An Interval Optimization Method Consider The Dependency And Tolerance Of Uncertain Variables

In practical engineering problems, there exist many uncertainties. The specificmodeling can be simplified because that single and a few uncertain factors have littleaffection on the system’s performance. The negative influence of structural system’sperformance cannot be neglected when these uncertain factors are coupled to affect it.Currently, the tools of describing uncertainty are mainly probabilistic method, fuzzymethod and interval approach. The interval method has little dependence on samplesand the number of experiments, and only the up and down bounds of uncertainparameters need to be obtained instead of accurate probabilistic distribution, so thismethod has strong application. The main work is as followed:(1) Based on the multidimensional parallelepiped model, an improved intervaloptimization algorithm is proposed to handle the uncertainty optimization problemsconcerning the correlation between uncertain parameters. Through affine coordinatetransformation and transformation matrix, the new uncertainty optimization problemscan be solved as the general form of interval optimization problem. Finally, throughsome examples, considering different correlation coefficients and related situations,the algorithm is validated.(2) According to interval optimization, a new method of tolerance design isproposed. This method can not only guarantee target performance but also maximizethe tolerance zones of design variables, so the manufacturing technology is enhancedand the manufacturing cost decreases. The interval median is converted as the basicsize, and interval length is converted as the tolerance zone width. Taking symmetrictolerance as the research object, a new tolerance zone evaluation coefficient is builtup, the original optimization problem converts multi-objective optimization problem.Pareto solution could be obtained through the existing multi-objective algorithms.Through numerical examples, the effectiveness of the algorithm is validated. Then theproposed approach can be enlarged and used to solve more complicated practicalengineering problems.