## 1 Introduction
The residual life prediction method based on multi-source data fusion mainly considers making full use of failure time data and performance degradation data for residual life prediction. Therefore, the sample size of multi-source data constrains the prediction accuracy of residual life. Generally, the data of accelerated life test is used as a priori information to predict the residual life of the system in real time by fusing field online data with the help of the Bayesian inference method. The residual life prediction method based on multi-source data fusion can improve the low accuracy of prediction results due to the lack of samples for small-sample data. In summary, the residual life prediction method based on failure time data can only obtain the overall life distribution of the system and does not consider the degradation information during the operation of the system, so it cannot well reflect the residual life distribution after a period of system operation. In order to ensure the accuracy of the prediction results, this method requires a large amount of experimental analysis and evaluation of various small samples of information. The residual life prediction model driven by performance degradation data is constructed from the historical monitoring data of system operation. The advantage is that it does not need the real mechanism expression formula of a complex physical system, and the model is not complicated, which is easier to be applied to practical engineering. However, the disadvantage is that a large amount of monitoring data is required to construct high precision models, which are not representative of the actual system and can be learned by collecting more monitoring data, thus improving the residual life accuracy. The disadvantage of the residual life prediction method based on multi-source data fusion is that the sample size of multi-source data restricts the accuracy of residual life prediction, and the advantage is that it can improve the problem of low accuracy of prediction results caused by the lack of samples for small-sample data. There are still some shortcomings in addressing the accuracy of residual life prediction of mechanical products in a small-sample environment, which mainly include:1 The problem of low accuracy of residual life prediction under multiple time scales and multiple failure states is that mechanical products undergo different internal structural degradation mechanisms according to different operating states (such as start-up, acceleration, shutdown, load, etc. ), and the failure time data monitored by different operating states are fragmented and have the characteristics of multiple time scales \"small samples.\" Also, the current failure state of mechanical products is not a simple two-state, which undergoes a gradual degradation process during the whole life service cycle and presents multiple failure states before failure, resulting in low accuracy of residual life prediction under multiple time scales and multiple failure states for small samples of mechanical products. 2 The adaptive capability of the parameters is an important means to maintain the real-time prediction of the residual life of small-sample mechanical products. However, most of them stay in the experimental stage with a long cycle time and a large sample size, which is not applicable to the conditions of small-sample data. To address the above problems, this paper proposes a small-sample adaptive residual life prediction model for mechanical products based on feature matching preprocessor-LSTM. First, to address the low accuracy of residual life prediction for small samples of mechanical products caused by multiple time scales and multiple fault states, this paper fuses failure time data and performance degradation data and introduces failure rate and standard deviation of life characteristics as the residual life.