###### Abstract
In [PERSON]'s Ph.D. thesis [13], a RUL prediction method named Trajectory Similarity Based Prediction (TSBP) was further developed from the author's previous work [12]. In the TSBP method, two relaxing variables, namely time lag and scaling factor, were introduced in the Euclidean distance-based similarity definition to accommodate minor discrepancies in the degradation process between two comparing instances. Minimizing the distance-based similarity with the time lag is used to deal with the discrepancy in degradation process alignment, the scaling factor for discrepancy in degradation acceleration rate. [PERSON] et al. proposed a new similarity measure for instance retrieval in their IBL approach to improve the prediction accuracy [8]. The algorithm includes a comparison of the degradation processes between the test and learning instances, while giving heavier weights to recent observations. In an IBL approach for RUL prediction proposed by [PERSON] et al. [9], the instance retrieval step is undertaken using a Euclidean distance measure only with respect to the last block of the test observation trajectory. In another paper presented by [PERSON] [14], for each instance the entire time series of health indicator was decomposed into a lower envelope and upper envelope. The two envelopes formed a planar figure called a polygon, which was considered an imprecise health indicator (IHI). The proposed similarity evaluation approach makes use of computational geometry tools in order to estimate the nearest instances to a given testing instance. It is important to recognize that system degradation behaviors are influenced by many factors including material and manufacturing variability. Hence, the same design and make of a component or a device may present different degradation behaviors under the same operating condition. It is challenging for the IBL approach to make accurate RUL estimations with limited historical degradation datasets. In this paper, we propose a novel IBL approach supported by data augmentation to address the shortage of historical data. We illustrate the method and its performance using the PRONOSTIA bearing datasets, which were provided to the IEEE PHM 2012 Prognostic Challenge [15, 16]. In addition to dealing with limited run-to-failure examples in the learning datasets, the proposed method is capable of handling situations where learning and test instances may have different degradation rates. A key idea is the application of a data augmentation technique to generate multiple synthetic prognostic feature sequences by modifying the learning instance (i.e., run-to-failure example). From the multiple synthetic prognostic feature sequences, an optimal RUL estimate for the test instance can be obtained using a similarity evaluation method. It is worth noting that the similarity measure used in this paper has a distance-based definition (named \"RMS difference measure\" in this paper) similar to the TSBP method [13] where the time lag and scaling factor are considered. In this paper, we introduce two manipulating variables in similarity evaluation accordingly from the data augmentation point of view. In the TSBP method, the similarity definition with the two relaxing variables was designed to accommodate minor discrepancies between the comparing instances for instance retrieval. Tighter constraints were applied to the two variables while implementing TSBP. In this paper, we implement a data augmentation strategy by modifying the degradation rate with either stretching or shrinking factor in scaling. Our proposed IBL approach can be implemented with different data augmentation strategies for different prognostic applications. More manipulating variables may be introduced in the similarity evaluation accordingly. The remainder of this paper is organized as follows. Section 2 introduces the bearing RUL estimation problem and the PRONOSTIA datasets. Section 3 describes the methodology of the proposed IBL approach. Section 4 presents the evaluation results and discussion.