自动化学报2026，Vol.52Issue(3)：463-480,18.DOI:10.16383/j.aas.c250602
基于双高斯分布混合的可解释自适应鲁棒神经网络建模方法
An Interpretable and Adaptive Robust Neural Network Modeling Method Based on Dual Gaussian Mixture Distribution
摘要
Abstract
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 mod-el 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 advant-ages:The noise model can approximate the characteristics of actual mixed noise through adaptive parameter learn-ing,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 inter-pretability;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.关键词
随机配置网络/双高斯分布混合/鲁棒建模方法/期望最大化算法Key words
stochastic configuration network/dual Gaussian distribution mixture/robust modeling method/expecta-tion-maximization algorithm引用本文复制引用
刘鑫,李琪琪,代伟..基于双高斯分布混合的可解释自适应鲁棒神经网络建模方法[J].自动化学报,2026,52(3):463-480,18.基金项目
国家自然科学基金(62573417,62373361,U24A20272),江苏省自然科学基金(BK20252089,BK20240102),中国博士后科学基金(2023M743776,2024T171003),江苏省研究生科研与实践创新计划(SJCX25_1396),中国矿业大学研究生创新计划(2025WLJCRCZL117)资助Supported by National Natural Science Foundation of China(62573417,62373361,U24A20272),Natural Science Foundation of Jiangsu Province(BK20252089,BK20240102),China Postdoctor-al Science Foundation(2023M743776,2024T171003),Postgradu-ate Research&Practice Innovation Program of Jiangsu Province(SJCX25_1396),and Graduate Innovation Program of China University of Mining and Technology(2025WLJCRCZL117) （62573417,62373361,U24A20272）
