An innovative numerical procedure for solving the viscoelastic arch problem based on variable fractional rheological models, directly in time domain, is proposed and investigated. First, the nonlinear integral‐differential governing equation is established according to the variable fractional constitutive relation and geometrical relationship. Second, the nonlinear integral‐differential governing equation is transformed into algebraic equations and solved by using the shifted Legendre polynomials. Furthermore, the accuracy and effectiveness of the algorithm are verified according to the mathematical example. A small value of the absolute error between numerical and accurate solution is obtained. Finally, the dynamic analysis of viscoelastic arch is investigated to determine the displacement at different times and positions. The displacement of the viscoelastic arch is compared under various loading (uniformly distributed load and linear load). The displacement of the viscoelastic arch of different materials under the same load conditions is also investigated. The results in the paper show the efficiency of the proposed numerical algorithm in the dynamical analysis of the viscoelastic arch.

Magnetic resonance (MR) images have distinctive advantages in radiation treatment (RT) planning due to their superior, anatomic and functional information compared with computed tomography (CT). For the RT dose calculation, MR images cannot be directly used because of the lack of electron density information. To address this issue, we propose to generate pseudo-CT (pCT) in terms of multiple matching Dixon MR images to support MR-only RT, particularly in the challenging body section of the abdomen. To this end, we design the dedicated multichannel residual conditional generative adversarial network (MCRCGAN). The significance of our efforts is threefold: 1) The MCRCGAN organically incorporates multiple theories and techniques, such as multichannel residual network (ResNet) and conditional generative adversarial network (cGAN), which facilitate its more authentic pCT generation than many existing methods. 2) The usage of residual modules effectively deepens the network without performance degradation, and the multichannel ResNet helps to simultaneously capture the substance of images, as extensively as possible, which is implicitly contained in the multiple different MR images of the same subject. 3) Due to the designed dedicated network structure, the MCRCGAN is capable of generating satisfactory pCTs under the condition of limited training data as well as prompt prediction response. Experimental studies on ten patients' paired MR-CT images demonstrate the effectiveness of our proposed MCRCGAN model on both the pCT generation quality and the performance stability. INDEX TERMS Generative adversarial network (GAN), pseudo-CT, abdomen, deep learning.

The condition monitoring of rotating machinery is always a focus of intelligent fault diagnosis. In view of the traditional methods’ excessive dependence on prior knowledge to manually extract features, their limited capacity to learn complex nonlinear relations in fault signals and the mixing of the collected signals with environmental noise in the course of the work of rotating machines, this article proposes a novel approach for detecting the bearing fault, which is based on deep learning. To effectively detect, locate, and identify faults in rolling bearings, a stacked noise reduction autoencoder is utilized for abstracting characteristic from the original vibration of signals, and then, the characteristic is provided as input for backpropagation (BP) network classifier. The results output by this classifier represent different fault categories. Experimental results obtained on rolling bearing datasets show that this method can be used to effectively diagnose bearing faults based on original time-domain signals.

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In this paper, a fractional viscoelastic model is proposed to describe the physical behaviour of polymeric material. The material parameters in the model are characterized by the experimental data obtained in the dynamical mechanical analysis. The proposed model is integrated into the fractional governing equation of polymethyl methacrylate (PMMA) above its glass transition temperature. The numerical algorithm based on the shifted Legendre polynomials is retained to solve the fractional governing equations in the time-domain. The accuracy and effectiveness of the algorithm are verified according to the mathematical examples. The advantage of this method is that Laplace transform and the inverse Laplace transform commonly used in fractional calculus are avoided. The dynamical response of the viscoelastic PMMA beam is determined with several loading conditions (uniformly distributed load and harmonic load). The effects of the loading condition and the temperature on the dynamic response of the beam are investigated in the results. The proposed approach shows great potentials for the highprecision calculation in solving the fractional equations in the science and engineering.