Abstract: To monitor the running state of hydraulic equipment online and in real-time by using new, sequentially input samples, we propose an online kernel extreme learning machine (OL-KELM) algorithm. OL-KELM applies Cholesky factorization to extend the kernel extreme learning machine (KELM) from offline mode to online mode. Unlike KELM, OL-KELM can complete the training recursively on the basis of new samples. The learning efficiency is improved by replacing the matrix inverse operation with arithmetic in OL-KELM. Simulations of the online prediction for the chaotic time series show that OL-KELM can achieve the same accuracy as KELM with 40% to 60% less training time. Results of the online and real-time monitoring of a hydraulic pump by OL-KELM show that OL-KELM is robust, with a prediction error 28.3% to 46.2% of SRELM (sequential regularized extreme learning machine). OL-KELM is proved effective for online, real-time monitoring of hydraulic equipment.