• 대한수학회지
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• 제60권2호
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• pp.255-271
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• 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.

• 한국정보전자통신기술학회논문지
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• 제10권5호
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• pp.462-468
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• 2017

본 논문에서는 IoT/WSN을 랜덤 기하 그래프를 이용하여 모델링하고 WSN에서 발생되는 데이터를 효율적으로 저장하기 위해 사용되는 지역 부호의 성능을 고찰하였다.. 노드 수가 n=100, 200인 무선 센서 네트워크를 랜덤 기하 그래프로 모델링하여 분산화된 저장 코드의 복호 성능을 시뮬레이션을 통해 분석하였다. 네트워크의 총 노드 수가 n=100일 때와 200일 때 복호율 ${\eta}$에 따른 복호 성공률은 노드 수 n보다는 소스 노드 수 k값에 따라 좌우됨을 알 수 있었다. 특히 n 값에 관계없이 $${\eta}{\leq_-}2.0$$일 때 복호 성공 확률은 70%를 상회함을 알 수 있었다. 복호 율 ${\eta}$에 따른 복호 연산 량을 살펴본 바, BP 복호 방식의 복호 연산 량은 소스 노드 수 k 값이 증가함에 따라 기하급수적으로 증가함을 알 수 있었다. 이는 소스 노드의 수가 증가할수록 LT 부호의 길이가 길어지고 이에 따라 복호 연산량이 크게 증가하는데 원인이 있는 것으로 생각된다.

• Steel and Composite Structures
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• 제46권6호
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• pp.731-744
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• 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.