Estimating the all-terminal network reliability by using artificial neural networks (ANNs) has emerged as a promissory alternative to classical exact NP-hard algorithms. Approaches based on traditional ANNs have usually considered the network reliability upper bound as part of the inputs, which implies additional time-consuming calculations during both training and testing phases. This paper proposes the use of Convolutional Neural Networks (CNNs), without the reliability upper-bound as an input, to address the all-terminal network reliability estimation problem. The present study introduces a multidimensional matrix format to embed the topological and link reliability information of networks. The unique contribution of this article is the method to capture the topology of a network in terms of its adjacency matrix, link reliability, and topological attributes providing a novel use of CNN beyond image classification. Since CNNs have been successful for image classification, appropriate modifications are needed and introduced to use them in the estimation of network reliability. A regression output layer is proposed, preceded by a sigmoid layer to achieve predictions within the range of reliability characteristic, a feature that some previous ANN-based works lack. Several training parameters together with a filter multiplier (CNN architecture parameter) were investigated. The actual values and the ones predicted with the best trained CNN were compared in the light of RMSE (0.04406) and p-value (0.3) showing non-significant difference. This study provides evidence supporting the hypothesis that the network reliability can be estimated by CNNs from its topology and link reliability information, embedded as an image-like multidimensional matrix. Another important result of the proposed approach is the significant reduction in computational time. An average of 1.18 ms/network was achieved by the CNN, whereas backtracking exact algorithm took around 500 s/network.

通过使用人工神经网络（ANN）估算全终端网络的可靠性已成为传统精确NP硬算法的一种替代方案。基于传统人工神经网络的方法通常将网络可靠性上限作为输入的一部分，这意味着在培训和测试阶段都需要进行更多耗时的计算。本文提出在没有可靠性上限作为输入的情况下使用卷积神经网络（CNN）解决全终端网络可靠性估计问题。本研究引入了多维矩阵格式来嵌入网络的拓扑和链接可靠性信息。本文的独特贡献是根据网络的邻接矩阵，链路可靠性，拓扑属性提供了CNN在图像分类之外的新颖用途。由于CNN已成功用于图像分类，因此需要进行适当的修改并将其引入网络可靠性评估中。提出了一个回归输出层，其后是一个S型层，以实现可靠性特征范围内的预测，这是以前基于ANN的某些工作所缺乏的功能。研究了几个训练参数以及一个滤波器乘数（CNN体系结构参数）。根据RMSE（0.04406）将实际值和训练有素的CNN预测的值进行比较 需要进行适当的修改并将其引入以用于估计网络可靠性。提出了一个回归输出层，其后是一个S型层，以实现可靠性特征范围内的预测，这是以前基于ANN的某些工作所缺乏的功能。研究了几个训练参数以及一个滤波器乘数（CNN体系结构参数）。根据RMSE（0.04406）将实际值和训练有素的CNN预测的值进行比较 需要进行适当的修改并将其引入以用于估计网络可靠性。提出了一个回归输出层，其后是一个S型层，以实现可靠性特征范围内的预测，这是以前基于ANN的某些工作所缺乏的功能。研究了几个训练参数以及一个滤波器乘数（CNN体系结构参数）。根据RMSE（0.04406）将实际值和训练有素的CNN预测的值进行比较p值（0.3）表示不显着差异。这项研究提供了支持以下假设的证据，即CNN可以根据其拓扑结构和链接可靠性信息（以像图像一样的多维矩阵形式嵌入）来估计网络可靠性。所提出的方法的另一个重要结果是大大减少了计算时间。CNN的平均速度为1.18 ms /网络，而回溯精确算法大约需要500 s /网络。