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Optimisation under uncertainty applied to a bridge collision problem

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Abstract
We consider the problem of modelling the load on a bridge pillar when hit by a vehicle. This load depends on a number of uncertain variables, such as the mass of the vehicle and its speed on impact. The objective of our study is to analyse their effect on the load. More specifically, we are interested in finding the minimum distance of the pillar to the side of the road passing under the bridge such that a given constraint on the load is satisfied in 99% of impact cases, i.e., such that the probability of satisfying the constraint is 0.99. In addition, we look for solutions to the following optimisation problem: find the distance that minimises a given cost function while still satisfying a given constraint on the load. This optimisation problem under uncertain constraints is not a well-posed problem, so we turn it into a decision problem under uncertainty. For both problems, we consider two typical cases. In the first, so-called precise-probability case, all uncertain variables involved are modelled using probability distributions, and in the second, so-called imprecise-probability case, the uncertainty for at least some of the variables (in casu the mass) is modelled by an interval of possible values, which is a special imprecise-probabilistic model. In the first case, we compute the joint distribution using simple Monte Carlo simulation, and in the second case, we combine Monte Carlo simulation with newly developed techniques in the field of imprecise probabilities. For the optimisation problem with uncertain constraints, this leads to two distinct approaches with different optimality criteria, namely maximality and maximinity, which we discuss and compare.
Keywords
linear-vacuous prevision, uncertainty, maximinity, constrained optimisation, decision making, Vehicle impact, bridge collision, maximality, Vehicle–pillar collision, linear prevision

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Chicago
Shariatmadar, Keivan, Raluca Andrei, Gert De Cooman, Pieter Baekeland, Erik Quaeghebeur, and Etienne Kerre. 2010. “Optimisation Under Uncertainty Applied to a Bridge Collision Problem.” In Proceedings of ISMA 2010: International Conference on Noise and Vibration Engineering, Including USD 2010, ed. P Sas and B Bergen, 5057–5065. Heverlee, Belgium: KU Leuven. Departement Werktuigkunde.
APA
Shariatmadar, K., Andrei, R., De Cooman, G., Baekeland, P., Quaeghebeur, E., & Kerre, E. (2010). Optimisation under uncertainty applied to a bridge collision problem. In P. Sas & B. Bergen (Eds.), Proceedings of ISMA 2010: international conference on noise and vibration engineering, including USD 2010 (pp. 5057–5065). Presented at the International conference on Noise and Vibration Engineering (ISMA 2010) ; Conference on Uncertainty in Structural Dynamics (USD 2010), Heverlee, Belgium: KU Leuven. Departement Werktuigkunde.
Vancouver
1.
Shariatmadar K, Andrei R, De Cooman G, Baekeland P, Quaeghebeur E, Kerre E. Optimisation under uncertainty applied to a bridge collision problem. In: Sas P, Bergen B, editors. Proceedings of ISMA 2010: international conference on noise and vibration engineering, including USD 2010. Heverlee, Belgium: KU Leuven. Departement Werktuigkunde; 2010. p. 5057–65.
MLA
Shariatmadar, Keivan, Raluca Andrei, Gert De Cooman, et al. “Optimisation Under Uncertainty Applied to a Bridge Collision Problem.” Proceedings of ISMA 2010: International Conference on Noise and Vibration Engineering, Including USD 2010. Ed. P Sas & B Bergen. Heverlee, Belgium: KU Leuven. Departement Werktuigkunde, 2010. 5057–5065. Print.
@inproceedings{973372,
  abstract     = {We consider the problem of modelling the load on a bridge pillar when hit by a vehicle. This load depends on a number of uncertain variables, such as the mass of the vehicle and its speed on impact. The objective of our study is to analyse their effect on the load. More specifically, we are interested in finding the minimum distance of the pillar to the side of the road passing under the bridge such that a given constraint on the load is satisfied in 99\% of impact cases, i.e., such that the probability of satisfying the constraint is 0.99. In addition, we look for solutions to the following optimisation problem: find the distance that minimises a given cost function while still satisfying a given constraint on the load. This optimisation problem under uncertain constraints is not a well-posed problem, so we turn it into a decision problem under uncertainty. For both problems, we consider two typical cases. In the first, so-called precise-probability case, all uncertain variables involved are modelled using probability distributions, and in the second, so-called imprecise-probability case, the uncertainty for at least some of the variables (in casu the mass) is modelled by an interval of possible values, which is a special imprecise-probabilistic model. In the first case, we compute the joint distribution using simple Monte Carlo simulation, and in the second case, we combine Monte Carlo simulation with newly developed techniques in the field of imprecise probabilities. For the optimisation problem with uncertain constraints, this leads to two distinct approaches with different optimality criteria, namely maximality and maximinity, which we discuss and compare.},
  author       = {Shariatmadar, Keivan and Andrei, Raluca and De Cooman, Gert and Baekeland,  Pieter and Quaeghebeur, Erik and Kerre, Etienne},
  booktitle    = {Proceedings of ISMA 2010: international conference on noise and vibration engineering, including USD 2010},
  editor       = {Sas, P and Bergen, B },
  isbn         = {9789073802872},
  keyword      = {linear-vacuous prevision,uncertainty,maximinity,constrained optimisation,decision making,Vehicle impact,bridge collision,maximality,Vehicle--pillar collision,linear prevision},
  language     = {eng},
  location     = {Leuven, Belgium},
  pages        = {5057--5065},
  publisher    = {KU Leuven. Departement Werktuigkunde},
  title        = {Optimisation under uncertainty applied to a bridge collision problem},
  year         = {2010},
}

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