Bounded-error Approach Research Articles

Guaranteed estimation of electrochemical parameters by set inversion using interval analysis

The bounded-error approach to parameter estimation, mainly developed in the context of control and signal processing, is applied in the electrochemistry field in order to obtain reliable estimates for kinetic parameters. The method is based on the assumption that an uncertainty bar is available for each measurement. A set guaranteed to contain all values of the parameter vector that lead to model outputs consistent with these error bars is then computed, based on interval analysis and set inversion. The resulting technique is applied on simulated and experimental data for several classical electrochemical models. Its merits are compared to those of a more traditional approach based on least square estimation by iterative local optimization. A first obvious difference is that the point estimate provided by the latter method may or may not belong to the set estimated by the former, because it does not take the bounds on the uncertainty into account. Moreover, as our approach is global, it escapes the difficult problem of initialization encountered with iterative optimization methods. Finally, the set obtained is a natural characterization of the uncertainty on the estimated parameters.

Computing bounds on greenhouse energy requirements using bounded error approach

The paper presents an approach, based on a linear, time-varying model to compute bounds on future energy requirements for greenhouse heating. Modelling errors and model parameter variations are bounded while no assumptions are necessary about their distributions. Bounds on model parameters are computed using an ellipsoidal parameter bounding approach. Wind speed is considered as the main external disturbance. Results forecasting real wind speed data are presented, and calculations are made of the future greenhouse energy needs using predicted as well as true wind speed values.

Parameter sets for bounded-error data

A simple approach to the development of user-friendly software for the bounded-error approach to parameter estimation is offered. It enables the computer determination of the boundaries of the set of all parameters satisfying the bounded-error constraints, whether the problem is linear or nonlinear, and whether the parameter set is connected or disconnected.

A bounded-error approach to accuracy analysis in ellipsometry

A nonlinear Bounded-Error Estimation method is applied to the case of ellipsometric measurement of film properties. It is shown that this method can be used with advantage for estimating the magnitude of the measurement errors including systematic errors.