The rank ordering of samples is widely used in robust nonlinear signal processing. Recent advances in nonlinear filtering algorithms have focused on combining spatial and rank (SR) order information into the filtering process to allow spatial correlations to be exploited while retaining the robust characteristics of strict rank order methods. Further generalization can be achieved by replacing the crisp, or binary, SR information utilized by most methods with more general fuzzy SR information. Indeed, by exploiting fuzzy methodologies real valued SR orderings can be defined that not only relate the spatial and rank orderings of samples, but also includes information on sample spread. This paper utilizes this approach to define fuzzy ranking and fuzzy order statistics. Properties of these concepts are discussed and several previously defined filters are generalized by including fuzzy concepts. Specifically, the fuzzy median, fuzzy rank conditioned rank selection, and fuzzy weighted median filters are defined. Optimization of the parameters for these filters are discussed. Simulation results are presented to show the advantages of these fuzzy filters over their crisp counterparts.

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To study the effects of sample width and sidewalls on downward flame spread over extruded polystyrene (XPS) slabs, a series of laboratory-scale experiments were conducted. Flame shape, flame spread rate, mass loss rate and temperature were recorded. For XPS without sidewalls, the average maximum flame height (H) and average flame area per unit of width (A/w) rise linearly with an increase in sample width (w) and mass loss rate per unit of width. When sidewalls are absent, flame spread rate first drops and then rises with an increase in width. This trend is determined by gas-phase heat transfer. When sidewalls are present, flame spread rate increases with a rise in width, and solid-phase heat conduction determines the trend. Sidewall effects are comprised of four aspects: oxygen concentration near the sidewalls and gypsum board is low, which leads to reduced flame heat flux; upward and front air flow is intensified; the flame is stretched, and the surface flame is weakened; and molten XPS mass decreases. For narrow samples, H and A/w with sidewalls are higher than those without sidewalls, while the reverse was observed in wider samples. The mass loss rate, preheating length and average flame spread rate with sidewalls are smaller than those obtained without sidewalls. Flame spread acceleration with sidewalls occurs at a broader width than that without sidewalls. The experimental results agree well with the theoretical analysis.

Based on the limit equilibrium theory and the circular slip surface method, the state equation of limit equilibrium and the calculation model of the most dangerous sliding surface for inner global stability of foundation pit supported by the prestressed anchor composite soil nailing is established with the disturbing force method. And the searching and solving method of the most dangerous sliding surface is optimized with the SLP optimization method and the simplex optimization method. Then with the mechanical parameters of soil as random variables, the reliability index of inner global stability of foundation pit is calculated with the design checking point method. Finally, a practical project is used to analyze the sensitivity of the reliability index to the coefficients of variability of all random variables.

In this paper, the influence of the local dented plate on ultimate strength is analyzed, and reliability calculation and sensitivity analysis expressions of the plate element with local dents are also proposed. For the structure system consisting of local dented plate elements, reliability analysis is developed, the calculation method of the global reliability index and sensitivity expressions of the reliability index are proposed. Finally, taking a numerical example of a cabin section of ship structure compares and contrasts reliability analysis of the structure system with the local dented plate with that of the system without the local dents. The method proposed in this paper provides a reference for the maintenance and renewal of structure system in use.