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In this paper, a fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media is derived. The determined imbibition height and imbibition mass of capillary rise are in satisfying agreement with the existing models reported in the literature. It is found that the imbibition height and imbibition mass of capillary decreases with increasing relative roughness. Besides, it is observed that the equilibrium time in a single tortuous capillary with roughened surfaces decreases with an increase in relative roughness. In addition, it is seen that the imbibition height and imbibition mass of capillary rise increases with imbibition time. With the proposed fractal model, the physical mechanisms of capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media are better elucidated. One advantage of our fractal analytical model is that it contains no empirical constant, which is usually required in previous models.

In this paper, a new particle swarm optimization particle filter (NPSO-PF) algorithm is proposed, which is called particle cluster optimization particle filter algorithm with mutation operator, and is used for real-time filtering and noise reduction of nonlinear vibration signals. Because of its introduction of mutation operator, this algorithm overcomes the problem where by particle swarm optimization (PSO) algorithm easily falls into local optimal value, with a low calculation accuracy. At the same time, the distribution and diversity of particles in the sampling process are improved through the mutation operation. The defect of particle filter (PF) algorithm where the particles are poor and the utilization rate is not high is also solved. The mutation control function makes the particle set optimization process happen in the early and late stages, and improves the convergence speed of the particle set, which greatly reduces the running time of the whole algorithm. Simulation experiments show that compared with PF and PSO-PF algorithms, the proposed NPSO-PF algorithm has lower root mean square error, shorter running time, higher signal-to-noise ratio and more stable filtering performance. It is proved that the algorithm is suitable for real-time filtering and noise reduction processing of nonlinear signals.

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