Multi-deconvolution in non-stationary conditions applied to experimental thermal response test analysis to obtain short-term transfer functions

Abstract

Thermal response test interpretation methods usually rely on the assumptions of constant operating conditions in time. However, through desired or undesired processes, these conditions often vary in time. Since interpretation is usually done with stationary methods, no current algorithm allows to account for non-stationarity in thermal response test, as encountered with varying flow rate. The goal of this article is to apply a multi-deconvolution algorithm to retrieve a set of short-term transfer functions during a thermal response test with changing operating conditions. The deconvolution algorithm uses an optimization-based technique as the inverse model, while considering non-stationarity in the forward model through a recent non-stationary convolution algorithm. By optimizing a set of nodes on each estimated short-term transfer function, precise reconstruction of the experimental temperatures is possible. Results show that temperature reconstruction is as precise as an error of 0.06 °C on numerical cases and 0.07 °C on field cases. The usable transfer function duration and an analysis of the objective function’s optimum are also demonstrated. With the proposed algorithm, only the dataset of a thermal response test is needed to obtain short-term transfer functions when operating conditions are changing.