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Sensitivity and Uncertainty Analysis Methods: with Applications to a Road Traffic Emission Model
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
2007 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Känslighets- och osäkerhetsanalysmetoder : med tillämpningar på en emissionsmodell för vägtrafik (Swedish)
Abstract [en]

There is always a need to study the properties of complex input–output systems, properties that may be very difficult to determine. Two such properties are the output’s sensitivity to changes in the inputs and the output’s uncertainty if the inputs are uncertain.

A system can be formulated as a model—a set of functions, equations and conditions that describe the system. We ultimately want to study and learn about the real system, but with a model that approximates the system well, we can study the model instead, which is usually easier. It is often easier to build a model as a set of combined sub-models, but good knowledge of each sub-model does not immediately lead to good knowledge of the entire model. Often, the most attractive approach to model studies is to write the model as computer software and study datasets generated by that software.

Methods for sensitivity analysis (SA) and uncertainty analysis (UA) cannot be expected to be exactly the same for all models. In this thesis, we want to determine suitable SA and UA methods for a road traffic emission model, methods that can also be applied to any other model of similar structure. We examine parts of a well-known emission model and suggest a powerful data-generating tool. By studying generated datasets, we can examine properties in the model, suggest SA and UA methods and discuss the properties of these methods. We also present some of the results of applying the methods to the generated datasets.

Abstract [sv]

Det finns alltid behov av att studera egenskaper hos komplexa input-output-system, egenskaper som kan vara mycket svåra att få fram. Två sådana egenskaper är ut fallets känslighet mot förändringar i ingångsvärdena och utfallets osäkerhet om ingångsvärdena har osäkerhet.

Ett system kan formuleras som en modell-en mängd funktioner, ekvationer och betingelser som tillsammans liknar systemet. Vi vill egentligen studera och lära oss det verkliga systemet, men med en modell som approximerar det verkliga systemet bra kan man studera modellen istället, vilket i de flesta fall är enklare. Det är oftast enklare att bygga en modell som en mängd kombinerade delmodeller, men bra kunskap om varje delmodell leder inte omedelbart till bra kunskap om hela modellen. Det enklaste tillvägagångssättet för modellstudier är oftast att studera datamängder som genererats av modellen genom ett datorprogram.

Metoder för känslighetsanalys (SA) och osäkerhetsanalys (UA) kan inte förväntas vara likadana för varje modell. I den här avhandlingen ska vi studera SA- och UA-metoder och resultat för en emissionsmodell för vägtrafik, men metoderna kan även användas för andra modeller av liknande struktur. Vi undersöker en välkänd emissionsmodell och föreslår ett kraftfullt verktyg för att generera data. Genom att studera genererade datamängder kan vi undersöka egenskaper i modellen, föreslå SA- och VA-metoder och diskutera metodernas egenskaper. Vi visar också några resultat när man tillämpar metoderna på de genererade datamängderna.

Place, publisher, year, edition, pages
Matematiska institutionen , 2007. , 24 + papers 1-5 p.
Series
Linköping Studies in Arts and Science, ISSN 0282-9800 ; 383Linköping Studies in Statistics, ISSN 1651-1700 ; 8
Keyword [en]
Emission, Grid, Model, Pollutant, Response surface, Road traffic, Sensitivity analysis, Simulation, Uncertainty analysis
Keyword [sv]
Avgaser, Vägtrafik, Miljöaspekter
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-8315ISBN: 978-91-85715-72-5 (print)OAI: oai:DiVA.org:liu-8315DiVA: diva2:23145
Public defence
2007-03-16, BL32, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2007-02-13 Created: 2007-02-13 Last updated: 2014-09-09Bibliographically approved
List of papers
1. A new program for fast emission calculations based on the COPERT III model
Open this publication in new window or tab >>A new program for fast emission calculations based on the COPERT III model
(English)Manuscript (Other academic)
Abstract [en]

Emissions from road traffic are hard to measure and therefore usually estimated in models. In this paper the construction of the widely used COPERT III model is examined, and the model is rewritten in mathematical notation. The original COPERT III software is easily handled but is not suitable as an emissiondata generating tool for fast calculations over a broad variety of driving conditions, which is required for sensitivity analysis. An alternative program has been developed to meet the desired properties of such a tool. The construction of the alternative program is discussed together with its new abilities and restrictions. Some differences between the results from the original COPERT III software and the alternative program are analyzed and discussed.

National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14295 (URN)
Available from: 2007-02-13 Created: 2007-02-13 Last updated: 2012-12-17
2. Basic sensitivity analysis methods: applied to the COPERT III road traffic emission model
Open this publication in new window or tab >>Basic sensitivity analysis methods: applied to the COPERT III road traffic emission model
(English)Manuscript (Other academic)
Abstract [en]

Many complex systems are simulated in models, and these models are hard to evaluate completely. For example, the sensitivity of the model output for different inputs is seldom analyzed. This paper provides an introduction to sensitivity analysis and proposes some basic sensitivity analysis methods. The results are important, for example, in choosing a sampling scheme. Themethods are applied to the COPERT III model, and the sensitivity results are compared and discussed. Certain theoretical results simplify the sensitivity analysis in a special case, and the paper ends by recommending a method.

National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14296 (URN)
Available from: 2007-02-13 Created: 2007-02-13 Last updated: 2012-12-17
3. Global sensitivity analysis methods using response surface descriptions: applied to the COPERT III road traffic emission model
Open this publication in new window or tab >>Global sensitivity analysis methods using response surface descriptions: applied to the COPERT III road traffic emission model
(English)Manuscript (Other academic)
Abstract [en]

Sensitivity analyses may be local or global, one at a time or all at a time, or classified in other ways. This paper examines some response surface methods for instant calculations of many sensitivities at the same time. The appropriateness of replacing the original model with a simpler response surface is discussed.The methods are also compared with one at a time methods. Sensitivity results are calculated by applying the methods to the COPERT III model. The conclusion is that a simple response surface method should be preferred.

National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14297 (URN)
Available from: 2007-02-13 Created: 2007-02-13 Last updated: 2012-12-17
4. Variance-based sensitivity analysis: with application to a road traffic emission model
Open this publication in new window or tab >>Variance-based sensitivity analysis: with application to a road traffic emission model
(English)Manuscript (Other academic)
Abstract [en]

This paper discusses sensitivity analysis based on methods that divide the total variation of a particular response into components associated with the explaining variables or factors. Two methods for estimating variance components in no-interaction multiway designs are discussed, and their dependence on balancein the sampling design is studied. The methods are applied to datasets generated from a road traffic emission model.

National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14298 (URN)
Available from: 2007-02-13 Created: 2007-02-13 Last updated: 2012-12-17
5. Uncertainty analysis with uncertain input distributions: applied to a road traffic emission model
Open this publication in new window or tab >>Uncertainty analysis with uncertain input distributions: applied to a road traffic emission model
(English)Manuscript (Other academic)
Abstract [en]

The output of a model or an experiment is often fairly uncertain because the underlying conditions have to some extent been guessed at or estimated. Such uncertainty is usually described by examining the distribution of the output given an input of known distribution. In this paper, we discuss why this approachmay not be suitable for some problems, and consider an alternate approach in cases in which we have only vague information concerning the distributions of the inputs, regardless as to whether these inputs are continm:ms or categorical. Our approach is well suited for a mean output that represents the weighted sum of the outputs of categories, if there is a large dataset with an uncertain input distribution. In this study, the method is applied to a road traffic emission scenario.

National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-14299 (URN)
Available from: 2007-02-13 Created: 2007-02-13 Last updated: 2012-12-17

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Eriksson, Olle

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