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For solving the problem that extreme learning machine (ELM) algorithm uses fixed activation function and cannot be residual compensation, a new learning algorithm called variable activation function extreme learning machine based on residual prediction compensation is proposed. In the learning process, the proposed method adjusts the steep degree, position and mapping scope simultaneously. To enhance the nonlinear mapping capability of ELM, particle swarm optimization algorithm is used to optimize variable parameters according to root-mean square error for the prediction accuracy of the mode. For further improving the predictive accuracy, the auto-regressive moving average model is used to model the residual errors between actual value and predicting value of variable activation function extreme learning machine (V-ELM). The prediction of residual errors is used to rectify the prediction value of V-ELM. Simulation results verified the effectiveness and feasibility of this method by using Pole, Auto-Mpg, Housing, Diabetes, Triazines and Stock benchmark datasets. Also, it was implemented to develop a soft sensor model for the gasoline dry point in delayed coking and some satisfied results were obtained. [ABSTRACT FROM AUTHOR]