Accurate vibration time series modeling can mine the internal law of data and provide valuable references for reliability assessment. To improve the prediction accuracy, this study proposes a hybrid model – called the AR–SVR–CPSO hybrid model – that combines the auto regression (AR) and support vector regression (SVR) models, with the weights optimized by the chaotic particle swarm optimization (CPSO) algorithm. First, the auto regression model with the difference method is employed to model the vibration time series. Second, the support vector regression model with the phase space reconstruction is constructed for predicting the vibration time series once more. Finally, the predictions of the AR and SVR models are weighted and summed together, with the weights being optimized by the CPSO. In addition, the data collected from the reliability test platform of high-speed train transmission systems and the “NASA prognostics data repository” are used to validate the hybrid model. The experimental results demonstrate that the hybrid model proposed in this study outperforms the traditional AR and SVR models.
The bogie 6-degree-of-freedom dynamic simulation test bench can simulate various operating conditions of the bogie through coordinated movement of the three parallel 6-degree-of-freedom motion platforms; however, the motion of the platforms will be interfered by some space obstacles. In order to obtain the collision-free workspace of the 6degree-of-freedom motion platforms, a limit boundary-search method based on the collision-detection model is proposed. The structure of three parallel 6-degree-of-freedom motion platforms is analyzed, and its inverse kinematics model is established. Considering its internal constraints, the constraint models of the actuators' stroke and the spherical hinges angle are established. Based on the collision-detection method between convex polygons, the minimum distancedetection models between platforms and obstacles as well as between actuators and obstacles are established. Then the limit boundary-search method is used to search for all boundary points that satisfy the constraint conditions. Finally, the correctness and feasibility of the proposed method and models are verified by some simulation examples. The proposed research avoids collisions effectively and provides a reference for the optimal design of the test bench.
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