Active Learning Kriging Method Based On Distance Constraint Strategy And Its Engineering Application

There are many uncertain factors in engineering.The generation of reliability theory is to study uncertain factors.At present,the main research direction of reliability analysis methods is to reduce the number of performance function evaluation and to improve the calculation accuracy of failure probability.In actual engineering,the performance function is generally a complicated implicit function of the random variables.The First-order Second-moment method(FOSM)is a commonly used reliability analysis method,but it is difficult to solve for some highly nonlinear performance functions and the precision is unsatisfactory sometimes.Although Monte Carlo Simulation(MCS)is applicable to any form of performance function,its main disadvantage is that the calculation is costly and time-consuming.In recent years,the surrogate model method has attracted attention.Using the surrogate model instead of the actual performance function for reliability analysis can improve the computational efficiency as well as accuracy.The main content of this paper can be summarized as follows:1.Introduction to the basic theories of engineering structural reliability is given,such as reliability,probability of reliability,random variables,limit state,failure probability and reliability index.Introduction to the methods of reliability analysis is also given,including the traditional first-order second-moment method,the Monte Carlo Simulation,and the surrogate model method,which is now widely studied.Quadratic polynomial is usually used to construct performance functions in the traditional response surface method(RSM).It is difficult to construct the implicit limit state surface with high nonlinearity by traditional RSM.At the same time,RSM is sensitive to the selection of sampling center and sampling method.The Kriging surrogate model method is more accurate and efficient than the traditional RSM.The work of this paper is based on the Kriging surrogate model.2.The Kriging surrogate model can provide not only the mean of the predicted points,but also their corresponding variances(estimations of the prediction uncertainty).This particular feature of the Kriging model is very suitable for establishing the“gradual approximation”active learning mechanism.The active learning Kriging method is a method combining Kriging and Monte Carlo Simulation for reliability analysis--AK-MCS,which actively selects sample points based on the learning function U.AK-MCS can be seen as a modification of the classic Monte Carlo Simulation.This method has good applicability for complex problems such as highly nonlinear performance functions,system reliability and multiple design points.However,because of the large number of candidate sample population,the best sample points selected may be close to one another,resulting in information redundancy.An active learning Kriging method based on distance constraint strategy is proposed in this paper by introducing minimum distance constraint.This method can significantly reduce the number of function calls and achieve higher calculation accuracy.3.Because of many influencing factors and uncertainties of slope stability,the traditional stability analysis method(safety factor method)cannot accurately express the possibility of slope damage.The strength reduction method continuously reduces the strength of the rock and soil,and the rock-soil body will be destroyed when the shear strength cannot resist the shear stress.The corresponding most dangerous sliding surface of the rock-soil body and the safety factor can then be obtained.In this paper,the strength reduction method is used to analyze the slope stability.Through the data interaction between MATLAB and FLAC~3DD software,the reliability analysis methods such as AK-MCS and AK-MDS are introduced into the slope stability analysis.The reliability analysis of slope stability is carried out by calculating the probability of slope failure.This method makes the analysis and evaluation of slope stability more comprehensive.Several types of slope examples show that that the AK-MCS method can obtain higher precision results than the traditional response surface method,but its efficiency is slightly poor.The proposed AK-MDS method has good applicability in the slope stability reliability analysis,which can obtain satisfactory calculation accuracy and high computational efficiency.