###### Abstract  
With the complexity of the task requirement, multiple operating conditions have gradually become the common scenario for equipment. However, the degradation trend of monitoring data cannot be accurately extracted in life prediction under multiple operating conditions, which is because some monitoring data is affected by the operating conditions. Aiming at this problem, this paper proposes an improved similarity trajectory method that can directly use the monitoring data under multiple operating conditions for life prediction. The morphological pattern and symbolic aggregate approximation-based similarity measurement method (MP-SAX) is first used to measure the similarity between the monitoring data under multiple operating conditions. Then, the similar life candidate set, and corresponding weight are obtained according to the MP-SAX. Finally, the life prediction results of equipment under multiple operating conditions can be calculated by aggregating the similar life candidate set. The proposed method is validated by the public datasets from NASA Ames Prognostics Data Repository. The results show that the proposed method can directly and effectively use the original monitoring data for life prediction without extracting the degradation trend of the monitoring data. [EMAIL_ADDRESS] 2021 11 10968 17 November  
However, although the excellent prediction results of equipment can be obtained by the life prediction method based on machine learning and deep learning, the accuracy of prediction results mostly depends on the design of network structure and the selection of parameters. At this time, the similarity trajectory method (STM) based on the case-based reasoning (CBR) which can be regarded as a form of intradomain analogy, and a branch of machine learning shown obvious advantages. CBR can solve the problem of a new instance only by measuring the similarity between a new instance and the historical instance and reusing the information and knowledge of the historical instance [15]. Therefore, STM can realize life prediction without constructing a specific prediction model and selecting parameters, which can reduce the influence of network structure design and parameter selection on the accuracy of prediction results. Therefore, STM has been widely discussed and applied to life prediction since it was proposed by [PERSON] et al. [16]. For example, [PERSON] et al. [17] pointed out that the traditional Euclidean distance cannot highlight the importance of the recent samples, and on the basis of the Euclidean distance, the decay coefficient was introduced to make the recent degradation samples have a larger weight. [PERSON] et al. [18; 19] improved the prediction accuracy of STM by improving the deficiency of degradation indicators construction. [PERSON] et al. [20] proposed evidential similarity-based regression for life prediction and related uncertainty based on both complete and incomplete degradation trajectories. [PERSON] et al. [21] proposed an integrated prediction model based on the similarity trajectory method and the differential evolution support vector regression for predicting the tool wear and life. A general data-driven based similarity-based approach was proposed by [PERSON] et al. [22] to predict the RUL of the electromagnetic relay. In addition, the similarity-based approach which was based on the framework of CBR was used for the fight trajectory prediction [23], pan-Arctic and regional sea ice area and volume anomalies prediction [24], and so on. Although STM can effectively use the trajectory of historical data to predict the life of the equipment, the original monitoring data were usually smoothed to reduce the impact of random fluctuations on the similarity measurement [25]. However, for multiple operating conditions, the monitoring data cannot be smoothed effectively to extract the degradation trend due to the influence of operating conditions (the detailed description was employed in Section 4.3).