On an application of graph neural networks in population based SHM
- URL: http://arxiv.org/abs/2203.01646v1
- Date: Thu, 3 Mar 2022 11:11:57 GMT
- Title: On an application of graph neural networks in population based SHM
- Authors: G. Tsialiamanis, C. Mylonas, E. Chatzi, D.J. Wagg, N. Dervilis, K.
Worden
- Abstract summary: The aim of this paper is to predict the first natural frequency of trusses of different sizes, across different environmental temperatures and having different bar member types.
The accuracy of the regression is satisfactory even in structures with higher number of nodes and members than those used to train it.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Attempts have been made recently in the field of population-based structural
health monitoring (PBSHM), to transfer knowledge between SHM models of
different structures. The attempts have been focussed on homogeneous and
heterogeneous populations. A more general approach to transferring knowledge
between structures, is by considering all plausible structures as points on a
multidimensional base manifold and building a fibre bundle. The idea is quite
powerful, since, a mapping between points in the base manifold and their
fibres, the potential states of any arbitrary structure, can be learnt. A
smaller scale problem, but still useful, is that of learning a specific point
of every fibre, i.e. that corresponding to the undamaged state of structures
within a population. Under the framework of PBSHM, a data-driven approach to
the aforementioned problem is developed. Structures are converted into graphs
and inference is attempted within a population, using a graph neural network
(GNN) algorithm. The algorithm solves a major problem existing in such
applications. Structures comprise different sizes and are defined as abstract
objects, thus attempting to perform inference within a heterogeneous population
is not trivial. The proposed approach is tested in a simulated population of
trusses. The goal of the application is to predict the first natural frequency
of trusses of different sizes, across different environmental temperatures and
having different bar member types. After training the GNN using part of the
total population, it was tested on trusses that were not included in the
training dataset. Results show that the accuracy of the regression is
satisfactory even in structures with higher number of nodes and members than
those used to train it.
Related papers
- On the topology and geometry of population-based SHM [0.0]
Population-Based Structural Health Monitoring aims to leverage information across populations of structures.
The discipline of transfer learning provides the mechanism for this capability.
New ideas motivate a new geometrical mechanism for transfer learning in data are transported from one fibre to an adjacent one.
arXiv Detail & Related papers (2024-09-30T10:45:15Z) - Generalization of Geometric Graph Neural Networks [84.01980526069075]
We study the generalization capabilities of geometric graph neural networks (GNNs)
We prove a generalization gap between the optimal empirical risk and the optimal statistical risk of this GNN.
The most important observation is that the generalization capability can be realized with one large graph instead of being limited to the size of the graph as in previous results.
arXiv Detail & Related papers (2024-09-08T18:55:57Z) - The Heterophilic Snowflake Hypothesis: Training and Empowering GNNs for Heterophilic Graphs [59.03660013787925]
We introduce the Heterophily Snowflake Hypothesis and provide an effective solution to guide and facilitate research on heterophilic graphs.
Our observations show that our framework acts as a versatile operator for diverse tasks.
It can be integrated into various GNN frameworks, boosting performance in-depth and offering an explainable approach to choosing the optimal network depth.
arXiv Detail & Related papers (2024-06-18T12:16:00Z) - Coordinated Multi-Neighborhood Learning on a Directed Acyclic Graph [6.727984016678534]
Learning the structure of causal directed acyclic graphs (DAGs) is useful in many areas of machine learning and artificial intelligence.
It is challenging to obtain good empirical and theoretical results without strong and often restrictive assumptions.
This paper develops a new constraint-based method for estimating the local structure around multiple user-specified target nodes.
arXiv Detail & Related papers (2024-05-24T08:49:43Z) - LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering [59.89626219328127]
Graph clustering is a fundamental problem in machine learning.
Deep learning methods achieve the state-of-the-art results in recent years, but they still cannot work without predefined cluster numbers.
We propose to address this problem from a fresh perspective of graph information theory.
arXiv Detail & Related papers (2024-05-20T05:46:41Z) - NodeFormer: A Scalable Graph Structure Learning Transformer for Node
Classification [70.51126383984555]
We introduce a novel all-pair message passing scheme for efficiently propagating node signals between arbitrary nodes.
The efficient computation is enabled by a kernerlized Gumbel-Softmax operator.
Experiments demonstrate the promising efficacy of the method in various tasks including node classification on graphs.
arXiv Detail & Related papers (2023-06-14T09:21:15Z) - Hybrid Bayesian network discovery with latent variables by scoring
multiple interventions [5.994412766684843]
We present the hybrid mFGS-BS (majority rule and Fast Greedy equivalence Search with Bayesian Scoring) algorithm for structure learning from discrete data.
The algorithm assumes causal insufficiency in the presence of latent variables and produces a Partial Ancestral Graph (PAG)
Experimental results show that mFGS-BS improves structure learning accuracy relative to the state-of-the-art and it is computationally efficient.
arXiv Detail & Related papers (2021-12-20T14:54:41Z) - Scaling Structured Inference with Randomization [64.18063627155128]
We propose a family of dynamic programming (RDP) randomized for scaling structured models to tens of thousands of latent states.
Our method is widely applicable to classical DP-based inference.
It is also compatible with automatic differentiation so can be integrated with neural networks seamlessly.
arXiv Detail & Related papers (2021-12-07T11:26:41Z) - The Separation Capacity of Random Neural Networks [78.25060223808936]
We show that a sufficiently large two-layer ReLU-network with standard Gaussian weights and uniformly distributed biases can solve this problem with high probability.
We quantify the relevant structure of the data in terms of a novel notion of mutual complexity.
arXiv Detail & Related papers (2021-07-31T10:25:26Z) - Multivariate Time Series Forecasting with Transfer Entropy Graph [5.179058210068871]
We propose a novel end-to-end deep learning model, termed graph neural network with Neural Granger Causality (CauGNN)
Each variable is regarded as a graph node, and each edge represents the casual relationship between variables.
Three benchmark datasets from the real world are used to evaluate the proposed CauGNN.
arXiv Detail & Related papers (2020-05-03T20:51:00Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.