Guaranteed parameter estimation in nonlinear dynamic systems using improved bounding techniques

This paper is concerned with guaranteed parameter estimation in nonlinear dynamic systems in a context of bounded measurement error. The problem consists of finding - or approximating as closely as possible - the set of all possible parameter values such that the predicted outputs match the corresponding measurements within prescribed error bounds. An exhaustive search procedure is applied, whereby the parameter set is successively partitioned into smaller boxes and exclusion tests are performed to eliminate some of these boxes, until a prespecified threshold on the approximation level is met. Exclusion tests rely on the ability to bound the solution set of the dynamic system for a given parameter subset and the tightness of these bounds is therefore paramount. Equally important is the time required to compute the bounds, thereby defining a trade-off. It is the objective of this paper to investigate this trade-off by comparing various bounding techniques based on interval arithmetic, Taylor model arithmetic and ellipsoidal calculus. When applied to a simple case study, ellipsoidal and Taylor model approaches are found to reduce the number of iterations significantly compared to interval analysis, yet the overall computational time is only reduced for tight approximation levels due to the computational overhead. © 2013 EUCA

Optimization-based domain reduction in guaranteed parameter estimation of nonlinear dynamic systems

This paper is concerned with guaranteed parameter estimation in nonlinear dynamic systems in a context of bounded measurement error. The problem consists of finding-or approximating as closely as possible-the set of all possible parameter values such that the predicted outputs match the corresponding measurements within prescribed error bounds. An exhaustive search procedure is applied, whereby the parameter set is successively partitioned into smaller boxes and exclusion tests are performed to eliminate some of these boxes, until a prespecified threshold on the approximation level is met. In order to enhance the convergence of this procedure, we investigate the use of optimization-based domain reduction techniques for tightening the parameter boxes before partitioning. We construct such bound-reduction problems as linear programs from the polyhedral relaxation of Taylor models of the predicted outputs. When applied to a simple case study, the proposed approach is found to reduce the computational burden significantly, both in terms of CPU time and number of iterations. © IFAC

Influence of magnetic field on germination, growth and production of tomato

In the study with tomatoes, there was ivestigated the impact of extremely low frequency electromagnetic fields on seed germination of tomato (Solanum lycopersicum L.) after treatment before sowing, as well as the growth of young plants that were exposed to low frequency electromagnetic field before planting in the field when growing transplants under cover. In the experiments conducted in two consecutive years (2012 and 2013), we followed the length of seed germination period of tomato variety „Pavlína", growth of young plants expressed in plant height and root length, and the fruit size. Magnetization of seeds and young plants was carried out in laboratory conditions, plant growth was evaluated under cover prior to planting, and fruit traits were followed in field conditions where plants were grown on experimental plots (80.0 m2). The plants were grown in accordance with the standards of an agricultural practice for tomato. At the generative phase, the fruits were collected at regular intervals, and their number and weight were evaluated. Low frequency electromagnetic fields acting at the three inductance levels (20, 40 and 60 mT) and exposure of 20 minutes a day with frequency of 50 Hz, significantly positively influenced the germination, plant growth and fruit size of the studied tomato variety

Nested sampling approach to set-membership estimation

This paper is concerned with set-membership estimation in nonlinear dynamic systems. The problem entails characterizing the set of all possible parameter values such that given predicted outputs match their corresponding measurements within prescribed error bounds. Most existing methods to tackle this problem rely on outer-approximation techniques, which perform poorly when the parameter host set is large due to the curse of dimensionality. An adaptation of nested sampling—a Monte Carlo technique introduced to compute Bayesian evidence—is presented herein. The nested sampling algorithm leverages efficient strategies from Bayesian statistics for generating an inner-approximation of the desired parameter set. Several case studies are presented to demonstrate the approach