TY - JOUR

T1 - Global uncertainty assessments by high dimensional model representations (HDMR)

AU - Li, Genyuan

AU - Wang, Sheng Wei

AU - Rabitz, Herschel Albert

AU - Wang, Sookyun

AU - Jaffe, Peter R.

N1 - Funding Information:
The authors acknowledge support from Department of Defense, the Environmental Protection Agency, the Hercules Incorporated, and the Natural and Accelerated Bioremediation Research (NABIR) program, Office of Biological and Environmental Research (OBER), Department of Energy (grant DE-FG02-98ER62705).

PY - 2002/11/4

Y1 - 2002/11/4

N2 - A general set of quantitative model assessment and analysis tools, termed high-dimensional model representations (HDMR), have been introduced recently for high dimensional input-output systems. HDMR are a particular family of representations where each term in the representation reflects the independent and cooperative contributions of the inputs upon the output. When data are randomly sampled, a RS(random sampling)-HDMR can be constructed, which is an efficient tool to provide a fully global statistical analysis of a model. The individual RS-HDMR component functions have a direct statistical correlation interpretation. This relation permits the model output variance σ2 to be decomposed into its input contributions σ2 = Σiσ2i + Σi σ2ij +. due to the independent variable action σ2i, the pair correlation action σ2ij, etc. The information gained from this decomposition can be valuable for attaining a physical understanding of the origins of output uncertainty as well as suggesting additional laboratory/field studies or model refinements to best improve the quality of the model. To reduce sampling effort, the RS-HDMR component functions are approximately represented by orthonormal polynomials. Only one randomly sampled set of input-output data is needed to determine all σi, σij, etc. and a few hundred samples may give reliable results. This paper presents its methodology and applications on an atmospheric photochemistry model and a trace metal bioremediation model.

AB - A general set of quantitative model assessment and analysis tools, termed high-dimensional model representations (HDMR), have been introduced recently for high dimensional input-output systems. HDMR are a particular family of representations where each term in the representation reflects the independent and cooperative contributions of the inputs upon the output. When data are randomly sampled, a RS(random sampling)-HDMR can be constructed, which is an efficient tool to provide a fully global statistical analysis of a model. The individual RS-HDMR component functions have a direct statistical correlation interpretation. This relation permits the model output variance σ2 to be decomposed into its input contributions σ2 = Σiσ2i + Σi σ2ij +. due to the independent variable action σ2i, the pair correlation action σ2ij, etc. The information gained from this decomposition can be valuable for attaining a physical understanding of the origins of output uncertainty as well as suggesting additional laboratory/field studies or model refinements to best improve the quality of the model. To reduce sampling effort, the RS-HDMR component functions are approximately represented by orthonormal polynomials. Only one randomly sampled set of input-output data is needed to determine all σi, σij, etc. and a few hundred samples may give reliable results. This paper presents its methodology and applications on an atmospheric photochemistry model and a trace metal bioremediation model.

KW - Global uncertainty analysis

KW - High dimensional model representation

KW - Monte Carlo method

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U2 - 10.1016/S0009-2509(02)00417-7

DO - 10.1016/S0009-2509(02)00417-7

M3 - Article

AN - SCOPUS:0037020570

SN - 0009-2509

VL - 57

SP - 4445

EP - 4460

JO - Chemical Engineering Science

JF - Chemical Engineering Science

IS - 21

ER -