Robust stochastic configuration networks for industrial data modelling with Student’s-t mixture distribution

Data collected from industrial sites commonly contains outliers or noise that obey unknown distributions, making it challenging to establish an accurate data-driven model. Therefore, this paper proposes a novel robust stochastic configuration network based on a Student’s-t mixture distribution (termed as SM-RSC). Firstly, a stochastic configuration algorithm is employed to determine the number of hidden nodes, the input weights and biases. Secondly, the maximum a posteriori (MAP) estimate is used to evaluate the output weights of the SCN learner model under the assumption that outliers or noises obey the Student’s-t mixture distribution. Because the output weights cannot be solved directly due to the unknown hyper-parameters of the mixture distribution, we apply the well-known expectation–maximization (EM) algorithm for optimizing the hyper-parameters of the mixture distribution and update the output weights iteratively. The proposed algorithm is evaluated by a function approximation, four benchmark datasets, and a case study on industrial data modelling for a waste incineration process. The results show that SM-RSC performs favorably compared with other methods.