There are many ways for gas (or high-pressure hazardous liquid) be transferred from one place to another. However, pipelines are considered as the fastest and the cheapest means to convey such flammable substances, for example natural gas, methane, ethane, benzene, propane and etc. Unavoidably, the pipelines may be affected by interference from third parties, for example human error while under its operation. Consequently, any accidental releases of gas that may occur due to the failure of the pipeline implies the risk that must be controlled. Therefore, it is necessary to evaluate the safety of the pipeline with quantitative risk assessment. Relative mass released of the leakage is introduced as the input for the simulation model and the data from the simulation model is taken at real time (on-line) to feed into the recursive algorithms for updating the linear weight. Radial basis function (RBF) is used to define the non-linear weight of the partial linear network. A new learning algorithm called the ensemble dual algorithm for estimating the mass-flow rate of the flow after leakage is proposed. Simulations with pressure liquid storage tanks problems have tested this learning approach. © 2011 Springer-Verlag Berlin Heidelberg.