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　algo-rithm　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.(c)　2022　Elsevier　Inc.　All　rights　reserved.