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Postmaneuver collision probability estimation using sparse polynomial chaos expansions
 Journal of Guidance, Control, and DynamicsUnder Review, Available from:. URL http://ccar.colorado.edu/bajones/files/jones_2014a.pdf
"... This paper describes the use of polynomial chaos expansions to approximate the probability of a collision between two satellites after at least one performs a translation maneuver. Polynomial chaos provides a computationally efficient means to generate an approximate solution to a stochastic differe ..."
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This paper describes the use of polynomial chaos expansions to approximate the probability of a collision between two satellites after at least one performs a translation maneuver. Polynomial chaos provides a computationally efficient means to generate an approximate solution to a stochastic differential equation without introducing any assumptions on the a posteriori distribution. The stochastic solution then allows for orbit state uncertainty propagation. For the maneuvering spacecraft in the presented scenarios, the polynomial chaos expansion is sparse, allowing for the use of compressive sampling methods to improve solution tractability. This paper first demonstrates the use of these techniques for possible intraformation collisions for the Magnetospheric Multiscale mission. The techniques are then applied to a potential collision with debris in low Earth orbit. Results demonstrate that these polynomial chaosbased methods provide a Monte Carlolike estimate of the collision probability, including adjustments for a spacecraft shape model, with only minutes of computation cost required for scenarios with a probability of collision as low as 10−6. A graphics processing unit (GPU) implementation of the polynomial chaos expansion analysis further reduces the computation time for the scenarios presented.
unknown title
, 2012
"... Access time optimization of SRAM memory with statistical yield constraint by T. Doorn, E.J.W. ter Maten, A. di Bucchianico, ..."
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Access time optimization of SRAM memory with statistical yield constraint by T. Doorn, E.J.W. ter Maten, A. di Bucchianico,
Access time optimization of SRAM memory with statistical yield constraint
, 2012
"... Abstract. A product may fail when design parameters are subject to large deviations. To guarantee yield one likes to determine bounds on the parameter range such that the fail probability P fail is small. For Static Random Access Memory (SRAM) characteristics like Static Noise Margin and Read Curre ..."
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Abstract. A product may fail when design parameters are subject to large deviations. To guarantee yield one likes to determine bounds on the parameter range such that the fail probability P fail is small. For Static Random Access Memory (SRAM) characteristics like Static Noise Margin and Read Current, obtained from simulation output, are important in the failure criteria. They also have nonGaussian distributions. With regular Monte Carlo (MC) sampling we can simply determine the fraction of failures when varying parameters. We are interested to efficiently sample for a tiny fail probability P fail ≤ 10 −10 . For a normal distribution this corresponds with parameter variations up to 6.4 times the standard deviation σ . Importance Sampling (IS) allows to tune Monte Carlo sampling to areas of particular interest while correcting the counting of failure events with a correction factor. To estimate the number of samples needed we apply Large Deviations Theory, first to sharply estimate the amount of samples needed for regular MC, and next for IS. With a suitably chosen distribution IS can be orders more efficient than regular MC to determine the fail probability P fail . We apply this to determine the fail probabilities the SRAM characteristics Static Noise Margin and Read Current. Next we accurately and efficiently minimize the access time of an SRAM block, consisting of SRAM cells and a (selecting) Sense Amplifier, while guaranteeing a statistical constraint on the yield target.
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"... Abstract. In this paper we study rare events associated to the solutions of an elliptic partial differential equation with a spatially varying random coefficient. The random coefficient follows the lognormal distribution, which is determined by a Gaussian process. This model is employed to study the ..."
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Abstract. In this paper we study rare events associated to the solutions of an elliptic partial differential equation with a spatially varying random coefficient. The random coefficient follows the lognormal distribution, which is determined by a Gaussian process. This model is employed to study the failure problem of elastic materials in random media in which the failure is characterized by the criterion that the strain field exceeds a high threshold. We propose an efficient importance sampling scheme to compute the small failure probability in the high threshold limit. The change of measure in our scheme is parametrized by two density functions. The efficiency of the importance sampling scheme is validated by numerical examples.