• Journal of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.255-271
• /
• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
• /
• v.10 no.5
• /
• pp.462-468
• /
• 2017

In this paper IoT/WSN(Internet of Things/Wireless Sensor Network) has been modeled with a random geometric graph. And a performance of the decentralized code for the efficient storage of data which is generated from WSN has been analyzed. WSN with n=100 or 200 has been modeled as a random geometric graph and has been simulated for their performance analysis. When the number of the total nodes of WSN is n=100 or 200, the successful decoding probability as decoding ratio ${\eta}$ depends more on the number of source nodes k rather than the number of nodes n. Especially, from the simulation results we can see that the successful decoding rate depends greatly on k value than n value and the successful decoding rate was above 70% when $${\eta}{\leq_-}2.0$$. We showed that the number of operations of BP(belief propagation) decoding scheme increased exponentially with k value from the simulation of the number of operations as a ${\eta}$. This is probably because the length of the LT code becomes longer as the number of source nodes increases and thus the decoding computation amount increases greatly.

• Steel and Composite Structures
• /
• v.46 no.6
• /
• pp.731-744
• /
• 2023

Vehicle load information is an important role in operating and ensuring the structural health of cable-stayed bridges. In this regard, an efficient and economic method is proposed for vehicle load detection based on the observed cable tension and vehicle position using a graph neural network (GNN). Datasets are first generated using the practical advanced analysis program (PAAP), a robust program for modeling and considering both geometric and material nonlinearities of bridge structures subjected to vehicle load with low computational costs. With the superiority of GNN, the proposed model is demonstrated to precisely capture complex nonlinear correlations between the input features and vehicle load in the output. Four popular machine learning methods including artificial neural network (ANN), decision tree (DT), random forest (RF), and support vector machines (SVM) are refereed in a comparison. A case study of a cable-stayed bridge with the typical truck is considered to evaluate the model's performance. The results demonstrate that the GNN-based model provides high accuracy and efficiency in prediction with satisfactory correlation coefficients, efficient determination values, and very small errors; and is a novel approach for vehicle load detection with the input data of the existing monitoring system.