非平稳非高斯随机过程插值模拟方法

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关键词：随机振动；非高斯随机过程；非平稳；演变功率谱；随机谐和函数 中图分类号：O324；TU311.3 文献标志码：A DOI：10.16385/j.cnki.issn.1004-4523.202309035

Abstract：Toaddresstheproblemsoflargenumberofrandomvariablesandtime-consumingcomputationinthesimulationof non stationary non-Gausianstochasticprocesss，afastcomputatiomethodofnonstatioaryno-Gausianstochastic proceeispro posedbasedonsampleinterpolationbycombiningthestochasticharmonicfunction.Withtheknownofthetargetevolutionarypow er spectrumandtarget densityfunctionofnon-Gaussianstochastic process，thecorelation function equations ofnon-Gausian stochasticprocessesandunderlyingGausianstochasticprocessareestablishedthroughMehler’sformula，andafastcalculation methodfor theevolutionarypower spectrumofuderlying Gausianstochastic proceses isproposed through interpolationmethod. Subsequently，afastsimulationmethodfornonstationary nonGausianstochastic procesesisproposedbycombiningstohastic harmonicfunctions，Theefectivenessof this methodisverifiedbysimulatingsingle-pointuniformlymodulatednon-Gaussiansto chastic processandmultipointnonuniformlymodulatednon-Gausianstochasticprocesses.Theresultsshowthat，whencalculat ingtheevolutionary powerspectrumoftheunderlying Gaussanrandomprocessunder theconditionofensuringaccuracy，thecalcu lationtimeofiterpolationsolutionislowerthanthatofMehler’sformulasolution，andasthenumberofexcitationsinceass，the eficiencyof interpolationsolutionincalculatingtheevolutionarypowerspectrumof theunderlyingGaussianrandomprocessis moreobvious.Theproposedfastcomputationalmethodofnon-stationarynon-Gausianstochasticprocessescanefectivelysimu late the non-Gaussian stochastic processes with the target evolutionary power spectrum and the targetdensity function.

Keywords：randomvibration；non-Gausianstochasticproceses；non-stationary；evolutionarypowerspectrum；stochastic harmonic functions

工程结构在服役期间所遭受的荷载具有非高斯 特性的现象，如地震[1]、风压[2]和火箭起飞的振动环境[3]等逐渐引起研究者关注。（剩余18921字）