Research On The Key Technologies For The Interval-based Robust Equilibrium Optimization Of Mechanical Structures’ Performance

There are various uncertain factors in the design,manufacture,assembly and operation of complex equipment,which lead to the uncertainty of the structural performance of the key component.In order to obtain high structural performance of equipment,the influence of uncertainty factors on the structural performance of key components must be fully considered at the design stage.It is relatively easy to determine the varying range of an uncertain factor although it is often difficult to determine its probabilistic distribution.Thus,robust design of structural performance by describing uncertain factors described as interval numbers becomes an effective way to achieve the high performance of complex equipment.However,the existing researches on the interval robust design of structural performance usually adopt indirect method based on model conversion to solve interval optimization model of structural performance.Different values of weighting factors and regularization parameters utilized in the model conversion process will produce different optimization results.In addition,the existing researches usually consider only the robustness of single objective performance index and seldom consider the robustness balance among multiple performance indicators.There also lack of methods for modeling and solving structural optimization problems containing heterogeneous performance indices.In view of these problems,the thesis carries out the research on the key technologies for the robust balanced optimization of mechanical structures based on interval theory,proposes and realizes the methods and techniques of the robust design of structural performance based on 3D vector of interval constraint violation,structural robust design which considering balanced performance of multiple objectives and constraints,and the measure on robustness and balanced design for heterogeneous multi-objective performance indices,which have important significance to improve the robustness and balance of comprehensive mechanical structural performance.The main contents of this thesis are as follows:The first chapter reviews the research status at home and abroad about non-probabilistic optimization design,robust optimization design,and multi-objective optimization design of structural performance,compares and analyzes the shortcomings in current research,and elaborates the research significance and research contents of this thesis.The second chapter summarizes the definition and basic operation rules of interval number,discusses the existing problems when interval order and interval possibility method are applied to the robust optimization design,and puts forward the concept of interval boundary closeness coefficient to measure structural performance of an interval constraint.The simulation analysis of mechanical structure’s performance index and the Kriging approximate prediction technique are also introduced.The third chapter expresses uncertain factors as interval numbers,establishes the robust optimization model of structural performance with multiple constraints,puts forward the feasibility evaluation method for design vectors based on 3D violation vector of an interval constraint as well as the normalized distance-based ranking rules for design vectors,and realizes the direct solution of multi-constraint robust optimization model by combining the Kriging technology and nested genetic algorithm.Finally,the effectiveness of the proposed algorithm is verified by two numerical examples and an engineering example of the upper beam in a high speed press.The fourth chapter establishes the multi-objective and multi-constraint robust design model of structural performance,puts forward the measurement method of robustness,the principle of robustness balance for structural performance indexes,and the ordering rules for design vectors based on robust balanced classification of structural performance and robust target distance,and realizes robust balanced optimization with multiple objectives and constraints by nested genetic algorithm.Finally,the effectiveness of the proposed algorithm is verified by a numerical example and an engineering example of actuating mechanism in press.The fifth chapter establishes the robust design model of mechanical structures with heterogeneous objectives including cost,fixation,benefit and deviation ones,puts forward the measurement method of robustness,the principle of robustness balance for heterogeneous performance indexes and the ordering rules based on robust target distance,and realizes the robust balanced optimization with heterogeneous objectives.Finally,the effectiveness of the proposed method is verified by a numerical example and an engineering example of actuating mechanism in press.The sixth chapter summarizes the main work of this thesis and points out the future work to be conducted.