Visibility is a measure of the transparency of the atmosphere, which is an important factor for road, air, and water transportation safety. Recently, features extracted from convolutional neural networks (CNNs) have obtained state-of-the-art results for the estimation of the visibility range for images of foggy weather. However, existing CNN-based approaches have only adopted visible images as observational data. Unlike these previous studies, in this paper, visible–infrared image pairs are used to estimate the visibility range. A novel multimodal deep fusion architecture based on a CNN is then proposed to learn the robust joint features of the two sensor modalities. Our network architecture is composed of two integrated residual network processing streams and one CNN stream, which are connected in parallel. In addition, we construct a visible–infrared multimodal dataset for various fog densities and label the visibility range. We then compare our proposed method with conventional deep-learning-based approaches and analyze the contributions of various observational and classical deep fusion models to the classification of the visibility range. The experimental results demonstrate that both accuracy and robustness can be strongly enhanced using the proposed method, especially for small training datasets.

Based on the ideas of the new information priority principle and the fractional-accumulation generating operator, in this paper we propose a novel weighted fractional GM(1,1) (WFGM(1,1)) prediction model. In the new model, the original sequence is first transformed by using the weighted fractional-accumulation generating operator, which involves two parameters. With special choices of these parameters, the proposed WFGM(1,1) model reduces to the classical GM(1,1) model and the fractional GM(1,1) (FGM(1,1)) model, as well as the new information priority GM(1,1) (NIPGM(1,1)) model studied recently. Stability property of the WFGM(1,1) model is studied in detail. In practice, the quantum particle swarm optimization algorithm is adopted to choose the quasi-optimal parameters for the new model so as to get the best fitting accuracy. Finally, four numerical examples from different practical applications are present. Numerical results show that the new proposed prediction model is very efficient and has both the best fitting accuracy and the best prediction accuracy compared with the GM(1,1) and the FGM(1,1) as well as the NIPGM(1,1) prediction models.

To avoid singular generalized Jacobian matrix and further accelerate the convergence of the generalized Newton (GN) iteration method for solving generalized absolute value equations Ax - B|x| = b, in this paper we propose a new relaxed generalized Newton (RGN) iteration method by introducing a relaxation iteration parameter. The new RGN iteration method involves the well-known GN iteration method and the Picard iteration method as special cases. Theoretical analyses show that the RGN iteration method is well defined and globally linearly convergent under suitable conditions. In addition, a specific sufficient condition is studied when the coefficient matrix A is symmetric positive definite. Finally, two numerical experiments arising from the linear complementarity problems are used to illustrate the effectiveness of the new RGN iteration method.