A two-dimensional entropy-based method for detecting the degree of segregation in asphalt mixture

Optimization of Particle Distribution for Asphalt Mixtures in Screw Conveyer of Paver Based on Discrete Element Method and Response Surface Methodology

“…Due to the different mean values of the particle mass ratio being measured, using the standard deviation of the deviation degree for further comparison is not very accurate. [25] Therefore, the coefficient of variation was introduced to characterize the degree of variation of the particle distribution. The coefficient of variation for large particles C x can be expressed as the ratio of the unbiased standard deviation of the deviation degree 𝜀 xi and the mean value εx : By following the above steps, the coefficient of variation for the middle particle and small particle C y and C z can be obtained.…”

“…g j (X) = y j (X) − U j for y j > U j g j (X) = 0 for L j ≤ y j ≤ U j g j (X) = L j − y j (X) for y j < L j (24) where X represents design variables in optimization space; g j is the constraint function of the j-th iteration; y j is the optimal response of the j-th iteration; and U j and L j are reactions constrained by upper and lower limits, respectively. This forms a constraint system, which can be solved as an unconstrained problem by the penalty function method, as shown in Equation (25). The goal of the penalty function is to provide a mountain to climb when the optimization starts at an undesired position.…”

“…Due to the different mean values of the particle mass ratio being measured, using the standard deviation of the deviation degree for further comparison is not very accurate. [ 25 ] Therefore, the coefficient of variation was introduced to characterize the degree of variation of the particle distribution. The coefficient of variation for large particles $${C_x}$$ can be expressed as the ratio of the unbiased standard deviation of the deviation degree $${\varepsilon _{x{\mathrm{i}}}}$$ and the mean value $${\bar \varepsilon _x}$$: $$$$\begin{equation}\;{C_x} = \frac{{\sqrt {\mathop \sum \nolimits_{{\mathrm{i}} = 1}^n \frac{{{{({\varepsilon _{x{\mathrm{i}}}} - {{\bar \varepsilon }_{x{\mathrm{i}}}})}^2}}}{{n - 1}}} }}{{{{\bar \varepsilon }_x}}}\;\end{equation}$$$$…”

Canny and Morphological Approaches to Calculating Area and Perimeter of Two-Dimensional Geometry

“…Zhang Z, et al [13] and Hu T, et al [14] use the support of the Canny edge detection method to solve image processing problems such as the detection of asphalt pavement thickness [14] and also the detection of quality of crosssectional fiber image [13].…”