Research On A Class Of Self-adaptive Solution And Efficient Optimization Algorithms For Structural Reliability Design

With the increasingly complex structure of mechanical products,the increasingly severe service environment and the continuous improvement of performance index requirements,the problem of product reliability reduction or even premature failure of product functions caused by uncertain factors has become more and more prominent.In response to this prominent problem,implementing reliability-based design optimization(RBDO)of mechanical products in the design stage has been proved to be a crucial tool to ensure the reliability of mechanical products and reduce maintenance costs.However,the theory of RBDO is still not mature and perfect at present,and there are still many problems in the RBDO of complex mechanical products,such as low computational efficiency and poor robustness when solving reliability index and performing inverse reliability analysis,no invalid constraint elimination strategy and efficient approximate model updating method when solving RBDO problems with implicit objective function or constraint functions,and the lack of efficient decoupling strategies for solving time-variant RBDO problems,etc.This paper conducts in-depth research on the above problems,and strives to provide effective assistance for perfecting RBDO theory and solving RBDO problems of complex mechanical product.Based on first-order reliability method,the efficient and robust RBDO of structure discussed in this paper is carried out from two aspects:time-invariant RBDO and time-variant RBDO.The main works are completed as follows:(1)A double-loop RBDO method based on adaptive finite-step length method is proposed.In order to obtain reliability indexes efficiently an d robustly to solve RBDO problems of complex mechanical products,a double-loop RBDO method based on adaptive finite step method is proposed.Firstly,an adaptive finite step method is proposed to obtain reliability indexes efficiently and robustly.On the basis of the original framework of HL-RF method,the negative gradient search direction used by HL-RF is modified by the search direction with finite step size.At the same time,the amplitude oscillation criterion is introduced to determine the oscillati on phenomenon of the iteration point,and the finite step size is adjusted adaptively by the established step size adjustment formula according to the judgment result of the oscillation phenomenon.Then,the adaptive finite step iteration method is integra ted into the double-loop method to solve RBDO problems.Finally,the computational performance of the proposed method is verified by two complex numerical examples.(2)An adaptive iterative analytic single-loop RBDO approach is proposed.In order to balance computational efficiency and robustness when solving complex RBDO problems with multiple probability constraints,high target reliability,large standard deviation,and non-normal probability distributions,etc.,an adaptive iterative analytic single-loop approach is proposed.First,the original gradient vector in the single-loop method is replaced by a new vector with a finite step size.Then,an adaptive step size update strategy is used to dynamically adjust the vector with a finite step size.Finally,the computational performance of the proposed method is verified by three numerical examples and three engineering cases.(3)A hybrid adaptive single-loop approach with Kriging approximating constraint functions is proposed.In order to efficiently and robustly solve complex RBDO problems with implicit constraint functions,a hybrid adaptive single-loop approach with Kriging approximating constraint functions is proposed.Firstly,Kriging is applied to the analytic single-loop approach to approximately replace constraint functions.Then,an adaptive updating strategy for Kriging mo dels of constraint functions is proposed,where Kriging models of constraint functions are adaptively updated by approximate most probable point or accurate most probable point obtained at each iteration according to a criterion combining KKT optimality condition and Kriging.In addition,in order to search for accurate most probable point efficiently and robustly,two different hybrid adaptive modified chaos control methods are proposed.Finally,the computational performance of the proposed method is verified by a complex numerical example and two engineering cases.(4)A single-loop approach with Kriging adaptively approximating objective function and constraint functions is proposed.To efficiently solve complex RBDO problems with implicit objective function and constraint functions,a single-loop approach with Kriging adaptively approximating objective function and constraint functions is proposed.First,the Kriging model is combined with the single-loop approach into a Kriging-assisted single-loop approach.Then,two different effective constraint identification strategies are derived to identify effective constraint whose Kriging models are updated by the approximate minimum target performance point obtained at each iteration.Moreover,the optimal solution of each iteration is used as the sampling center to generate a candidate sample set for updating the objective function,and an optimal solution-based learning function is proposed to select new sample points from the candidate sample set to sequentially update the Kriging model of the objective function.Finally,the computational performance of the proposed method is verified by a numerical example and two engineering cases.(5)A sequential approximate decoupled time-variant RBDO approach is proposed.To efficiently solve time-variant RBDO problems,a sequential approximate decoupled time-variant RBDO approach is presented in this paper.Firstly,the stochastic process of time-variant performance function in probability constraint is discretized,and the original time-variant RBDO mathematical model is transformed into a time-variant RBDO model with percentile formulation.Then,a time-variant adaptive advanced mean method is proposed,and the time-variant inverse reliability is evaluated at the target percentile.The time-variant RBDO model with percentile formulation is converted into an equivalent deterministic optimization model.Moreover,the solution of the nested equivalent deterministic optimization model is transformed into an iterative solution process of alternating deterministic optimization and time-variant reliability evaluation by constructing shifting vectors.Finally,the computational performance of the proposed method is demonstrated by a numerical example and four engineering cases.