Symbolic Dynamic Programming for Continuous State MDPs with Linear Program Transitions

Recent advances in symbolic dynamic programming (SDP) have significantly broadened the class of MDPs for which exact closed-form value functions can be derived. However, no existing solution methods can solve complex discrete and continuous state MDPs where a linear program determines state transitions --- transitions that are often required in problems with underlying constrained flow dynamics arising in problems ranging from traffic signal control to telecommunications bandwidth planning. In this paper, we present a novel SDP solution method for MDPs with LP transitions and continuous piecewise linear dynamics by introducing a novel, fully symbolic argmax operator. On three diverse domains, we show the first automated exact closed-form SDP solution to these challenging problems and the significant advantages of our SDP approach over discretized approximations.

A Fault Diagnosis Approach for Rolling Bearing Integrated SGMD, IMSDE and Multiclass Relevance Vector Machine

The vibration signal induced by bearing local fault has strong nonstationary and nonlinear property, which indicates that the conventional methods are difficult to recognize bearing fault patterns effectively. Hence, to obtain an efficient diagnosis result, the paper proposes an intelligent fault diagnosis approach for rolling bearing integrated symplectic geometry mode decomposition (SGMD), improved multiscale symbolic dynamic entropy (IMSDE) and multiclass relevance vector machine (MRVM). Firstly, SGMD is employed to decompose the original bearing vibration signal into several symplectic geometry components (SGC), which is aimed at reconstructing the original bearing vibration signal and achieving the purpose of noise reduction. Secondly, the bat algorithm (BA)-based optimized IMSDE is presented to evaluate the complexity of reconstruction signal and extract bearing fault features, which can solve the problems of missing of partial fault information existing in the original multiscale symbolic dynamic entropy (MSDE). Finally, IMSDE-based bearing fault features are fed to MRVM for achieving the identification of bearing fault categories. The validity of the proposed method is verified by the experimental and contrastive analysis. The results show that our approach can precisely identify different fault patterns of rolling bearings. Moreover, our approach can achieve higher recognition accuracy than several existing methods involved in this paper. This study provides a new research idea for improvement of bearing fault identification.

Health condition identification for rolling bearing based on hierarchical multiscale symbolic dynamic entropy and least squares support tensor machine–based binary tree

Bearing health condition identification plays a crucial role in guaranteeing maximum productivity and reducing maintenance costs. In this article, a novel tensorial feature extraction approach called hierarchical multiscale symbolic dynamic entropy is developed, which can be used to assess the dynamic characteristic of the measured vibration data at different hierarchical layers and different scales. Besides, the influence of parameters in hierarchical multiscale symbolic dynamic entropy is investigated so as to select the optimal parameters. Then, a new multi-fault classifier called least squares support tensor machine–based binary tree is presented to achieve the fault identification automatically. In the least squares support tensor machine–based binary tree method, the divisibility measure strategy is constructed by two new separability measures (i.e. the average center distance of samples in one class, the center distance of samples between sub-class and global class). Finally, a novel intelligent fault diagnosis scheme based on hierarchical multiscale symbolic dynamic entropy and least squares support tensor machine–based binary tree is developed, which is applied to analyze the experimental data of rolling bearing. The results indicate that the proposed scheme has a superior performance in health condition identification. Compared with the existing symbolic dynamic entropy–based fault diagnosis methods, the proposed method has higher diagnostic accuracy and better stability.