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Dislocations first appeared as an abstract mathematical concept. In the late 19th century, Italian mathematician Vito Volterra examined mathematical properties of singularities produced by cutting and shifting matter in a continuous solid body [1]. As happened to some other mathematical concepts, dislocations could have remained a curious product of mathematical imagination known only to a handful of devoted mathematicians. In 1934, however, three scientists, Taylor, Polanyi and Orowan, independently proposed that dislocations may be responsible for a crystal’s ability to deform plastically [2, 3, 4]. While successfully explaining most of the puzzling phenomenology of crystal plasticity, crystal dislocations still remained mostly a beautiful hypothesis until the late 1950s when first sightings of them were reported in transmission electron microscopy (TEM) experiments [5]. Since then, the ubiquity and importance of dislocations for crystal plasticity and numerous other aspects of material behavior have been regarded as firmly established as, say, the role of DNA in promulgating life. Dislocations define a great many properties of crystalline materials. In addition to a crystal’s ability to yield and flow under stress, dislocations also control other mechanical behaviors such as creep and fatigue, ductility and brittleness, indentation hardness and friction. Furthermore, dislocations affect how a crystal grows from solution, how a nuclear reactor wall material is damaged by radiation, and whether or not a semiconductor chip in an electronic device will function properly. It can take an entire book just to describe the various roles dislocations play in materials behavior. However, the focus of this book is on the various computational models that have been developed to study dislocations. This chapter is an introduction to the basics of dislocations, setting the stage for subsequent discussions of computational models and associated numerical issues. Like any other crystal defect, dislocations are best defined with respect to the host crystal structure. We begin our discussion by presenting in Section 1.1 the basic elements and common terminology used to describe perfect crystal structures. Section 1.2 introduces the dislocation as a defect in the crystal lattice and discusses some of its essential properties. Section 1.3 discusses forces on dislocations and atomistic mechanisms for dislocation motion.

To improve the fault diagnosis performance for rotating machinery, an efficient, noise-resistant end-to-end deep learning (DL) algorithm is proposed based on the advantages of the wavelet packet transform in vibration signal processing (the capability to extract multiscale information and more spectral distribution features) and deep convolutional neural networks (good classification performance, data-driven design and high transfer-learning ability). First, a vibration signal is subjected to pyramid wavelet packet decomposition, and each sub-band coefficient is used as the input for each channel of a deep convolutional network (DCN). Then, based on the lightweight modeling requirements and techniques, a new DCN structure is designed for the fault diagnosis. The proposed algorithm is compared with the support vector machine algorithm and the published DL algorithms based on a bearing dataset produced by Case Western Reserve University. The experimental results show that the proposed algorithm is superior to the existing algorithms in terms of accuracy, memory space, computational complexity, noise resistance, and transfer performance, producing good results.

This paper proposes an efficient and noise-insensitive end-to-end lightweight deep learning method. The method synthesizes the characteristics of a frequency domain transform and a deep convolutional neural network. The former can extract multiscale information in vibration signal processing and the latter has a good classification performance, data-driven, and high transfer-learning ability. A vibration signal is decomposed into a pyramidal wavelet packet, and each sub-band coefficient is used as an input of a channel in the deep network. A deep residual convolutional network based on a separable convolution and concatenated rectified linear unit (CReLU) lightweight convolution technology is used for fault diagnosis. The proposed algorithm is compared with related deep learning algorithms using two bearing datasets produced by Case Western Reserve University (CWRU) and the Center for Intelligent Maintenance Systems (IMS), University of Cincinnati. Compared with the existing algorithms, the experimental results show that the comprehensive performance of the algorithm proposed in this paper is ''small, light, and fast,'' and satisfactory diagnostic results are obtained in the fault diagnosis of rotating machinery. INDEX TERMS Residual convolutional neural networks, depthwise separable convolutions, deep learning, fault diagnosis, wavelet packet transform.

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