11,883 research outputs found
A local, un-structured, re-meshing technique capable of handling large body-motion in rotating machinery
In this paper we propose a simple, unstructured mesh generation technique that is capable of handling the large and complex blade motion that is encountered in certain rotating machines, such as vertical axis wind turbines or cycloidal propellers. The technique is characterised by localised re-meshing and interpolation, so as to keep the mesh generation cost and interpolation error as low as possible
Detection of spatial pattern through independence of thinned processes
Let N, N' and N'' be point processes such that N' is obtained from N by
homogeneous independent thinning and N''= N- N'. We give a new elementary proof
that N' and N'' are independent if and only if N is a Poisson point process. We
present some applications of this result to test if a homogeneous point process
is a Poisson point process.Comment: 11 pages, one figur
Sectional curvature and Weitzenb\"ock formulae
We establish a new algebraic characterization of sectional curvature bounds
and using only curvature terms in the Weitzenb\"ock
formulae for symmetric -tensors. By introducing a symmetric analogue of the
Kulkarni-Nomizu product, we provide a simple formula for such curvature terms.
We also give an application of the Bochner technique to closed -manifolds
with indefinite intersection form and or , obtaining new
insights into the Hopf Conjecture, without any symmetry assumptions.Comment: LaTeX2e, 25 pages, final version. To appear in Indiana Univ. Math.
Strongly positive curvature
We begin a systematic study of a curvature condition (strongly positive
curvature) which lies strictly between positive curvature operator and positive
sectional curvature, and stems from the work of Thorpe in the 1970s. We prove
that this condition is preserved under Riemannian submersions and Cheeger
deformations, and that most compact homogeneous spaces with positive sectional
curvature satisfy it.Comment: LaTeX2e, 26 page
Fleet Prognosis with Physics-informed Recurrent Neural Networks
Services and warranties of large fleets of engineering assets is a very
profitable business. The success of companies in that area is often related to
predictive maintenance driven by advanced analytics. Therefore, accurate
modeling, as a way to understand how the complex interactions between operating
conditions and component capability define useful life, is key for services
profitability. Unfortunately, building prognosis models for large fleets is a
daunting task as factors such as duty cycle variation, harsh environments,
inadequate maintenance, and problems with mass production can lead to large
discrepancies between designed and observed useful lives. This paper introduces
a novel physics-informed neural network approach to prognosis by extending
recurrent neural networks to cumulative damage models. We propose a new
recurrent neural network cell designed to merge physics-informed and
data-driven layers. With that, engineers and scientists have the chance to use
physics-informed layers to model parts that are well understood (e.g., fatigue
crack growth) and use data-driven layers to model parts that are poorly
characterized (e.g., internal loads). A simple numerical experiment is used to
present the main features of the proposed physics-informed recurrent neural
network for damage accumulation. The test problem consist of predicting fatigue
crack length for a synthetic fleet of airplanes subject to different mission
mixes. The model is trained using full observation inputs (far-field loads) and
very limited observation of outputs (crack length at inspection for only a
portion of the fleet). The results demonstrate that our proposed hybrid
physics-informed recurrent neural network is able to accurately model fatigue
crack growth even when the observed distribution of crack length does not match
with the (unobservable) fleet distribution.Comment: Data and codes (including our implementation for both the multi-layer
perceptron, the stress intensity and Paris law layers, the cumulative damage
cell, as well as python driver scripts) used in this manuscript are publicly
available on GitHub at https://github.com/PML-UCF/pinn. The data and code are
released under the MIT Licens
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