Estimation of speed-related car body acceleration limits with quantile regression

Purpose–This study aimed to facilitate a rapid evaluation of track service status and vehicle ride comfort based on car body acceleration.Consequently,a low-cost,data-driven approach was proposed for analyzing speed-related acceleration limits in metro systems.Design/methodology/approach–A portable sensing terminal was developed to realize easy and efficient detection of car body acceleration.Further,field measurements were performed on a 51.95-km metro line.Data from 272 metro sections were tested as a case study,and a quantile regression method was proposed to fit the control limits of the car body acceleration at different speeds using the measured data.Findings–First,the frequency statistics of the measured data in the speed-acceleration dimension indicated that the car body acceleration was primarily concentrated within the constant speed stage,particularly at speeds of 15.4,18.3,and 20.9 m/s.Second,resampling was performed according to the probability density distribution of car body acceleration for different speed domains to achieve data balance.Finally,combined with the traditional linear relationship between speed and acceleration,the statistical relationships between the speed and car body acceleration under different quantiles were determined.We concluded the lateral/vertical quantiles of 0.8989/0.9895,0.9942/0.997,and 0.9998/0.993 as being excellent,good,and qualified control limits,respectively,for the lateral and vertical acceleration of the car body.In addition,regression lines for the speedrelated acceleration limits at other quantiles(0.5,0.75,2s,and 3s)were obtained.Originality/value–The proposed method is expected to serve as a reference for further studies on speedrelated acceleration limits in rail transit systems.

A Contribution to Analysis of Collapse of High-Rise Building Inspired by the Collapses of WTC1 and WTC2: Derivation of Simple Formulas for Collapse Upper Speed and Acceleration

The paper is a contribution to the technical discussion concerning the collapses of the WTC buildings. It returns to the problem of the dynamics of the collapses;it does not concern the reason why the buildings started collapsing, but investigates the dynamics of the collapse itself. It works with the same assumptions as the official NIST report [1], i.e. that the falling mass hits the motionless mass beneath;the supporting columns loose stability and the mass of the pertinent floor starts to fall together with the falling mass. The aim was to derive the theoretical upper limit of the speed of the collapse, supposing that influence of the columns which resist the fall, is neglected. The differential equation of the fall was obtained using two independent laws of mechanics, with the identical result. Its solution can be found from a very simple explicit formula. The theoretical upper limit acceleration of the fall obtained by such formula is one third of the gravitational acceleration, which is faster than it was observed in the case of the collapses of WTC1 and WTC2. This leads to the conclusion that the mechanism of the collapse must be different from the assumed and the falling mass must not hit the motionless mass bellow it, but rather a mass which had started to fall before the impact of the falling mass occurred.