Precise temperature reconstruction in acoustic pyrometry: Impact of domain discretization and transceiver count

The present study delves into the complex relationship of domain discretization and transceiver allocation in enhancing the accuracy of acoustic pyrometry. Six distinct cases encompassing variations in resolution and transceiver numbers are examined. Each case involves the central and edge region cell size adjustments ranging from coarse to fine, achieved through bias factor. The temperature reconstruction process is evaluated with three different intricate temperature profiles. In the present study, two inverse methodologies namely, pseudo-inverse and Tikhonov regularization are critically evaluated in the presence of 5% and 10% additive noise. Findings highlighted the decisive role of the bias factor in influencing the accuracy of the reconstructed temperature profiles while understanding the significant impact of discretization error. Across various noise conditions, instances where the transceiver count matches the number of domain cells exhibit exceptional performance when employing the pseudo-inverse approach. Conversely, the strategic application of Tikhonov regularization emerges as a potent strategy, resulting in a substantial reduction of reconstruction errors across multiple orders of magnitude. This reduction along with the role of bias factor not only paves the way for a judicious reduction in transceiver count without compromising resolution and overall reconstruction accuracy, but also offers a new dimension to the advancement of acoustic pyrometry.