### Abstract

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 σ^{2} to be decomposed into its input contributions σ^{2} = Σ_{i}σ^{2}_{i} + Σ_{i<j} σ^{2}_{ij} +. due to the independent variable action σ^{2}_{i}, the pair correlation action σ^{2}_{ij}, 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 σ_{i}, σ_{ij}, 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.

Original language | English (US) |
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Pages (from-to) | 4445-4460 |

Number of pages | 16 |

Journal | Chemical Engineering Science |

Volume | 57 |

Issue number | 21 |

DOIs | |

State | Published - Nov 4 2002 |

### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Chemical Engineering(all)
- Industrial and Manufacturing Engineering

### Keywords

- Global uncertainty analysis
- High dimensional model representation
- Monte Carlo method

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## Cite this

*Chemical Engineering Science*,

*57*(21), 4445-4460. https://doi.org/10.1016/S0009-2509(02)00417-7