A Distributed Newton Method for Processing Signals Defined on the Large-Scale Networks

In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously perform the local computation,which calls for heavy computational and communication costs.Moreover,in many real-world networks,such as those with straggling nodes,the homogeneous manner may result in serious delay or even failure.To this end,we propose active network decomposition algorithms to select non-straggling nodes(normal nodes)that perform the main computation and communication across the network.To accommodate the decomposition in different kinds of networks,two different approaches are developed,one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes,which constitutes the main contribution of this paper.By incorporating the active decomposition scheme,a distributed Newton method is employed to solve the least squares problem in GSP,where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node.The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost.Numerical examples demonstrate the effectiveness of the proposed algorithm.

Performance Investigation of 2D Lattice Boltzmann Simulation of Forces on a Circular Cylinder

The lattice Boltzmann method (LBM) is employed to simulate the uniform flow past a circular cylinder. The performance of the two-dimensional LBM model on the prediction of force coefficients and vortex shedding frequency is investigated. The local grid refinement technique and second-order boundary condition for curved walls are applied in the calculations. It is found that the calculated vortex shedding frequency, drag coefficient and lift coefficient are consistent with experimental results at Reynolds numbers lower than 300. For the high Reynolds number flow, although the simulation by the combined model of LBM and large eddy simulation method is numerically stable, the simulated results deviate from those of experiments, similar to the reported results by conventional numerical methods. It is suggested that this is mainly due to the three-dimensionality of the flow.

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.

Bi-level Planning for Integrated Energy Systems Incorporating Demand Response and Energy Storage Under Uncertain Environments Using Novel Metamodel

The optimal planning and design of an integrated energy system(IES)is of great significance to facilitate distributed renewable energy(DRE)technology and improve the overall energy efficiency of the energy system.With the increased penetration of distributed generation(DG),the power supply and load sides of an IES present more increased levels of uncertainties.Demand response(DR)and the energy storage system(ESS)serve as important means to shift energy supply and use across time to counter the indeterminate variations.However,the current IES planning methods are unable to effectively deal with the uncertainties of DREs and loads,and to optimize the operations of DG-DR-ESS due to the enormous possible combinations.In this paper,a new method for the optimal planning and design of an integrated energy system has been introduced and verified.The new method consists of three integrated elements.First,the method of the probability scenario has been used to model the uncertainties of the DREs and loads so as to better characterize the impact of uncertainty on the planning and design of the IES.Secondly,the optimal operation of the IES under different probability scenarios is ensured using the second-order cone optimization for quick solutions due to the simplicity of this sub-problem,serving as the bottom-level optimization.Thirdly,the optimal planning and design of IES through optimal sizing of the power generating components and ESS are performed using a special meta-model based global optimization method due to the complex,black-box,and computation intensive nature of this top-level optimization in a nested,bi-level global optimization problem.The combined approach takes full account of the interrelated operations of DG-DR-ESS under different design configurations to support a better optimal planning and design of the IES.The simulation has been carried out on an IES system modified from the IEEE 33-node distribution system.The simulation results show that the proposed method and model are effective.