Small Sample Inference Method For Variable Load Of Building Structure

When determining the statistical characteristics and the variable load representative value of wind,snow,floor live load,etc.,most studies usually uses classical statistical inference method in our country,which is large sample inference method with sufficient data.However,the wind or snow load data is actually not in line with the requirements of a large sample of statistics in some areas.According to the historical data to infer the variable load representative value of specific area or specific structure,the load data has a limitation.In this condition,the traditional large sample method might have an aggressive inference results due to the statistical uncertainty.For a constant load that follows normal distribution,a small sample inference method has been proposed in the reliability identification of existing structures.For the variable load which follows maximum type I distribution,there is no corresponding inference method.Given the importance of variable loads in structural design and reliability control,it is necessary to establish a small sample inference method for variable load representative value.This paper established a small sample inference method for variable load representative value by solving the basic problems about wind,snow and floor live load in statistics.The main study contents include:(1)Linear-regression estimation method with the parameter-free for maximum type I distribution parameters and fractile.According to the basic principle of optimal linear unbiased estimation and invariant estimation of the minimum type I distributionparameters and the fractile,the linear-regression estimation method for maximum type I distribution parameters and fractile has been proposed,which lays the foundation for the establishment of linear-regression estimation method for variable load representative value.(2)Linear-regression estimation method with known coefficient of variation for maximum type I distribution parameters and fractile.Using the basic principle of linear-regression estimation method and Monte Carlo numerical simulation method to build the linear-regression estimation method with known coefficient of variation for maximum type I distribution parameters and fractile,which lays the foundation for establishment of linear-regression estimation method for variable load representative value with known coefficient of variation.(3)Linear-regression estimation method and statistical analysis for wind and snow load representative value.Using linear regression estimation method for maximum type I distribution parameters and fractile to build the linear-regression estimation method for wind and snow load representative value under the condition of parameter-free and known coefficient of variation respectively.According to the measured small sample data,the standard value of wind and snow load in some typical areas are re-inferred,meanwhile,the influence of statistical uncertainty on the inferred result is revealed.(4)Linear-regression estimation method for floor live load standard value.Floor live load consists of persistent and temporary floor live load,which is a function random process in essential and totally different from wind and snow load.The linearregression estimation method of the floor live load standard value is established by fitting the parameters of the floor live load model and using the linear-regression estimation method of maximum type ? distribution parameters and fractile simultaneously.(5)Jeffreys non-information prior distribution for extremum type I distribution parameters.Although the above-mentioned methods solves the estimation problem of variable load representative value under the small sample condition,the convenience of the application needs to be improved.In order to establish a practical Bayesianinference method of variable load representative value under the small sample condition,the Jeffreys non-information prior distribution for maximum type I distribution parameters of Bayesian inference should be established at first.According to the the Fisher's information matrix provided by Jeffreys,the maximum type I distribution parameters of Jeffreys non-information prior distribution are established,which lays the foundation for establishment of Bayesian small sample inference method for variable load representative value.Furthermore,it can establish the Jeffreys non-information prior distribution of the minimum type I distribution parameters and extend the application of Bayesian inference method in statistics.(6)Bayesian small sample inference method for variable load representative value.According to Bayesian theory,this study uses Jeffreys non-information prior distribution of maximum type I distribution and the joint probability density function of simplified samples to establish Bayesian inference method for wind,snow load and floor live load standard value under small sample condition.This thesis proposes two kinds of small sample inference methods for variable load representative value named linear-regression estimation method and Bayesian inference method separately.The former is more accurate,while the latter is more simple to use and has a wider range of application.The study results fill the current gap of the small sample inference method for variable load representative value,it also solves some basic statistical problems,such as linear-regression estimation of maximum type I distribution parameters and fractile and Jeffreys non-information prior distribution for extremum type I distribution.The results promote the development of statistics and the application of statistics in engineering structure.