Transient Effects of Uncertainties on the Sensitivities of Temperatures and Heat Fluxes Using Stochastic Finite Elements

This paper addresses the question in the design of experiments of where to place sensors for optimal sensitivity and the post-experiment determination of which sensors yield relevant data. The authors in their previous works have described the spatial dependence of the response sensitivities and the importance of conducting a sensitivity analysis for a better understanding of the system response. This paper describes the formulation of the method for a transient analysis and its application to thermal problems. The results have been verified using the Monte Carlo sampling technique to simulate the variations in the parameters. The results show that there are not only optimal locations to maximize the sensitivities of the responses, but also optimal times of measurement. Sample test cases are used to demonstrate the effects of time of measurement and placement of sensors on the accuracy of the measured temperatures.