Improved Sequential Kriging-monte Carlo Simulation Reliability Analysis Methods And Their Applications To Ship Structural Design

Uncertainties are inevitable factors during the processes of designing,manufacturing,and sailing of a ship structure.How to design a new ship structure that satisfying the reliability requirements under various random uncertainties is a critical problem.Therein,the core bottleneck is to evaluate the time-consuming highly non-linear black-box integral problem for calculating the failure probability.The estimated accuracies of the traditional approximation-based methods(such as First-/ Second-order reliability methods)are hard to be guaranteed because of the limitation of approximated orders.Meanwhile,the simulationbased approaches need tremendous samples to obtain an accurate estimation of failure probability,which encumbers their usage in the engineering domain.Recently,the activelearning(sequential,adaptive)Kriging-based approaches for structural reliability analysis have been widely investigated by researchers as they have great potential to reduce computational resources while maintaining estimated accuracy.To be specific,those approaches establish an initial Kriging model based on several samples in the design space to replace the costly simulation process.Then,the Kriging model is refined by adding new samples around the limit state through a specific learning function,in that case,the final Kriging model can provide the right safe/failure status prediction of any sample in the design space.In this thesis,the aim to improve the efficiency of active-learning Kriging-based methods for structural reliability analysis,and the investigations are elaborated as follows:(1)Firstly,a new learning function called Reliability-based Lower Confidence Bounding(RLCB)and an error-based Stopping Criterion using Bootstrap confidence estimation(BSC)were developed to overcome the shortages of the single-fidelity activelearning Kriging-based approaches for a component.The RLCB learning function considers the predicted uncertainty,statistical information of design variables,and the distribution of samples In this case,the new sample with the largest improvement to the limit state could be determined by minimizing the RLCB learning function.The BSC stopping criterion was derivated by quantifying the predicted uncertainty of the Kriging model in the failure probability.Therefore,the active-learning process of the proposed BSC+RLCB algorithm can be halted under a pre-determined predicted relative error threshold.Results based on four numerical examples show that the proposed BSC+RLCB algorithm is superior to state-ofthe-art approaches because it saves about 10%～50% computational burden while converging to the given accuracy level.(2)Secondly,to facilitate the usage of the multi-fidelity(MF)Kriging model in the structural reliability analysis domain,two active-learning MF Kriging-based approaches,i.e.,BSC+AEF algorithm and MF-BSC-Believer algorithm,were proposed.In the BSC+AEF algorithm,the original efficient feasibility(EF)function was extended to the MF scenario by considering the efficient feasibilities and cross-correlation of different fidelities,cost function,and sampling density.The location and fidelity of the update sample could be ascertained by maximizing the augment EF(AEF)function.In the MF-BSC-Believer algorithm,a twophase algorithm was introduced to determine the location and fidelity of the update sample separately.Specifically,the location of the update sample was determined by minimizing the RU learning function(a revised version of the RLCB learning function),then an extra BSCBeliever strategy was proposed to determine the fidelity of the update sample objectively in light of reducing the more estimated relative error of failure probability.The efficiency of the proposed two MF Kriging-based algorithms was demonstrated by several numerical examples,and those two approaches were excellent supplements to the method library.(3)Thirdly,to handle the tricky system structural reliability problem whose safe/failure state is determined by several limit state functions simultaneously,the SRU learning function and SBSC stopping criterion were developed according to different uncertainty coupling relationships of the series and parallel systems.The location and index of the component for the update sample can be determined simultaneously by minimizing the SRU learning function.Meanwhile,the proposed SBSC stopping criterion also could terminate the activelearning process for system structural reliability analysis under the desired accuracy.Results show that the proposed SBSC+SRU algorithm could converge to the real failure probability effectively and it could save about 5%～10% computational resources compared with recently reported approaches for system problems.(4)The proposed approaches for component and system structural reliability analysis were applied to solve two realistic engineering problems which were the structural reliability analysis of global stability of a ship deck grillage and component/system reliability analysis of an underwater cylindrical shell with variable ribs.Results show that the proposed approaches had excellent performances when dealing with engineering problems.The proposed approaches improved the efficiency and effectiveness of the traditional active-learning Kriging method for structural reliability analysis.The proposed methods in this thesis enriched the technical means of structural reliability analysis methods,and provided new solutions and valuable references for the reliability analysis of ship engineering structures and the design of ship engineering structures considering reliability.