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Set Membership Approach to Identification and Prediction of Lake Eutrophication
Author(s) -
Keesman Karel,
Straten Gerrit
Publication year - 1990
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr026i011p02643
Subject(s) - identification (biology) , set (abstract data type) , pointwise , bounded function , probabilistic logic , fuzzy set , mathematics , data mining , computer science , mathematical optimization , fuzzy logic , statistics , artificial intelligence , ecology , mathematical analysis , biology , programming language
Generally, ecosystems modeling is obstructed by the problem of sparse and unreliable data, and lack of knowledge about processes dominating the system. Under these circumstances, set theoretic uncertainty models are an appropriate alternative to probabilistic models. The only requirement is that the uncertainty is pointwise bounded. A newly developed set membership identification procedure is presented and demonstrated by an application to the modeling of shallow lake eutrophication. First, a set of parameter vectors is identified. Analysis of the set reveals a dominant direction spanned by four algal growth and death parameters. Second, on the basis of additional fuzzy set theoretic assumptions, a formal min‐max estimation is performed to obtain information about the model validity. If the model appears to be (partially) invalid, the degree of invalidity, affecting the model prediction uncertainty, can be represented by an estimate of the model structure error in addition to the uncertainty contained in the identified set of parameter vectors.