Optimization Design Of Mechanical Structures Considering Uncertainties Of Interval And Probability

Various uncertainties which affect structural performance widely exist in practical engineering.Uncertainty optimization design is an effective way to deal with these uncertainties,which can obtain a high performance,high robustness and reliability structural design scheme.At present,many domestic and foreign scholars have carried out a series of studies on the uncertainty optimization design of mechanical structures,but there are still some shortcomings.On the one hand,in terms of solving the interval-based structural optimization design model,the existing research often firstly introduce penalty factor,regularization factor and so on to transform the interval model into the deterministic model,then use weighting method to turn the multi-objective optimization problem into the single objective problem.The indirect solving process based on model transformation is relatively complicated and different parameters of model transformation will lead to different results.On the other hand,probabilistic and non-probabilistic uncertainties usually exist in practical engineering structural design at the same time.Therefore,it is very significant to carry out the research on the optimization design of mechanical structures considering interval and probabilistic uncertainties and propose and realize the direct solving method of the optimization design model of mechanical structures,which can improve robustness and reliability of structural performance.The main contents of this thesis are as follows:The first chapter reviews the research status at home and abroad of probabilistic uncertainty optimization design,non-probabilistic uncertainty optimization design and probabilistic and non-probabilistic mixed uncertainties optimization design,analyses the shortcomings of existing research,puts forward the research significance and research content of this thesis.The second chapter summarizes the interval mathematical theory such as interval order relation and interval possibility degree,introduces the mathematical description method of robustness and reliability index of mechanical structures based on interval model,probabilistic model and hybrid model,and gives the construction methods of the polynomial response surface model and Kriging approximation model for predicting the performance index of mechanical structures.The third chapter uses interval numbers to describe uncertain factors and establishes the interval-based robustness design model of mechanical structures and proposes the concept of interval constraint violation vector and preferential guidelines based on interval constraint violation vector and realizes the direct solution of the interval-based robustness design model of mechanical structures combined with the double nested genetic algorithm and Kriging approximation model.Finally,the validity and superiority of the proposed method are verified by a numerical example and a robustness design example of the upper beam of the press.The fourth chapter uses interval numbers to describe uncertain factors and establishes the interval-based reliability design model of mechanical structures and proposes the unified formula for calculating interval reliability based on graphic method and puts forward the concept of interval reliability violation degree and preferential guidelines based on interval reliability violation degree and realizes the direct solution of the interval-based reliability design model of mechanical structures combined with the double nested genetic algorithm and Kriging approximation model.Finally,the validity and superiority of the proposed method are verified by a numerical example and a reliability design example of the upper beam of the press.The fifth chapter utilizes probability variables to describe design parameters and uses interval variables to describe uncertain factors and establishes the reliability design model of mechanical structures based on probability and interval and chooses the minimum value of reliability under the influence of interval variables as the reliability index,selects the polynomial response surface model as the approximate surrogate model and realizes the solution of the reliability design model of mechanical structures based on probability and interval combined with the genetic algorithm and the improved first order second moment method.At last,the validity of the proposed method is verified by the reliability design example of the slider mechanism and the base of the press.The sixth chapter summarizes the research contents of this thesis and prospects the future research directions.