter sensitivities in the transformed model and examples are given of optimum designs, not only for single-response models, but also for experiments in which multivariate responses are measured and for experiments in which the model is defined by a set of differential equations which cannot be solved analytically. The extension to designs for checking models is discussed. Copyright 2003 Royal Statistical Society.

"T"-optimum designs for discrimination between two multiresponse dynamic models

The paper is concerned with a problem of finding an optimum experimental design for discriminating between two rival multiresponse models. The criterion of optimality that we use is based on the sum of squares of deviations between the models and picks up the design points for which the divergence is maximum. An important part of our criterion is an additional vector of experimental conditions, which may affect the design. We give the necessary conditions for the design and the additional parameters of the experiment to be optimum, we present the algorithm for the numerical optimization procedure and we show the relevance of these methods to dynamic systems, especially to chemical kinetic models. Copyright 2005 Royal Statistical Society.