| With the refinement of the engineering research,the influence of the uncertainty factors on system reliability analysis is increasingly important.There is an urgent need to develop an analytical method that can solve the engineering reliability problems efficiently and accurately while considering the influence of uncertainties.To balance the contradiction of the efficiency and accuracy,this paper makes a systematical research on the current sampling methods based on the probabilistic model and then proposes an improved method for satellite reliability analysis.Firstly,the existing reliability analysis methods based on sampling simulation are studied.A brief introduction is made to the widely used Monte Carlo Simulation(MCS)method,including its principle,convergence speed and the factors that affect the convergence precision.The principle of the improved importance sampling method based on MCS and how to choose the important sampling density function are studied.They are the foundation of the following research.Secondly,based on the research of the Most Probable Point(MPP)-based Importance Sampling(IS)and the First Order Reliability Method(FORM),an improved method for reliability analysis is proposed.FORM is a quite simple and efficient method.In this paper,an improved sequential reliability approach combining FORM and MPP-based IS in critical region is proposed.Based on the MPP-based IS,the samples in the region outside the ?-sphere is further divided into three parts,namely the critical region,the unimportant region and the assured failure or safe region.Only the samples located in the critical region need the calls to the actual performance function,while the samples located in the other two regions can be directly analyzed by linear approximation.The key of the proposed method is how to reasonably determine the critical region.In this paper,an iterative algorithm is proposed,which sets the convergence condition according to the accuracy and efficiency requirement of reliability analysis and balances the efficiency and accuracy by gradually expanding the critical region until convergence.Thirdly,the proposed approach is validated by some numerical examples and applied to a satellite first-order frequency reliability analysis problem.The proposed method is tested by numerical examples with probabilistic convexity and concavity respectively,including the feasibility verification and the realization of the method.The parameters of the algorithm which has the great influence on the calculation accuracy and efficiency are discussed in detail.Moreover,the actual “Tian Tuo-3” satellite support structure is analyzed by using the proposed method,which verifies the practical value of the method.Finally,based on the improved sampling reliability analysis method in this paper,the collision probability of space target under uncertainties is studied.Considering the uncertainties of spacecraft initial state(position and velocity)and disturbance during flight,the collision probability of spacecraft caused by trajectory deviation is analyzed.Compared to the traditional MCS,the proposed method can achieve a comparable result,while the computational cost is greatly reduced,which verifies the applicability of the method.To sum up,a relatively comprehensive study on probabilistic reliability analysis method considering uncertainties is studied in this paper.Based on the widely used methods of FORM and MPP-based IS,an improved method which combines the advantages of the two methods is proposed for reliability analysis,which can effectively balance the accuracy and efficiency of reliability analysis in engineering.The proposed method is applied to the reliability analysis of a satellite structure and the collision probability analysis of spacecraft,which verifies its validity and applicability.What's more,the proposed method is universal,which means it can applied not only to the satellite system,but also to the reliability analysis of other systems. |
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