Construction of prediction intervals for carbon residual of crude oil based on deep stochastic configuration networks

Complex components lead to large fluctuations in the physicochemical properties of crude oil which make accurate prediction more difficult. To quantify the potential uncertainty associated with prediction, this paper proposes a novel approach to construct prediction intervals (PIs) for the carbon residual content of crude oil based on the lower-upper bound estimation (LUBE) method and deep stochastic configuration networks (DSCNs). According to the principle of stochastic configuration networks, the input weights and biases of DSCN are randomly assigned with a supervisory mechanism and only the output weights need to be evaluated which can greatly reduce the number of parameters to be optimized. Then, combining the coverage width-based criterion and mean accumulated width deviation, a new cost function of DSCN for constructing PIs based on the LUBE method is proposed to center the mean values of the PIs as near as possible to the targets, hence the average of lower and upper bounds of the PI is calculated as the deterministic output, which can solve the problem that the PIs based on the original LUBE method cannot provide the deterministic prediction. Moreover, a modified backtracking search optimization algorithm, improving the population diversity and increasing the search capability while maintaining the convergence speed, is presented to obtain the optimal PIs. Finally, experiments using real-world data are carried out and the results demonstrate that the proposed approach can construct PIs with high quality.