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In order to analyze the process of bearing vibration variation, the original vibration data of four kinds of damage diameters are grouped, and the intrinsic data sequence is selected after grouping. Then, the non-ordered gray relation between data sequence of different groups and the intrinsic data sequence is established and the gray confidence level is obtained. The gray confidence level is compared with the set threshold of 90%. Then the variation of the bearing vibration is evaluated. The correctness and feasibility of the proposed method are verified by comparing the assessment with the actual situation. Introduction During the service period of bearings, the vibration performance of the bearing decreases gradually with time due to the loss of the constituent element, the movement of the auxiliary sub-gap or the friction, that is, the vibration variation[1]. Rolling bearings as the important implementation of components and wearing parts of a mechanical transmission system, the health condition of its performance is of great significance to maintain the stable operation of the system[2]. For example, the bearing fatigue life, friction torque, vibration and noise and other performances will directly affect operation status of the host[3]. Vibration variation means that the bearing damage occurred and its sustainable development will inevitably lead to functional failure of the host, resulting in huge losses or even disaster. In order to avoid serious disaster, bearing vibration variation evaluation is very important. Therefore, the evaluation of bearing vibration variation process has aroused great concern of scholars at home and abroad. L.D. Chen proposed creatively the use of atomic absorption spectrometry to determine bearing abnormal sound failure of car engine crankshaft[4]. Based on the derivation of bearing failure model of subway vehicle bogie, J.Q. Liu proposed a intelligent method for fault diagnosis of subway vehicle bogie[5]. EL Morsy used the optimal morlet wavelet filtering and envelope detection to analyze the experimental signals of the inner ring failure of rolling bearing[6]. Uddin S proposed a K-NN classification algorithm which can improve performance in bearing fault diagnosis[7]. The existing method of bearing vibration variation is largely presumed that the probability distribution is known, that is, the data obeys a particular distribution. However, during the service of the bearing, the probability distribution of the vibration sample data is unknown and belongs to the problem of poor information category[8]. Poor information is also called lack of information and the research object presents incomplete feature information, lack of a priori information. Gray system theory, fuzzy set theory, chaos theory and so on can be attributed to the poor information system theory. For example, in the mechanical system assessment, the overall probability distribution is unknown or the probability distribution is complex, and only the small sample data is available for reference, which belongs to the poor information problem[9-10]. In this paper, the non-ordering gray relation in the gray system theory is applied to the evaluation of the vibration variation process of the bearing. The vibration data are grouped and the intrinsic data sequence is selected to calculate the

Evaluation of the Variation Process of Bearing Vibration Based on Non-ordered Gray Relation (Part I: Theory)