Copula method of the kinematic accuracy of cylindrical roller bearing

The kinematic accuracy of cylindrical rollers bearing isn’t only influenced by the dimensional and form precision of its parts, but also more influenced by the cooperation among them. For cylindrical rollers bearing, the main indices of the kinematic accuracy are the ending beat and the radial run out of bearings. There must be dependent relationship between the cooperative action among the parts of bearings and the ending beat or the radial run out of bearings. This relationship is hardly expressed by mathematical formula. However, because the parts dimension deviation and the run out of bearings follow statistic law and have their distribution characteristics, while the copula joint distribution function can connect the run out of bearings with multiple parts dimension accuracy, the copula function is introduced to analyze the dependent relationship between bearing parts cooperative action and its kinematic accuracy. Based on the copula function of statistic theory, the kinematic accuracy of bearings can be forecast by parts geometric accuracy.

Double Entropy Joint Distribution Function and Its Application in Calculation of Design Wave Height

Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period.

Synchronous asynchronous encounter analysis of runoff between reservoirs based on Copula function

Based on goodness-of-fit test on Copula function, we got the best fitted joint distribution function of runoff between D and H reservoirs. Then we analyzed the synchronous asynchronous encounter probability of runoff. The synchronous encounter probability of runoff was 72.46%, while the asynchronous of dryness-wetness or wetness-dryness encounter probability was only 1.06% between D and H reservoirs. The results showed that the runoff conditions were not conducive to the runoff compensation. In order to satisfy the target of water supply, we should also study the reservoir optimization operation, store water in advance and exploit the reservoir regulating potentialities on flood water resources.

Vulnerability Analysis of Ancient Timber Architecture by Considering the Correlation of Different Failure Modes

The paper proposes an innovative method of analyzing the seismic fragility of ancient timber architecture. The method is based on the Copulas, in which correlation between different failure modes is considered. This method is applied to assess the vulnerability of ancient timber architecture in Ming dynasty. The assessment includes four steps. In the first step, the incremental dynamic analysis is employed to establish seismic vulnerability curves of different failure modes for the structure. After that, Copula joint distribution function is used to analyze the correlation among different failure modes. In the third step, fragility curves considering correlation among different failure modes are established. In the last step, the fragility curves are compared with those obtained by first-order bound method. The results show that seismic vulnerability of ancient timber architecture based on the Copulas is greater than that of any single failure modes. Moreover, the occurrence probability ranges between the upper and lower boundaries of the first-order bound method, but is close to the lower boundary.

Method of Fusion Diagnosis for Dam Service Status Based on Joint Distribution Function of Multiple Points

The traditional methods of diagnosing dam service status are always suitable for single measuring point. These methods also reflect the local status of dams without merging multisource data effectively, which is not suitable for diagnosing overall service. This study proposes a new method involving multiple points to diagnose dam service status based on joint distribution function. The function, including monitoring data of multiple points, can be established with t-copula function. Therefore, the possibility, which is an important fusing value in different measuring combinations, can be calculated, and the corresponding diagnosing criterion is established with typical small probability theory. Engineering case study indicates that the fusion diagnosis method can be conducted in real time and the abnormal point can be detected, thereby providing a new early warning method for engineering safety.