As crucial mechanical components, predicting the remaining useful life (RUL) of bearings holds significant importance. The current data-driven methods have made substantial progress in this domain. However, data-driven approaches require substantial quantities of high-quality data to train efficient RUL prediction models. Nevertheless, each client places a premium on the privacy protection of their data, making direct data sharing impractical. To address this issue of data isolation, a federated learning-based RUL method is proposed. In this method, each client employs their local data to train identical Convolutional Autoencoder (CAE), which consists of an encoder and a decoder. After CAE training is completed, all client encoders are uploaded to the server for aggregation. To mitigate the impact of low-quality data on the overall model performance, a dynamic weighted validation strategy is proposed. On the server, this strategy aggregates an optimal global encoder based on the performance of different encoders on the validation dataset. This global encoder is then distributed to each client for feature extraction, and the extracted features are uploaded to the server for training the RUL predictor. Experimental results using a novel dataset demonstrate that the proposed method offers a promising solution for distributed RUL prediction.