An Interpretable and Adaptive Robust Neural Network Modeling Method Based on Dual Gaussian Mixture Distribution

Industrial process data are often contaminated by mixed noise interference. Traditional robust modeling methods based on single heavy-tailed distributions exhibit certain limitations in both accuracy and interpretability when dealing with mixed noise problems. To address these issues, an interpretable robust adaptive modeling method based on a mixed dual Gaussian distribution is proposed. First, the proposed method begins by constructing a base learning model by using the stochastic configuration network (SCN) framework to determine the number of hidden nodes, input weights, and biases. Secondly, to ensure robustness against mixed noise, a noise characterization model is established through a weighted combination of dual Gaussian distribution with large and small variances. And then the expectation-maximization algorithm is employed to adaptively and iteratively learn both the output weights of the SCN and the parameters of the Gaussian mixture model, ultimately forming the robust stochastic configuration network model based on dual Gaussian distribution. The proposed method offers two main advantages: The noise model can approximate the characteristics of actual mixed noise through adaptive parameter learning, where the large-variance Gaussian component handles coarse approximation of anomalous noise while the small-variance Gaussian component achieves fine-grained characterization of dominant noise, thereby enhancing interpretability; During the estimation of network output weights, the model ensures robust performance by adaptively assigning penalty weights to each output data point. To validate the effectiveness of the proposed method, multiple comparative experiments are conducted on function approximation, benchmark datasets, and an industrial case study. The results consistently demonstrate that the proposed method achieves satisfactory reliability and practicality.