Grey relation analysis of natural frequency and semi-active robust optimal control of a multi-dimensional isolator based on parallel mechanism and magneto-rheological damper

For isolating multi-dimensional vibrations experienced by precise facilities carried on a vehicle, a novel isolator is proposed based on 2-RPC/2-SPC parallel mechanism with magneto-rheological dampers. Kinematics and dynamics of the isolator are analyzed by geometrics and the Lagrange method. Grey relation analysis approach is conducted to determine the contributions of geometric parameters on natural frequency conveniently. Through analysis, the first order natural frequency of the isolator is affected by the length of the fixed platform most significantly. Due to manufacturing and assembling errors which could not be avoided in the isolator, robust optimal control algorithm is conducted to ensure control effect and robustness of the isolator at the same time. The gain of robust optimal control algorithm is obtained by deducing and solving linear matrix inequality. Compared to passive control, velocity root mean square values of robust optimal semi-active control decreased obviously in horizontal, longitudinal, vertical, and roll directions.

A hybrid forecasting model for ageing breast deformation during yoga practice

In this work, the deformation of bilateral breasts was investigated with an established hybrid model to predict the nipple movement specifically for senior women during yoga exercise. A motion capture system was used to collect the displacement of 10 markers on the breasts from 11 senior women (average age of 62) during yoga practice and then the data were analyzed by integrating the absolute grey relation analysis (AGRA) and extreme learning machine (ELM). The right and left breasts had the maximum motion amplitude in the horizontal direction but they were respectively featured with contraction and extension during yoga practice. AGRA showed that the nipple motion was highly associated with the vertical region above the nipple for the left breast but the parallel region along with the nipple for the right breast. The ELM model is able to predict the nipple movement within tolerable error (∼0.0037). This study lays a foundation for a better understanding of ageing breast kinematics during yoga poses with limited practical experiments. Besides, the accurate and efficient results can be used not only for yoga pose instruction but also for ergonomic sports bra design.

Comprehensive Evaluation Model and Empirical Research on Railway Freight Rates in a Competitive Environment

This study aims to establish criteria to evaluate performance in railway freight pricing policy and to strengthen the marketing ability of the railway freight enterprise. The evaluation method used in our study is known as the improved grey relation analysis evaluation. Fifteen factors that influence freight pricing strategy are selected in this paper to establish a freight rate evaluation index system and comprehensive evaluation index values for monthly freight rates are calculated. The improved grey relation analysis not only considers the relation between each index and freight rate but also examines the relationship between each index. We find that the comprehensive evaluation state using the improved grey relation analysis evaluation method can better fit the 2015–2017 changes in monthly railroad freight revenue than the traditional grey relation analysis evaluation. Furthermore, an optimal pricing model for freight shipping by train is built and calculated using the bi-level programming model. Finally, the S Railway Bureau’s actual coal transportation in 2017 is taken as an experiment to support the validity of the improved grey relation analysis method. We find that when the monthly results of improved grey evaluation grades are compared with the grade evaluation of the gap between the historical shipping coal rates and the optimal freight shipping rates, the comparison of results matches well. The research work is helpful to policymakers who need to judge the performance of the market price.