Stackelberg games have been widely used to model interactive decision-making problems in a variety of domains such as energy systems, transportation, cybersecurity, and human-robot interaction. However, existing algorithms for solving Stackelberg games often require knowledge of the follower’s cost function or learning dynamics and may also require the follower to provide an exact best response, which can be difficult to obtain in practice. To circumvent this difficulty, we develop an algorithm that does not require knowledge of the follower’s cost function or an exact best response, making it more applicable to real-world scenarios. Specifically, our algorithm only requires the follower to provide an approximately optimal action in response to the leader’s action. The inexact best response is used in computing an approximate gradient of the leader’s objective function, with which zeroth-order bilevel optimization can be applied to obtain an optimal action for the leader. Our algorithm is proved to converge at a linear rate to a neighborhood of the optimal point when the leader’s cost function under the follower’s best response is strongly convex and smooth.
A new complex variable method is presented for stress and displacement problems in a non-circular deep tunnel with certain given boundary conditions at infinity. In order to overcome the complex problems caused by non-circular geometric configurations and the multiply-connected region, a complex variable method and continuity boundary conditions are used to determine stress and displacement within the tunnel lining and within the surrounding rock. The coefficients in the conformal mapping function and stress functions are determined by the optimal design and complex variable method, respectively. The new method is validated by FLAC3D finite difference software through an example. Both the new method and the numerical simulation obtained similar results for the stress concentration and the minimum radial displacement occurred at a similar place in the tunnel. It is demonstrated that the new complex variable method is reliable and reasonable. The new method also provides another way to solve non-circular tunnel excavation problems in a faster and more accurate way.
Stackelberg games have been widely used to model interactive decision-making problems in a variety of domains such as energy systems, transportation, cybersecurity, and human-robot interaction. However, existing algorithms for solving Stackelberg games often require knowledge of the follower's cost function or learning dynamics and may also require the follower to provide an exact best response, which can be difficult to obtain in practice. To circumvent this difficulty, we develop an algorithm that does not require knowledge of the follower's cost function or an exact best response, making it more applicable to real-world scenarios. Specifically, our algorithm only requires the follower to provide an approximately optimal action in response to the leader's action. The inexact best response is used in computing an approximate gradient of the leader's objective function, with which zeroth-order bilevel optimization can be applied to obtain an optimal action for the leader. Our algorithm is proved to converge at a linear rate to a neighborhood of the optimal point when the leader's cost function under the follower's best response is strongly convex and smooth.
Bionic design for improving the energy absorption performance of thin-walled structures has become one of the research hotspots in the field of structural crashworthiness. In this study, a novel bio-inspired multicell tube (UCGS) mimicking the unique microstructure of deep-sea glass sponge was proposed and fabricated by additive manufacturing. Crashworthiness analysis of UCGS was carried out via Abaqus/Explicit and validated by quasi-static axial crushing tests. Results showed that the specific energy absorption ( SEA ) of UCGS was as high as 30.7 J/g, exceeding that of conventional multi-cell tubes and other bio-inspired tubes by 32.2% to 53.1 % and 7.7% to 28.1%, respectively. Subsequently, the effects of geometric parameters and hierarchical designs on the energy absorption performance were investigated by numerical simulation. Finally, a theoretical model was proposed to predict the mean crushing force, which was in good agreement with the numerical results. The research findings might provide a good reference for the design of an energy absorber.
A complex variable method is presented of stress and displacement problems for non-circular cold region tunnels. The complex variable method considers the non-circle tunnel support, the frost heaving circle and the unfrozen surrounding rock at the same time, making the problem from the single connected domain to multi connected domain problem, and can not directly apply the classical complex function theory to solve the problem of the stress and displacement of the non-circular tunnel. The analytical formula in Zeta plane orthogonal curvilinear coordinate system of non-circular tunnel lining to frozen surrounding rock to unfrozen surrounding rock system is derived by using classical complex variable method and continuity condition with power series and conformal transformation. Then, the frost heaving force and frost heaving deformation of the non-circular cold region tunnel are obtained by conformal transformation. This complex variable method is applied to Zhegushan tunnel research, and the analytical solution of Zhegushan tunnel openning frost heave stress and frost heave displacement is obtained. Comparing the analytical solution with the numerical solution to verify the correctness of the analytical solution. It can be seen from the results that frost heaving force has an obvious influence on the lining, and the additional circumferential stresses caused by frost heaving at the vault, arch foot and arch bottom are significantly increased. The additional normal stresses caused by frost heaving at the vault and both sides of arch shoulder are significantly increased. Because of the geometric configurations of lining, the frost heaving deformation is uneven, which leads to uneven distribution of frost heaving forces. Compared with previous studies, which consider the frost heaving ring as a single ring, the complex variable method is more practical. And the research results were expected to provide a referenced basis for elasto-plastic analysis of cold-region tunnel.
With the increasing development of international economy and the international trade,the demand of containerized transport will increase by a large margin.And then advance the maximization trend of the container ships.This paper starts with the present situation of the development of the maximization of the container ships,and then it analyzes the important impacts of large container ships on ports,and it proposes the countermeasures of the ports.
Chinese construction industry is gradually transforming to industrialization, which promotes the development of prefabricated buildings. As an efficient lateral force resisting system, prefabricated steel-plate concrete composite shear wall structure has become a research hotspot in the field of architecture at home and abroad. Based on the mechanical characteristics of the shear wall, this paper proposes a end steel plate connection prefabricated composite shear wall structure. Through numerical simulation and analysis of the prefabricated composite shear wall with different connection areas and the cast-in-place composite shear wall, which verified the feasibility and reliability of end steel plate connection. Based on the above verification, the influence of different parameters on the seismic performance of the prefabricated composite shear wall with end steel plate connection has been further studied, and the theoretical calculation of bearing capacity is carried out. The results show that the length of the connector should be controlled within a reasonable range. The tie bars in the node connection area can improve the strength and ductility of the prefabricated composite shear wall. The aspect ratio and axial pressure ratio have obvious influence on the seismic performance of the wall, which should be reasonably selected in design.
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