Testing the Goodness of Model Fit in Tunable Diode Laser Absorption Tomography

Abstract

Tunable diode laser absorption tomography (TDLAT) has emerged as a popular nonintrusive technique for simultaneous sensing of gas concentration and temperature by making light absorbance measurements. Major challenge of TDLAT imaging is that the measurement data is very sparse. Therefore, precise models are required to describe the measurement process (forward model) and the behavior of the gas flow properites (prior model) to get accurate reconstructions. The sparsity of the measurement data makes TDLAT very sensitive to the accuracy of the models and makes it prone to overfitting. Both the forward and prior models can have systematic errors due to several reasons. So far, substantial amount of work has been done by researchers on developing reconstruction methods and formulating models, forward and prior. Yet, there has not been significant research work done on constructing a metric for goodness of the model fit that can indicate when there is an inaccuracy in the forward or the prior model. In this paper, we present a metric for goodness of model fit that can be used to indicate if the models used in the reconstruction are inaccurate. Results show that our metric can reliably quantify the goodness of model fit for sparese data reconstruction problems such as TDLAT.