Application Of Robust Regression Analysis Method In Deformation Monitoring

Morden error theory argues that, in data of scientific experiments and production practices, appearing of gross error is unavoidable. In order to acquire correct result of deformation analysis, appropriate methods should be used to detect and reject gross errors. The approach to eliminate gross errors is generally divided into two categories:one is to reject the contaminated observations by statistical test first, then to process the remaining data; another is to view the contaminated observations as abnormal variance, and to use robust estimation methods, which classify gross error as stochastic model, and eliminate the effect of gross error on result by determining weights. The selection of weight function is kernel of robust estimation. Therefore, many scholars presented the different forms of weight functions, and constructed many robust estimation methods, but the capabilities of these methods are different. Taking simple linear regression and some level networks with different structure and total reliability, this paper uses repeated experiments based on program developed by VC++.NET to compare the capabilities of 14 robust estimation methods, and confirms several relative more efficient methods for simple linear regression and special forms of level networks, as well as the relationship between capabilities of these methods and observations. The simulation experiments show that, for simple linear regression, when observations contain one gross error also the number of observations is less than or equal to 3, or when observations contain two errors also the number of observations is less than or equal to 5, various robust estimation methods have failed to eliminate or weaken the effect of gross errors on parameter estimation. When observations contain one gross error, if the number of observations is 4-6, L1 method and Geman-McClure method are two more effective robust estimation methods; if the number of observations is 7-12, all the robust estimation methods can effectively eliminate the effect of gross error on parameter estimation. When observations contain two gross errors, if the number of observations is 6-8, L1 method and Geman-McClure method are two more effective robust estimation methods; if the number of observation is 9-12, L1 method, Danish method, Geman-McClure method and IGGâ…¢scheme are four more effective robust estimation methods.For height control networks, the capabilities of robust estimation methods are connected with total reliabilities and structures of height control networks. When observations contain one gross error, if total reliability is greater than 0.4 and less than 0.5, L1 method and Geman-McClure method, to some extent, can eliminate the effect of gross error on adjustment system; if total reliability is equal to 0.5, L1 method and Geman-McClure method can completely eliminate the effect of gross error on adjustment system; if total reliability is greater than 0.5 and less than 0.6, Danish method and IGGâ…¢scheme can also eliminate effectively the effect of gross error on adjustment system; if total reliability is greater than or equal to 0.6, all methods can eliminate effectively the effect of gross error on adjustment system. When the observations contain two gross errors, if total reliability is less than 0.5, all the robust estimation methods can not eliminate the effect of gross errors on adjustment system; if total reliability is greater than or equal to 0.5, except for the level networks shaped as geodetic quadrangle, L1 method and Geman-McClure method can effectively eliminate the effect of gross errors on adjustment system.