John Lataire

Georgios Birpoutsoukis, Anna Marconato, John Lataire et al.

In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing higher dimensional impulse responses in the series, are considered to be realizations of multidimensional Gaussian processes. Based on this, prior information about the structure of the Volterra kernel is introduced via an appropriate penalization term in the least squares cost function. It is shown that the proposed method is able to deliver accurate estimates of the Volterra kernels even in the case of a small amount of data points.

Freja Vandeputte, Bart van den Boorn, Matthijs van Berkel et al.

The efficiency of water electrolysis in a photoelectrochemical cell is largely limited by the oxygen evolution reaction (OER) at its semiconductor photoanode. Reaction rate constants are key to investigating the slow kinetics of the multistep OER, as they indicate the rate-determining step. While these rate constants are usually calculated based on first-principles simulations, this research aims to estimate them from experimental electrochemical impedance spectroscopy (EIS) data. Starting from a microkinetic model for charge transfer at the semiconductor-electrolyte interface, an expression for the impedance as a function of the rate constants is derived. At lower potentials, the order of this impedance model is reduced, thus eliminating the rate constants corresponding to the last reaction steps. Moreover, it is shown that EIS data from at least two potentials needs to be combined in order to uniquely identify the rate constants of a particular reduced order model. Therefore, this work details a sample maximum likelihood estimator that integrates not only multiple frequencies, but also multiple potentials simultaneously. Measuring multiple periods of the current density and potential signals, allows this frequency domain estimator to take measurement uncertainty into account. In addition, due to the large numerical range of the rate constants, various scaling methods are implemented to achieve numerical stability. To find suitable initial values for the highly nonlinear optimization problem, different global estimation methods are compared. The complete estimation procedure of the rate constants is illustrated on simulated EIS data of a hematite photoanode.

Sadegh Ebrahimkhani, John Lataire

The choice of parameterization in Nonlinear (NL) system models greatly affects the quality of the estimated model. Overly complex models can be impractical and hard to interpret, necessitating data-driven methods for simpler and more accurate representations. In this paper, we propose a data-driven approach to simplify a class of continuous-time NL system models using linear approximations around varying operating points. Specifically, for sparse additive NL models, our method identifies the number of NL subterms and their corresponding input spaces. Under small-signal operation, we approximate the unknown NL system as a trajectory-scheduled Linear Parameter-Varying (LPV) system, with LPV coefficients representing the gradient of the NL function and indicating input sensitivity. Using this sensitivity measure, we determine the NL system's structure through LPV model reduction by identifying non-zero LPV coefficients and selecting scheduling parameters. We introduce two sparse estimators within a vector-valued Reproducing Kernel Hilbert Space (RKHS) framework to estimate the LPV coefficients while preserving their structural relationships. The structure of the sparse additive NL model is then determined by detecting non-zero elements in the gradient vector (LPV coefficients) and the Hessian matrix (Jacobian of the LPV coefficients). We propose two computationally tractable RKHS-based estimators for this purpose. The sparsified Hessian matrix reveals the NL model's structure, with numerical simulations confirming the approach's effectiveness.