A novel multi-step interval prediction model for uncertain data using iterative lower upper bound estimation method

For complex systems, most sensor data are biased, resulting in low accuracy of multi-step prediction results. Based on the lower upper bound estimation (LUBE) method, this paper proposes a multi-step iterative interval prediction model suitable for interval input, which not only maintains the simple structure of the original model, but also realizes single-step and multi-step prediction point (PP) and prediction interval (PI) in different fields. Firstly, an iterative LUBE (ILUBE) network structure, characterized by interval-valued inputs and outputs, is constructed. Secondly, according to this structure, a set of multi-step interval performance indicators are redefined, and a new indicator linear decrease multi-step prediction interval normalized center deviation (LMPINCD) is proposed to measure the prediction horizon, which is added to the multi-step coverage width-based criterion (MCWC). Finally, because MCWC is a non-analytic function, the particle swarm optimization (PSO) meta-heuristic optimization algorithm is used to find the optimal parameters of the ILUBE model. The performance of the model is evaluated using real wind speed and power load datasets. The experimental results show that the model is superior to all other benchmark models in multi-step PI, and also achieves good results in multi-step PP.