Abstract: ThemethodbasedontheSimplexB-splinefunctionhasbeenproposedtoreducethefittingerrorandcomplexity，whichcanalsoimprovethereal-timecharacteristicsinsteady-statemodelingofanaero-en.gine.Asthefunctioniscomprisedoflocalpolynomialbasisfunctions，linearregressionandgeneralizedleastsquaresmethodcanbeappliedtosolvetheBcoefficients.Inthisway，thecomputingefficiencyandtheaccura.cyofthemodelaresignificantlyimproved.Atlast，themodelverificationresultswiththisnewmethodarecom.paredwiththatofmuti-inputmuti-outputrecursivereducedleastsquaressupportvectorregression(MRR-LSS.VR)intwo-andfour-dimensionalsteady-statemodellingoftheturbofanengine，respectively.Itshowsthatthenewmodelingmethodhasalowercomplexity，lessdatacapacityandhigherperformanceofinstantaneity.Fur.thermore，itcanovercometheshortcomingsofMRR-LSSVRthatcannotwellbeappliedforlargesamplesets.Moreover，whilefittingdiscretesamples，itwillbebetterthanMRR-LSSVR.

Key words: SimplexB-splines；Leastsquaressupportvectorregression；Steady-statemodelingoftheturbofanengine；LinearRegression；LeastSquares

摘要： 为了减小航空发动机稳态建模的模型误差、降低复杂度及提升其实时性，提出了一种基于单纯B样条函数的航空发动机稳态模型建模方法。该函数是局部多项式基函数的线性组合，因此求解该函数为线性回归问题，通过运用广义最小二乘方法来求解B系数，从而提高计算效率和提高模型精度。最后建立了基于该算法的二维和四维涡扇发动机稳态模型，并分别与相同建模样本条件下的多输入多输出约简迭代最小二乘支持向量机稳态模型进行了比较，表明了单纯B样条建模方法不仅继承了B样条的算法复杂度低、存储数据量小和实时性好等优点，同时避免了最小二乘支持向量回归机不能拟合大样本数据的缺点，且拟合效果优于最小二乘支持向量机。

关键词: 单纯B样条；最小二乘支持向量回归机；航空发动机稳态建模；线性回归；最小二乘中图分类号:V2331文献标识码:A文章编号:1001-4055(2015)12-1887-08DOI:10.13675/j.cnki.tjjs.2015.12.019