The　belief-rule-base　(BRB)　inference　methodology　using　the　evidential　reasoning　(ER)　approach　is　widely　used　in　different　fields,　such　as　fault　diagnosis,　system　identification,　and　decision　analysis.　However,　the　calculation　characteristic　of　the　conventional　rule　activation　weight　makes　the　inference　system　have　the　rule　zero　activation　problem.　The　difficulty　of　constructing　partial　derivatives　restricts　the　optimization　of　parameters　using　the　gradient　method.　Hence,　this　paper　proposes　a　new　belief　rule　structure　and　its　gradient　training　method　to　solve　the　rule　zero　activation　problem　during　the　inference　process　and　improve　inference　accuracy.　The　Gaussian　function　is　applied　to　calculate　the　activation　weight　of　the　rule　with　the　new　structure.　Its　characteristics　avoid　the　zero　activation　problem　caused　by　the　attribute　reference　value　set　in　the　original　method.　Based　on　the　newly　proposed　method,　the　corresponding　distance-sensitive　parameter　is　set　for　each　attribute,　and　the　weight　parameter　of　each　rule　is　discarded.　It　simplifies　the　calculation　of　rule　activation　weights　in　the　inference　process　and　enables　the　partial　derivatives　of　the　parameters　of　the　inference　system　to　be　easily　constructed.　In　the　parameter　optimization,　the　momentum　optimization　gradient　stochastic　descent　method　is　used　to　train　the　new　BRB　system,　which　improves　the　training　speed　and　accuracy　compared　with　the　conventional　methods.　Experiments　with　nonlinear　function　fitting,　oil　pipeline　leak　detection,　and　classification　of　several　public　datasets　are　carried　out　to　verify　whether　the　new　BRB　system　trained　with　momentum　stochastic　gradient　descent　(SGDM-BRB)　has　better　performance　than　other　conventional　methods.　The　experimental　results　show　that　in　the　case　of　complete　data,　SGDM-BRB　has　higher　accuracy　and　faster　training　speed　than　the　conventional　methods.　©　2013　IEEE.