Deep learning-based methods, especially convolutional neural networks, have been developed to automatically process the images of concrete surfaces for crack identification tasks. Although deep learning-based methods claim very high accuracy, they often ignore the complexity of the image collection process. Real-world images are often impacted by complex illumination conditions, shadows, the randomness of crack shapes and sizes, blemishes, and concrete spall. Published literature and available shadow databases are oriented towards images taken in laboratory conditions. In this paper, we explore the complexity of image classification for concrete crack detection in the presence of demanding illumination conditions. Challenges associated with the application of deep learning-based methods for detecting concrete cracks in the presence of shadows are elaborated on in this paper. Novel shadow augmentation techniques are developed to increase the accuracy of automatic detection of concrete cracks.

Detection and assessment of cracks in civil engineering structures such as roads, bridges, dams and pipelines are crucial tasks for maintaining the safety and cost-effectiveness of those concrete structures. With the recent advances in machine learning, the development of ANN- and CNN-based algorithms has become a popular approach for the automated detection and identification of concrete cracks. However, most of the proposed models are trained on images taken in ideal conditions and are only capable of achieving high accuracy when applied to the concrete images devoid of irregular illumination conditions, shadows, shading, blemishes, etc. An overview of challenges related to the automatic detection of concrete cracks in the presence of shadows is presented in this paper. In particular, difficulties associated with the application of deep learning-based methods for the classification of concrete images with shadows are demonstrated. Moreover, the limitations of the shadow removal techniques for the improvement of the crack detection accuracy are discussed.

A control scheme for finite-time stabilization of unstable orbits of the fractional difference logistic map is proposed in this paper. The presented technique is based on isolated perturbation impulses used to correct the evolution of the map’s trajectory after it deviates too far from the neighborhood of the unstable orbit, and does not require any feedback control loops. The magnitude of the control impulses is determined by means of H-rank algorithm, which helps to reveal the pseudo-manifold of non-asymptotic convergence of the fractional difference logistic map. Numerical experiments are used to illustrate the effectiveness and the feasibility of the proposed approach, which is applicable beyond the studied fractional difference logistic map.

Analytical solutions to the fractional Riccati equation are considered in this paper. Solutions to fractional differential equations are expressed in the form of fractional power series in the Caputo algebra. It is demonstrated that solutions to higher-order Riccati fractional equations inherit some solutions from lower-order Riccati equations under special initial conditions. Such nested and fractal-like structure of solutions is investigated by means of analytical fractional differentiation operator techniques and computational experiments.

An operator-based scheme for the numerical integration of fractional differential equations is presented in this paper. The generalized differential operator is used to construct the analytic solution to the corresponding characteristic ordinary differential equation in the form of an infinite power series. The approximate numerical solution is constructed by truncating the power series, and by changing the point of the expansion. The developed adaptive integration step selection strategy is based on the controlled error of approximation induced by the truncation. Computational experiments are used to demonstrate the efficacy of the proposed scheme.