Trend Removal in Measurements of Best Linear Time-Varying Approximations—With Application to Operando Electrochemical Impedance Spectroscopy

Equilibria evolving over time, also called trends, are often present in ongoing measurements of real-life systems. These trends are considered as disturbances when computing the best linear time-varying approximation (BLTVA) of the system. Current techniques for dealing with trends in BLTVA measurements consist of modeling the trend with a finite number of basis functions. However, in measurements with dominant trends, the trend cannot always be captured well enough by this set of basis functions, and hence, the uncertainty on the BLTVA increases. As a consequence, one loses low-frequency information. In this article, the state-of-the-art method for estimating the BLTVA is extended by removing the trend with a differencing operator. It is shown that with this novel technique, low-frequency information becomes more visible. Moreover, the novel method decreases the variance on the BLTVA and allows to measure fewer periods. Hence, the novel technique improves the route for treating arbitrary out-of-equilibrium or also called operando, measurements. As an illustration, it is applied to operando time-varying impedance measurements of three electrochemical processes: the charging of a Li-ion battery cell, the electrorefining of copper, and the anodizing of aluminum.