Gerd Vandersteen

Johan Schoukens, Rik Pintelon, Yves Rolain et al.

In this paper we show that it is possible to retrieve structural information about complex block-oriented nonlinear systems, starting from linear approximations of the nonlinear system around different setpoints.The key idea is to monitor the movements of the poles and zeros of the linearized models and to reduce the number of candidate models on the basis of these observations. Besides the well known open loop single branch Wiener-, Hammerstein-, and Wiener-Hammerstein systems, we also cover a number of more general structures like parallel (multi branch) Wiener-Hammerstein models, and closed loop block oriented models, including linear fractional representation (LFR) models.

Adam Cooman, Piet Bronders, Dries Peumans et al.

A Distortion Contribution Analysis (DCA) obtains the distortion at the output of an analog electronic circuit as a sum of distortion contributions of its sub-circuits. Similar to a noise analysis, a DCA helps a designer to pinpoint the actual source of the distortion. Classically, the DCA uses the Volterra theory to model the circuit and its sub-circuits. This DCA has been proven useful for small circuits or heavily simplified examples. In more complex circuits however, the amount of contributions increases quickly, making the interpretation of the results difficult. In this paper, the Best Linear Approximation (BLA) is used to perform the DCA instead. The BLA represents the behaviour of a sub-circuit as a linear circuit with the unmodelled distortion represented by a noise source. Combining the BLA with a classic noise analysis yields a DCA that is simple to understand, yet capable to handle complex excitation signals and complex strongly non-linear circuits.

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.

Maarten Schoukens, Anna Marconato, Rik Pintelon et al.

Block-oriented nonlinear models are popular in nonlinear modeling because of their advantages to be quite simple to understand and easy to use. To increase the flexibility of single branch block-oriented models, such as Hammerstein, Wiener, and Wiener-Hammerstein models, parallel block-oriented models can be considered. This paper presents a method to identify parallel Wiener-Hammerstein systems starting from input-output data only. In the first step, the best linear approximation is estimated for different input excitation levels. In the second step, the dynamics are decomposed over a number of parallel orthogonal branches. Next, the dynamics of each branch are partitioned into a linear time invariant subsystem at the input and a linear time invariant subsystem at the output. This is repeated for each branch of the model. The static nonlinear part of the model is also estimated during this step. The consistency of the proposed initialization procedure is proven. The method is validated on real-world measurements using a custom built parallel Wiener-Hammerstein test system.