A Bivariate Gamma Model for a Latent Degradation Process

Shemehsavar, Soudabeh

doi:10.1080/03610926.2012.677300

“…This ratio is independent of the scale parameter. In deterioration modelling particularly, gamma process has been widely applied to model the temporal uncertainty (e.g., Shemehsavar 2014;Zhang & Zhou 2014). A comprehensive survey of the application of Gamma process in maintenance engineering can be found in Van Noortwijk (2007).…”

Section: Gamma Processmentioning

confidence: 99%

“…Also, Zhang (2014) extended Elsayed and Liao (2004)'s model by formulating a defect-specific hierarchical Bayesian corrosion growth model. Gamma processes have been widely used to model temporal variability of deterioration (Pandey et al 2009;Zhang 2014;Shemehsavar 2014). Lawless and Crowder (2004) and Tsai et al (2012) incorporated random effects into their gamma process models.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Modelling of Spatio-Temporal Uncertainties in Degradation

Adegbola¹,

Yuan²

2022

Preprint

0

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Deterioration is a major problem facing engineering structures, systems and components (SSCs). To maintain the structural integrity and safe operation of such SSCs all through their service life, it is important to understand how degradation phenomena progress over time and space. Hence degradation modelling has been increasingly used to model existing deterioration, predict future deterioration as well as provide input for infrastructure management in terms of inspection and maintenance decision making. As deterioration is known to be random, modelling of spatial and temporal uncertainty remains a crucial challenge for infrastructure asset professionals. The main objective of the thesis is to develop sophisticated models for characterizing spatial and temporal uncertainties in deterioration modelling with a view to enhancing decision making under uncertainty. The thesis proposes a two-dimensional copula-based gamma distributed random field for the spatial uncertainties, and a copula-based multivariate gamma process model to characterize stochastic dependence of multiple degradation phenomena. Techniques for estimating the model parameters and simulating the field or process, prediction of the remaining lifetime distribution as well as condition-based maintenance optimization are also presented. To study the extreme value distribution of the random field, the thesis also presents a numerical method based on the Karhunen-Loève expansion for evaluating extrema of both one- and two-dimensional homogeneous random fields. The simulation results are benchmarked against existing analytical models for special cases. In addition, the study also investigates the effect of parameter (epistemic) uncertainty on the extreme value distribution of the field. Finally, the thesis presents a practical application of the proposed copula-based gamma field by treating the wall profile of a feeder pipe as one- and twodimensional gamma fields. The thesis demonstrates a practical application of the multivariate gamma process model to rutting, cracking, and surface roughness of highway pavements. In summary, the proposed models have advanced the knowledge and techniques of stochastic deterioration modelling in the engineering field.

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“…This ratio is independent of the scale parameter. In deterioration modelling particularly, gamma process has been widely applied to model the temporal uncertainty (e.g., Shemehsavar 2014;Zhang & Zhou 2014). A comprehensive survey of the application of Gamma process in maintenance engineering can be found in Van Noortwijk (2007).…”

Section: Gamma Processmentioning

confidence: 99%

“…Also, Zhang (2014) extended Elsayed and Liao (2004)'s model by formulating a defect-specific hierarchical Bayesian corrosion growth model. Gamma processes have been widely used to model temporal variability of deterioration (Pandey et al 2009;Zhang 2014;Shemehsavar 2014). Lawless and Crowder (2004) and Tsai et al (2012) incorporated random effects into their gamma process models.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Modelling of Spatio-Temporal Uncertainties in Degradation

Adegbola¹,

Yuan²

2022

Preprint

0

View full text Add to dashboard Cite

Deterioration is a major problem facing engineering structures, systems and components (SSCs). To maintain the structural integrity and safe operation of such SSCs all through their service life, it is important to understand how degradation phenomena progress over time and space. Hence degradation modelling has been increasingly used to model existing deterioration, predict future deterioration as well as provide input for infrastructure management in terms of inspection and maintenance decision making. As deterioration is known to be random, modelling of spatial and temporal uncertainty remains a crucial challenge for infrastructure asset professionals. The main objective of the thesis is to develop sophisticated models for characterizing spatial and temporal uncertainties in deterioration modelling with a view to enhancing decision making under uncertainty. The thesis proposes a two-dimensional copula-based gamma distributed random field for the spatial uncertainties, and a copula-based multivariate gamma process model to characterize stochastic dependence of multiple degradation phenomena. Techniques for estimating the model parameters and simulating the field or process, prediction of the remaining lifetime distribution as well as condition-based maintenance optimization are also presented. To study the extreme value distribution of the random field, the thesis also presents a numerical method based on the Karhunen-Loève expansion for evaluating extrema of both one- and two-dimensional homogeneous random fields. The simulation results are benchmarked against existing analytical models for special cases. In addition, the study also investigates the effect of parameter (epistemic) uncertainty on the extreme value distribution of the field. Finally, the thesis presents a practical application of the proposed copula-based gamma field by treating the wall profile of a feeder pipe as one- and twodimensional gamma fields. The thesis demonstrates a practical application of the multivariate gamma process model to rutting, cracking, and surface roughness of highway pavements. In summary, the proposed models have advanced the knowledge and techniques of stochastic deterioration modelling in the engineering field.

show abstract