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This paper addresses the current existence of attribute reduction algorithms for incomplete hybrid decision-making systems, including low attribute reduction efficiency, low classification accuracy and lack of consideration of unlabeled data types. To address these issues, this paper first redefines the weakly labeled relative neighborhood discernibility degree and develops a non-dynamic attribute reduction algorithm. In addition, this paper proposes an incremental update mechanism for weakly tagged relative neighborhood discernibility degree and introduces a new dynamic attribute reduction algorithm for increasing the set of objects based on it. Meanwhile, this paper also compares and analyses the improved algorithm proposed in this study with two existing attribute reduction algorithms using 8 data sets in the UCI database. The results show that the dynamic attribute reduction algorithm proposed in this paper achieves higher attribute reduction efficiency and classification accuracy, which further validates the effectiveness of the algorithm proposed in this paper. [ABSTRACT FROM AUTHOR]

Analytical and numerical investigations are carried out for harbor oscillations on a piecewise bottom of two different slopes. With the shallow water approximation, the longitudinal and transverse oscillations are analyzed by coupling the solutions on each segment of the bottom with the coupling conditions at the point of inflection in ignoring the nonlinear interactions between them. The longitudinal ones are the combinations of the Bessel functions of the first and second kinds, and the transverse ones are expressed with Kummer's equations. As the transverse oscillations trapped within the harbor are typically standing edge waves, their dispersion relationship is also derived for the two-slope-piecewise bottom. With the analytical predictions of the oscillation behaviors and based on Boussinesq equations, a range of numerical tests are made for the oscillations induced by seafloor motions on this type of piecewise bottom. Different combinations of the two slopes of the bottom are firstly tested and the numerical eigenfrequencies and wave profiles are compared with analytical ones. The transverse oscillations are revealed to be sensitive to the positions of the seafloor movements, and the importance of the position of the seafloor motions is manifested in their relative positions against the nodal lines and anti-nodal lines of the transverse modes. Although the longitudinal oscillations generated by seafloor motions of harbor width may not reach a steady state without forcing terms at the entrance, some patterns of several low-mode ones occur and are also sensitive to the position of the moveable seafloor. Wavelet spectra are used to analyze their evolutions and comparisons are made with theoretical predictions for the three principle longitudinal modes. [ABSTRACT FROM AUTHOR]

Based on the linear shallow water approximation, longitudinal and transverse oscillations in a rectangular harbor with a parabolic bottom are analyzed. The longitudinal ones are combinations of the Legendre functions of the first and second kinds and the transverse ones are expressed with modified Bessel equations. Analytic results for longitudinal oscillations show that the augmentation of rapidity of variation of the water depth shifts the resonant wave frequencies to larger values and slightly changes the positions of the nodes for the resonant modes. For the transverse oscillations trapped within the harbor which are typically standing edge waves, the dispersion relationship is derived and the spatial structures of the first four modes are presented. The solutions illustrate that all the trapped modes are affected by the varying water depth parameters, especially for the higher modes whose profiles extend farther and the distribution of the energy of transverse oscillations is influenced by the rapidity of variation of the bottom within the harbor. [ABSTRACT FROM AUTHOR]

Numerical simulation in Computational Fluid Dynamics mainly relies on discretizing the governing equations in time or space to obtain numerical solutions, which is expensive and time-consuming. Deep learning significantly reduces the computational cost due to its great nonlinear curve fitting capability, however, the data-driven models is agnostic to latent relationships between input and output. In this paper, a novel deep learning named Navier–Stokes Generative Adversarial Network integrated with physical information is proposed. The Navier–Stokes Equation is added to the loss function of the generator in the form of residuals, which means physics loss in this paper. Then, the proposed model is trained in the framework of generative adversarial network. Experimental results show that proposed model significantly outperform similar models, mean absolute error are decreased by 62.29, 78.42 and 78.61% on pressure and velocity components. What’s more, effectiveness of introducing physics loss is also verified. [ABSTRACT FROM AUTHOR]