Details
| Original language | English |
|---|---|
| Pages (from-to) | 229-249 |
| Number of pages | 21 |
| Journal | International Journal of Reliability and Safety |
| Volume | 5 |
| Issue number | 3-4 |
| Early online date | 11 Jul 2011 |
| Publication status | E-pub ahead of print - 11 Jul 2011 |
Abstract
In the engineering sciences, observation uncertainty often consists of two main types: random variability due to uncontrollable external effects and imprecision due to remaining systematic errors in the data. Interval mathematics is well suited to treat this second type of uncertainty if settheoretical overestimation is avoided. Overestimation means that the true range of parameter values is only quantified by rough, meaningless outer bounds. If recursively formulated estimation algorithms are used, overestimation becomes a key problem. This occurs in state-space estimation which is relevant in real-time applications and which is essentially based on recursions. Hence, overestimation has to be analysed thoroughly to minimise its impact. In this study, observation imprecision is referred to physically meaningful influence parameters. This allows to reformulate the recursion algorithm yielding an increased efficiency and to rigorously avoid overestimation. In order to illustrate and discuss the theoretical results, a damped harmonic oscillation and the monitoring of a lock are presented as examples.
Keywords
- Damped harmonic oscillation, Imprecision, Interval data, Interval mathematics, Least-squares estimation, Observation uncertainty, Overestimation, Recursive estimation, Recursive parameter estimation, State-space estimation
ASJC Scopus subject areas
- Engineering(all)
- Safety, Risk, Reliability and Quality
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In: International Journal of Reliability and Safety, Vol. 5, No. 3-4, 11.07.2011, p. 229-249.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Recursive least-squares estimation in case of interval observation data
AU - Kutterer, Hansjörg
AU - Neumann, Ingo
PY - 2011/7/11
Y1 - 2011/7/11
N2 - In the engineering sciences, observation uncertainty often consists of two main types: random variability due to uncontrollable external effects and imprecision due to remaining systematic errors in the data. Interval mathematics is well suited to treat this second type of uncertainty if settheoretical overestimation is avoided. Overestimation means that the true range of parameter values is only quantified by rough, meaningless outer bounds. If recursively formulated estimation algorithms are used, overestimation becomes a key problem. This occurs in state-space estimation which is relevant in real-time applications and which is essentially based on recursions. Hence, overestimation has to be analysed thoroughly to minimise its impact. In this study, observation imprecision is referred to physically meaningful influence parameters. This allows to reformulate the recursion algorithm yielding an increased efficiency and to rigorously avoid overestimation. In order to illustrate and discuss the theoretical results, a damped harmonic oscillation and the monitoring of a lock are presented as examples.
AB - In the engineering sciences, observation uncertainty often consists of two main types: random variability due to uncontrollable external effects and imprecision due to remaining systematic errors in the data. Interval mathematics is well suited to treat this second type of uncertainty if settheoretical overestimation is avoided. Overestimation means that the true range of parameter values is only quantified by rough, meaningless outer bounds. If recursively formulated estimation algorithms are used, overestimation becomes a key problem. This occurs in state-space estimation which is relevant in real-time applications and which is essentially based on recursions. Hence, overestimation has to be analysed thoroughly to minimise its impact. In this study, observation imprecision is referred to physically meaningful influence parameters. This allows to reformulate the recursion algorithm yielding an increased efficiency and to rigorously avoid overestimation. In order to illustrate and discuss the theoretical results, a damped harmonic oscillation and the monitoring of a lock are presented as examples.
KW - Damped harmonic oscillation
KW - Imprecision
KW - Interval data
KW - Interval mathematics
KW - Least-squares estimation
KW - Observation uncertainty
KW - Overestimation
KW - Recursive estimation
KW - Recursive parameter estimation
KW - State-space estimation
UR - http://www.scopus.com/inward/record.url?scp=79960221840&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:79960221840
VL - 5
SP - 229
EP - 249
JO - International Journal of Reliability and Safety
JF - International Journal of Reliability and Safety
SN - 1479-389X
IS - 3-4
ER -