The Significance Test And Effect Analysis Of Functional Parameters

Functional parameters refer to those parameters that are externally represented as a series of discrete points and whose inherent nature is functional.Because of the uniqueness of the functional parameters,the significance test should be divided into two categories,one is the overall significance,one is the overall significance,including the significance of the main effect and the interaction effect,and the second is the piecewise significance.Previous researches mostly involved the overall significance test,while ignoring the simultaneous observation of the two aspects of integrity and segmentation.In response to the above problems,this thesis has mainly studied from the following three aspects:(1)Aiming at the overall significance test criterion of functional parameters,the method of variance analysis with no requirement for input parameter types is selected.Firstly,the basis function expansion method is used to transform the discrete functional sampling points into continuous functional curves to further divide the horizontal number.Secondly,the observed values are classified according to the level of the influencing parameters,and the original hypothesis of the main effects and their interaction effects of each parameter are established.Finally,the level of the significance test is given,and the significances of the main effect and interaction effect of each parameter are judged by the criterion of variance analysis.(2)Aiming at the piecewise significance test criterion of functional parameters,the significance is evaluated from the perspective of independent variables referenced by functional parameters.Firstly,the data analysis of the functional parameters is carried out,which based on the functional principal component analysis.Then,the sequence of principal components causing variation is obtained,and the significance of each principal component at different time intervals is determined according to the effect diagram of the main components deviating from the mean.Secondly,cluster analysis is used to cluster the principal component scores of each sample to classify the categories of the functional curves.Further,the graph of F statistics is obtained by using functional ANOVA,and the significances atdifferent time intervals are judged by comparing with the critical value of a given significance level.Finally,the feasibility of the proposed method can be verified by comparing the analysis results of the two methods mentioned above.(3)Aiming at the overall significance test criterion and the piecewise significance test criterion of the functional parameters mentioned in this thesis,empirical studies and simulation studies are carried out respectively.Firstly,the applicability of the proposed method is verified by introducing a complex higher-order simulation function.Secondly,the injection process of a green slope system fastener is studied by using the proposed method,which includes two scalar parameters and a functional parameter.Then,scalar parameters,functional parameters and the interaction between the two have been identified,and the piecewise significant test is carried out on the functional parameters with significant influence.Thus,the significant time intervals are determined.In this thesis,the overall significance test criterion and the piecewise significance test criterion of functional parameters are presented,and the basic ideas,key problems and steps of the corresponding methods are also given.The applicability of the proposed methods is verified by empirical and simulation studies.