Irina Sivergina

Source Identification for Parabolic Equations

AbstractThis paper treats an inverse problem of source identification in systems modeled by partial differential equations of parabolic type. Regularization procedures and recursive estimation algorithms are developed to estimate the location and the intensity of the source.

Comments on "Model-based solution techniques for the source localization problem"

For original paper see ibid., vol. 8, p. 895-904, (Nov. 2000). The above-mentioned paper treats the problem of locating a source in a distributed parameter system. The aim of these comments is to point out some subtleties that must be taken into account when applying the techniques proposed in the above-mentioned paper since ignoring these may lead to erroneous results.

A Reduced-order Photo-chemical Air Quality Model

We report on a reduced-order photo-chemical model (TAPOM-Lite) designed for calculating ozone levels for varying urban scenarios and calibrated for the city of Geneva, Switzerland. The TAPOM-Lite model is an atmospheric-environmental model designed to be incorporated into a larger energy-economy-environment (E 3) model and run in an optimization framework. The motivation for the TAPOM-Lite model was the design of a fast ozone calculator needed for the CPU intensive optimization environment where many iterations are potentially required before a best solution is found. Three principal advances in this model are (1) a simplified chemical scheme for O 3 production, (2) linearization of the O 3 production function needed for the overseeing linear optimization program, and (3) the extraction of gradient (sensitivity) information calculated from the O 3 production function which in turn is needed as “directional” information in the optimization method. Results show that the TAPOM-Lite model is consistent with the full-scale TAPOM model throughout the optimization/iteration process. The TAPOM-Lite model provides a first coupled energy-economy-environment (E 3) program for optimization and also provides a framework for global applications, for example, the linking of global indicators (e.g. mean temperatures) and world energy consumption.

Combined input and parameter estimation with input observers and set-membership parameter bounding

The paper addresses an online, simultaneous input and parameter estimation problem for a first order system affected by measurement noise. This problem is motivated by practical applications in the area of engine control. Our approach combines an input observer for the unknown input with a set-membership procedure to estimate the parameter.

A REDUCED-ORDER PHOTOCHEMICAL AIR QUALITY MODEL

We report on reduced-order photo-chemical model (TAPOM-Lite) designed for calculating ozone levels for varying urban scenarios and calibrated for the city of Geneva, Switzerland. The TAPOM-Lite model is an atmospheric-environmental model designed to be incorporated into a larger energy–economy–environment (E3) model and run in an optimization framework. The motivation for the TAPOM-Lite model was the design of a fast ozone calculator needed for the CPU-intensive optimization environment where many iterations are potentially required before a best solution is found. Three principal advances in this model are (1) a simplified chemical scheme for O3 production, (2) linearization of the O3 production function needed for the overseeing linear optimization program, and (3) the extraction of gradient (sensitivity) information calculated from the O3 production function which in turn is needed as “directional” information in the optimization method. Results show that the TAPOM-Lite model is consistent with the full-scale TAPOM model throughout the optimization/iteration process. The TAPOM-Lite model provides a first coupled E3 program for optimization and also provides a framework for global application such as the linking of global indicators (e.g., mean temperatures) and world energy consumption.

Identification of the Heat Flux in a Quasi-Static Thermoelastic System

This paper treats the problem of estimating the heat flux through the free end of a thermoelastic rod, which is allowed to come into contact with a rigid obstacle. This problem is motivated by the need to develop techniques for indirect measurement of heating in applications, such as, brake systems and machine tools. Under a quasi-static approximation, the problem becomes that of characterizing thermal processes in the rod. Assuming that direct and exact measurements at the contacting end of the rod cannot be taken, the problem is to determine if there is contact with the obstacle; and if there is contact, to characterize the conductivity processes at the contacting end. We study the case of weighted-average temperature measurements throughout the rod. Identifiability results and on-line recursive estimation procedures are developed.

Adaptive reconstruction of multiple source intensities for parabolic PDEs

The paper treats an inverse problem of source identification in systems modeled by partial differential equations (PDEs) of parabolic type. Assuming the locations of all sources are known, regularization procedures and recursive estimation algorithms are developed to estimate the intensity of each of the multiple sources.