A novel two-stage approach for energy-efficient timetabling for an urban rail transit network

Urban rail transit (URT) is the backbone transport mode in metropolitan areas to accommodate large travel demands. The high energy consumption of URT becomes a hotspot problem due to the ever-increasing operation mileages and pressing agendas of carbon neutralization. The high model complexity and inconsistency in the objectives of minimizing passenger travel time and operational energy consumption are the main challenges for energy-efficient timetabling for a URT network with multiple interlinked lines. This study proposes a general model framework of timetabling and passenger path choice in a URT network to minimize energy consumption under passenger travel time constraints. To obtain satisfactory energy-efficient nonuniform timetables, we suggest a novel model reformulation as a tree knapsack problem to determine train running times by a pseudo-polynomial dynamic programming algorithm in the first stage. Furthermore, a heuristic sequencing method is developed to determine nonuniform headways and dwell times in the second stage. The suggested model framework and solution algorithm are tested using a real-world URT network, and the results show that energy consumption can be considerably reduced given certain travel time increments

L2L^2 norm error estimates of BDF methods up to fifth-order for the phase field crystal model

The well-known backward difference formulas (BDF) of the third, the fourth and the fifth orders are investigated for time integration of the phase field crystal model. By building up novel discrete gradient structures of the BDF-\rmk (\rmk=3,4,5) formulas, we establish the energy dissipation laws at the discrete levels and then obtain the priori solution estimates for the associated numerical schemes (however, we can not build any discrete energy dissipation law for the corresponding BDF-6 scheme because the BDF-6 formula itself does not have any discrete gradient structures). With the help of the discrete orthogonal convolution kernels and Young-type convolution inequalities, some concise $L^2$ norm error estimates (with respect to the starting data in the $L^2$ norm) are established via the discrete energy technique. To the best of our knowledge, this is the first time such type $L^2$ norm error estimates of non-A-stable BDF schemes are obtained for nonlinear parabolic equations. Numerical examples are presented to verify and support the theoretical analysis.Comment: 25 pages, 8 figures. arXiv admin note: text overlap with arXiv:2008.0021

Determination of Stray Inductance of Low-Inductive Laminated Planar Multiport Busbars Using Vector Synthesis Method

Laminated busbars connect capacitors with switching power modules, and they are designed to have low stray inductance to minimize electromagnetic interference. Attempts to accurately measure the stray inductance of these busbars have not been successful. The challenge lies with the capacitors, as they excite the busbar producing their individual stray inductances. These individual stray inductances cannot be arithmetically averaged to establish the total stray inductance that applies when all the capacitors excite the busbar at the same time. It is also not possible to measure the stray inductance by simultaneous excitation of each capacitor port using impedance analyzers. This paper presents a solution to the above dilemma. A vector synthesis method is proposed, whereby the individual stray inductance from each capacitor port is measured using an impedance analyzer. Each stray inductance is then mapped into an xyz frame with a distinct direction. This mapping exercise allows the data to be vectored. The total stray inductance is then the sum of all the vectors. The effectiveness of the proposed method is demonstrated on a busbar designed for H-bridge inverters by comparing the simulation and practical results. The absolute error of the total stray inductance between the simulation and the proposed method is 0.48 nH. The proposed method improves the accuracy by 14.9% compared to the conventional technique in measuring stray inductances

A Deep Ordinal Distortion Estimation Approach for Distortion Rectification

Distortion is widely existed in the images captured by popular wide-angle cameras and fisheye cameras. Despite the long history of distortion rectification, accurately estimating the distortion parameters from a single distorted image is still challenging. The main reason is these parameters are implicit to image features, influencing the networks to fully learn the distortion information. In this work, we propose a novel distortion rectification approach that can obtain more accurate parameters with higher efficiency. Our key insight is that distortion rectification can be cast as a problem of learning an ordinal distortion from a single distorted image. To solve this problem, we design a local-global associated estimation network that learns the ordinal distortion to approximate the realistic distortion distribution. In contrast to the implicit distortion parameters, the proposed ordinal distortion have more explicit relationship with image features, and thus significantly boosts the distortion perception of neural networks. Considering the redundancy of distortion information, our approach only uses a part of distorted image for the ordinal distortion estimation, showing promising applications in the efficient distortion rectification. To our knowledge, we first unify the heterogeneous distortion parameters into a learning-friendly intermediate representation through ordinal distortion, bridging the gap between image feature and distortion rectification. The experimental results demonstrate that our approach outperforms the state-of-the-art methods by a significant margin, with approximately 23% improvement on the quantitative evaluation while displaying the best performance on visual appearance