Graph Laplacian Matrix Learning from Smooth Time-Vertex Signal

In this paper,we focus on inferring graph Laplacian matrix from the spatiotemporal signal which is defined as“time-vertex signal”.To realize this,we first represent the signals on a joint graph which is the Cartesian product graph of the time-and vertex-graphs.By assuming the signals follow a Gaussian prior distribution on the joint graph,a meaningful representation that promotes the smoothness property of the joint graph signal is derived.Furthermore,by decoupling the joint graph,the graph learning framework is formulated as a joint optimization problem which includes signal denoising,timeand vertex-graphs learning together.Specifically,two algorithms are proposed to solve the optimization problem,where the discrete second-order difference operator with reversed sign(DSODO)in the time domain is used as the time-graph Laplacian operator to recover the signal and infer a vertex-graph in the first algorithm,and the time-graph,as well as the vertex-graph,is estimated by the other algorithm.Experiments on both synthetic and real-world datasets demonstrate that the proposed algorithms can effectively infer meaningful time-and vertex-graphs from noisy and incomplete data.

Discrete element method study of parameter optimization and particle mixing behaviour in a soil mixer

Soil mixing is an emerging research in the field of construction resource recovery.In this study,the mixing behaviour of soil particles in a mixer is numerically simulated by the discrete element method(DEM).A four-factor,three-level orthogonal experiment is designed to optimize the mixer design by selecting the fly-cutter speed,spindle speed,number of blades and fly-cutter diameter,using Lacey mixing index and power consumption as evaluation indicators.Then,the impact of soil cohesion and type on the mixing behaviour is investigated.The results show that the optimal parameter combination of this experiment is 280 rpm fly-cutter speed,40 rpm spindle speed,4 blades and 250 mm fly-cutter diameter.This optimal combination reaches a comparatively uniform state mix in 5.9 s with an average power consumption of 704.11 W.In addition,the wear and tear of the mixer increases as soil cohesion increases,while the mixing quality of materials declines,resulting in a“shaft hugging”phenomenon.The mixing efficiency varies greatly among different soil types,but the radial and tangential velocities have a similar law.This work can provide some guidance for the optimization design of a mixer and study of soil mixing.