A standard assumption adopted in the multi-armed bandit (MAB) framework is that the mean rewards are constant over time. This assumption can be restrictive in the business world as decision makers often face an evolving environment in which the mean rewards are time-varying. In this paper, we consider a non-stationary MAB model in which the mean rewards vary over time in a periodic manner. The unknown periods of the arms can be different and scale with the length of the decision horizon T polynomially. For this setting, we propose a two-stage policy that combines the Fourier analysis with a confidence-bound-based learning procedure to learn the periods and minimize the regret. In stage one, the policy correctly estimates the periods of all arms with high probability. In stage two, the policy explores the periodic mean rewards of arms using the periods estimated in stage one and exploits the optimal arm in the long run.We show that our policy achieves the rate of regret Õ( T K k=1 T k ), where K is the number of arms and T k is the length of period of the k-th arm. This rate of regret matches the optimal one of the classic MAB problem O( √ T K) if we regard each phase of an arm in the period as a separate arm.
As an important part of the transportation network, the reliability of bridge structures is of great significance to people’s personal safety, as well as to the national economy. In order to evaluate the performance of complex bridge structures, their mechanical behavior and fundamental characteristics need to be studied. Structural health monitoring (SHM) has been introduced into bridge engineering, and the structural response assessment, load effects monitoring, and reliability evaluation have been developed based on the collected SHM information. In this study, a performance evaluation method for complex bridge structures based on non-destructive field loading tests is proposed. The cable-stayed bridge in Guangxi with the largest span (Pingnan Xiangsizhou Bridge) was selected as the research object, and loading on the main girder was transferred to the piers and tower through the stay cables, whose structural responses are critical in the process of bridge operation. Therefore, the field loading tests—including deflection and strain testing of the main girder, as well as cable force tests—were also conducted for Pingnan Xiangsizhou Bridge by using non-destructive measurement techniques (multifunctional static strain test system, radar interferometric deformation measurement technology, etc.). Based on the numerically simulated results of a finite element model for Pingnan Xiangsizhou Bridge, reasonable field loading test conditions and loading arrangement were determined. Non-destructive field loading test results showed that the quality of the bridge’s construction is up to standard, due to a good agreement between the calculated and measured frequencies of the bridge. In addition, the calibration coefficients of displacement and strain were less than 1, indicating that Pingnan Xiangsizhou Bridge has satisfactory stiffness and strength.
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