This paper develops a long-term time series prediction model based on echo state networks for health monitoring. Convolutional dynamics are built by extending randomly connected reservoirs to convolutional structures in the input-to-state transition. Also, a new particle swarm optimization-gravitational search algorithm is put forward to make the convolutional reservoir near the chaotic edge, in which memory information-based decision-making and lèvy flight random walk are utilized to improve its local and global search capabilities, respectively. Finally, the validity of the model is verified by the real health index data set. The experiment illustrates that the system can exhibit powerful computing ability by adopting the evolutionary algorithm close to the chaotic edge. These results also show that our proposed algorithm exceeds the test error of the least squares support vector machine by 50% on average.