Based on the analysis of the error backpropagation algorithm, we propose an innovative training criterion of depth neural network for maximum interval minimum classification error. At the same time, the cross entropy and M 3 CE are analyzed and combined to obtain better results. Finally, we tested our proposed M3 CE-CEc on two deep learning standard databases, MNIST and CIFAR-10. The experimental results show that M 3 CE can enhance the cross-entropy, and it is an effective supplement to the cross-entropy criterion. M3 CE-CEc has obtained good results in both databases.

A new type of radially sandwiched piezoelectric short cylindrical transducer is developed and its radial vibration is studied. The transducer is composed of a solid metal disk, a radially polarized piezoelectric ceramic short tube and a metal tube. The radial vibrations of the solid metal disk, the radially polarized piezoelectric tube and the metal tube are analyzed and their electromechanical equivalent circuits are introduced. Based on the mechanical boundary conditions among the metal disk, the piezoelectric tube and the metal tube, a three-port electromechanical equivalent circuit for the radially sandwiched transducer is obtained and the frequency equation is given. The theoretical relationship of the resonance and anti-resonance frequencies and the effective electromechanical coupling coefficient with the geometrical dimensions is analyzed. The radial vibration of the sandwiched transducer is simulated by using two different numerical methods. It is shown that the analytical resonance and anti-resonance frequencies are in good agreement with the numerically simulated results. The transducer is expected to be used in piezoelectric resonators, actuators and ultrasonic radiators in ultrasonic and underwater sound applications.

This paper presents a detailed study of the high-order superdirectivity of circular sensor arrays, which is aimed at completing the authors' recently proposed analytical superdirectivity model. From the limit expression of the maximum directivity factor, it is shown that the circular arrays possess good potential for directivity improvement. It is found that the sensitivity function used as a robustness measurement can also be accurately decomposed into a series of closed-form sensitivity functions of eigenbeams, similar to the optimal beampattern and its corresponding directivity factor. Moreover, the performance of eigenbeams can be regarded as an indicator of error sensitivity, and the robustness constraint parameters can be estimated easily. Two specific approaches are proposed for obtaining robust superdirectivity on the basis of robustness analyses, and their performance is demonstrated experimentally.

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In this paper, the original discrete unified gas kinetic scheme (DUGKS) is extended to arbitrary Lagrangian-Eulerian (ALE) framework for simulating the low-speed continuum and rarefied flows with moving boundaries. For ALE method, the mesh moving velocity is introduced into the Boltzmann-BGK equation. The remapping-free scheme is adopted to develop the present ALE-type DUGKS, which avoids the complex rezoning and remapping process in traditional ALE method. As in some application areas, the large discretization errors will be introduced into the simulation if the geometric conservation is not guaranteed. Three compliant approaches of the geometric conservation law (GCL) are discussed and a uniform flow test case is conducted to validate these schemes. To illustrate the performance of present ALE-type DUGKS, four test cases are carried out. Two of them are the continuum flow cases, which are the flows around the oscillating circular cylinder and the pitching NACA0012 airfoil, respectively. Others are the rarefied flow cases, one is the moving piston driven by the rarefied gas, another is the flow caused by the plate oscillating in its normal direction. The results of all test cases are in good agreement with the other numerical and/or experimental results, demonstrating the capability of present ALE-type DUGKS to cope with the moving boundary problems at