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The frequency domain evaluation of mathematical models for dynamic systems
Author(s) -
Hays James R.,
Clements William C.,
Harris Thomas R.
Publication year - 1967
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690130231
Subject(s) - parseval's theorem , frequency domain , minification , transformation (genetics) , mathematics , domain (mathematical analysis) , algebraic number , inversion (geology) , mathematical optimization , algorithm , fourier transform , mathematical analysis , fourier analysis , fractional fourier transform , gene , biochemistry , chemistry , paleontology , structural basin , biology
An important problem in the mathematical modeling of dynamic systems is the testing of model applicability and the determination of the best model parameters through the minimization of the squared difference of the observed and predicted responses. This paper discusses the advantages of the transformation of the expression for the integral of the squared deviations ϕ to the frequency domain by the use of parseval's theorem. Two important advantages of the minimization of ϕ in the frequency domain are the ease with which the transform of the predicted response can be obtained and the algebraic nature of frequency domain operations. Other advantages are discussed and techniques for the numerical transformation and inversion of the observed and predicted responses are given.