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Distributed event-triggered generalized Nash equilibrium seeking for aggregative games on unbalanced digraphs

Cai Xin, Nan Xinyuan, Gao Bingpeng

Archives of Control Sciences

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2022

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Vol. 32, No. 4

783--800

EN

This paper addresses the problem of seeking generalized Nash equilibrium for constrained aggregative games with double-integrator agents who communicate with each other on an unbalanced directed graph. An auxiliary variable is introduced to balance the consensus terms in the designed algorithm by estimating the left eigenvector of the Laplacian matrix associated with the zero eigenvalue in a distributed manner. Moreover, an event-triggered broadcasting scheme is proposed to reduce communication loads in the network. It is shown that the proposed communication scheme is free of the Zeno behavior and the asymptotic convergence of the designed algorithm is obtained. Simulation results are demonstrated to validate the proposed methods.

2

The role of water content in rate dependence of tensile strength of a fine-grained sandstone

Cai Xin, Cheng Chuanqing, Zhao Yuan, Zhou Zilong, Wang Shaofeng

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e58, 2022

EN

Rocks in nature are commonly in partially saturated conditions and exposed to dynamic loads. In this study, to explore the coupled effects of water content and loading rate, dynamic Brazilian disc experiments were conducted on Yunnan sandstone samples with four levels of water content (from air-dried to water-saturated) under various loading rates (from 100 to 600 GPa/s) using a split Hopkinson pressure bar. The test results show that for each water content, the dynamic tensile strength of sandstone is positively sensitive to loading rate. The rate dependence of tensile strength increases as the rise of water content. The change trends of tensile strength against water content depend on loading rate: as water content rises, the tensile strength displays the manner of “no change followed by fast drop” at loading rates of 10–4 and 100 GPa/s. However, when the loading rate is above 200 GPa/s, the tensile strength increases first and then declines. The turning point occurs at water content between 1.0 and 2.0%. These observations can be interpreted with the competition between water weakening and enhancing effects under different loading conditions.

3

New approach to spindle thermal extension measuring based on machine vision for the vertical maching centre

Su Dongxu, Cai Xin, Li Yang, Zhao Wanhuan, Zhang Huijie

Metrology and Measurement Systems

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2021

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Vol. 28, nr 2

357--370

EN

When machine tool spindles are running at a high rotation speed, thermal deformation will be introduced due to the generation of large amounts of heat, and machining accuracy will be influenced as a result, which is a generalized issue in numerous industries. In this paper, a new approach based on machine vision is presented for measurements of spindle thermal error. The measuring system is composed of a Complementary Metal-Oxide-Semiconductor (CMOS) camera, a backlight source and a PC. Images are captured at different rotation angles during end milling process. Meanwhile, the Canny edge detection and Gaussian sub-pixel fitting methods are applied to obtain the bottom edge of the end mill which is then used to calculate the lowest point coordinate of the tool. Finally, thermal extension of the spindle is obtained according to the change of the lowest point at different time steps of the machining process. This method is validated through comparison with experimental results from capacitive displacement sensors. Moreover, spindle thermal extension during the processing can be precisely measured and used for compensation in order to improve machining accuracy through the proposed method.