Research On Forecasting Method Of Spatiotemporal Dynamic Deformation Under The Condition Of Deficient Information And Small Sample Data Set

The main research purpose of this paper is modeling and forecastingspatiotemporal dynamic deformation system characterized by deficient informationand small sample. In order to detect multi-dimensional gross error in deformation dataunder the condition of small sample and unknown probability distribution, a greyenvelope curve is constructed. GM (1,1)(GM) model is adopted to establish asingle-point deformation forecasting model. In order to make the GM (1,1) modelmore precise and adaptive, the quantity of deformation information is taken intoaccount, and a single-point forecasting model group is established. Therefore twoaspects are employed to improve its performance, including integration equation usedto eliminate the error term resulted from the conventional calculation of backgroundvalue method and the nthcomponent of x(1)assumed to be initial condition of GMmodel based on latest information priority principle. Then, a dual optimization modeladapted to various deformation status is proposed. With consideration of correlationof monitoring points, the multi-point spatial deformation forecasting model isdeveloped. The structure form of combined model of deformation is analyzed anddefined for the first time, and series and parallel combination model is alsodemonstrated. The semi-parametric model is introduced to deal with the model error(ME) stemming from deformation forecasting model, according to penalized leastsquares. The estimators of ME are then derived and the selection of smoothingparameter α and regular matrix R upon solving are further discussed.Function Xu (α), a new model for determiningα, is developed and the effectivenessof semi-parametric model in dealing with ME is also confirmed.