Probabilistic design | EPFL Graph Search

Probabilistic design is a discipline within engineering design. It deals primarily with the consideration of the effects of random variability upon the performance of an engineering system during the design phase. Typically, these effects are related to quality and reliability. Thus, probabilistic design is a tool that is mostly used in areas that are concerned with quality and reliability. For example, product design, quality control, systems engineering, machine design, civil engineering (particularly useful in limit state design) and manufacturing. It differs from the classical approach to design by assuming a small probability of failure instead of using the safety factor. Designer's perspective When using a probabilistic approach to design, the designer no longer thinks of each variable as a single value or number. Instead, each variable is viewed as a probability distribution. From this perspective, probabilistic design predicts the flow of variability (or distribu

Vieillissement et fiabilité des parcs de poteaux bois des réseaux de lignes aériennes

Yann Benoit

The reliability of new overhead electric and telecommunication lines depends principally on the quality of their support structures. These structures are generally made of wood, metal or concrete. The complexity of a natural substance such as wood requires a thorough analysis of the various factors that influence its overall quality. In the case of wood poles, such factors include initial forest growth pattern, the species of wood and its preservative treatment, ageing characteristics, and its various mechanical defects such as knots, cracks etc. The accumulation of knowledge on the effect of the various variables that contribute to the overall quality of a wood support structure permits an optimum use of such a resource. For example, less variability and higher strength of wood support structures permits optimum loading and spacing between structures, thus reducing the number needed in a specific length of an overhead line. If one assumes that in Western Europe 1 wood pole is employed for every 2 inhabitants, and that this proportion increases in less densely populated countries such as the US and Scandinavia, the economics of optimum use of wood as a resource soon become apparent. In less developed countries, the proportions and the economics vary depending on the natural resources such as wood that they employ. The goal of this research is to establish, thanks to non destructive evaluations, a general ageing probabilistic law of the wooden pole based on two distinguished laws: one on the new pole in studying the influence of a grading of the bad elements based on a normal law: "left-truncation of a normal distribution", point 1; and another one based on the in-field wooden pole in exploiting the different parameters such as: the age of the pole, its chemical treatment, its species, its knots etc. in order to define the pole's damage law, point 2. Statistical distribution law of the new wooden pole after grading by non destructive sorting (ultrasounds) of the high mechanical performances supports: This new distribution law is a Gaussian law or evolves to a Log or Weibull's law with 3 parameters according to the inspected species. This grading allows a revalorization of the properties of the new poles and of the design values while guaranteeing an index of reliability required by the design standards, or in improving directly this nominal reliability (economic gain and reliability gain). Statistical distribution law of an aged in-field population (20-50 years old) approached by a bi-modal law which depends on: The distribution law of the new component (see point 1) and its minimal extreme law, which is asymmetrical, for an observation on 50 years. The statistical distribution at the time t of the residual mechanical performances of a group of supports making a local net, evaluated by non destructive methods. The non destructive evaluation is based on the measurements of physical variables (density, biological moisture content) and some descriptive variables from natural origins (diameter, knots, cracks...) and from accidental origins (diameter reduction, lightning cracks...). The statistical distribution at the time t is then obtained on the basis of a model of multivariate non destructive evaluation, generalized to the whole of species and treatments. This model is the other concrete goal to reach in this thesis. As a conclusion, the research demonstrates the influence and the interaction of the new pole grading (distribution at t0) on the modelisation of the distribution at ti (multivariate non destructive model). The data used for the mentioned modelisations come from a significant international database with a large amount of inspected wood poles and with studied cases. This database is the synthesis of about 15 years of research and development leaded by IBOIS-EPFL and its international partners. The probabilistic approaches are then validated by a huge database allowing thus to be directly exploitable. On this basis, all the standards dealing with the new poles and dealing with the controls and maintenances of a wooden pole networks, could be re-examined for a double gain: Concerning the economy: by increasing the capacity of the new poles profiting of an objective quality assurance, and by increasing the life time of the in-field pole, in knowing how to purge only the ones which are under the critical threshold of damage Concerning the reliability: by increasing the reliability of the network from the stage "new pole", by eliminating the weakest components, and by maintaining this reliability during all the life time of the network thanks to a cyclic preventive maintenance (every 5 to 8 years) and the replacement of only the weakened poles.

EPFL2004

Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Assyr Abdulle, Giacomo Garegnani

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, we show that a probability measure over the numerical solution of ODEs can be obtained by introducing suitable random time-steps in a classical time integrator. This intrinsic randomization allows for the conservation of geometric properties of the underlying deterministic integrator such as mass conservation, symplecticity or conservation of first integrals. Weak and mean-square convergence analysis are derived. We also analyse the convergence of the Monte Carlo estimator for the proposed random time step method and show that the measure obtained with repeated sampling converges in the mean-square sense independently of the number of samples. Numerical examples including chaotic Hamiltonian systems, chemical reactions and Bayesian inferential problems illustrate the accuracy, robustness and versatility of our probabilistic numerical method.

2020

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Assyr Abdulle, Giacomo Garegnani

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, we show that a probability measure over the numerical solution of ODEs can be obtained by introducing suitable random time-steps in a classical time integrator. This intrinsic randomization allows for the conservation of geometric properties of the underlying deterministic integrator such as mass conservation, conservation of first integrals, symplecticity and conservation of Hamiltonians over long time. Weak and mean-square convergence analysis are derived. We also analyse the convergence of the Monte Carlo estimator for the proposed random time step method and show that the measure obtained with repeated sampling converges in mean-square sense independently of the number of samples. Numerical examples including chaotic Hamiltonian systems, chemical reactions and Bayesian inferential problems illustrate the accuracy, robustness and versatility of our probabilistic numerical method.

MATHICSE2018