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Modelling of casings
Published in Marek Pawelczyk, Stanislaw Wrona, Noise-Controlling Casings, 2023
Marek Pawelczyk, Stanislaw Wrona, C. W. Isaac, J. Klamka, J. Wyrwal
With direct model assuming given inputs and model parameters the output can be determined. In contrast, if for given inputs and outputs we want to determine model parameters or assuming given model parameters and outputs we want to determine the input the inverse model should be used. If we ask for parameter values, the resulting problem is also called a parameter identification problem. If we ask for input, the resulting problem is also called a control problem, since in this case the problem is to control the input in a way that generates some desired output.
Measuring stiffness of soils in situ
Published in Fusao Oka, Akira Murakami, Ryosuke Uzuoka, Sayuri Kimoto, Computer Methods and Recent Advances in Geomechanics, 2014
Fusao Oka, Akira Murakami, Ryosuke Uzuoka, Sayuri Kimoto
Poromechanical interpretation of pulse and drying tests combines numerical modeling (direct problem) with an inversion algorithm (inverse problem) in order to identify transfer, as well as poromechanical, parameters. This parameter identification problem is formulated as an optimization problem aiming at fitting numerically calculated data to experimental measurements. These data are the pressures in the upstream and downstream reservoirs for the pulse test and the mass variation, even the deformations, for the drying test. This is an inverse problem that has been detailed in Giot et al. (2011, 2012). The cost-functional is of the least-squares type and consists of a term accounting for previous knowledge on the parameters: χ[c]=12∑i=1Nmesωiγc,ti-γmesti2+12∑j=1Nparvicj-cjprior2
An efficient optimization methodology of respiration rate parameters coupled with transport properties in mass balances to describe modified atmosphere packaging systems
Published in Inverse Problems in Science and Engineering, 2020
Guillermo Badillo, Patricio Cumsille, Luis Segura-Ponce, Gianpiero Pataro, Giovanna Ferrari
Given a parameters vector , the direct problem consists of finding the (unique) solution of the mathematical model given by Equations (10)–(11). The solution to the direct problem is required to solve the inverse problem. The present study aimed to develop a clear, reproducible, and modern methodology to solve the parameter identification problem and compare the fit performance of different mathematical models to experimental data in such a way as to be able to decide which model best fits a given dataset. This procedure is referred to as the inverse problem, i.e. given experimental data that measures the vector of concentrations at some time points to identify the parameters vector such that the mathematical model given by Equations (10)–(11) fits the data in the sense of the least-squares. More precisely, to solve the inverse problem of parameter estimation, it is necessary to find the vector so that the sum of squares