An Improved Algorithm Of Design Of Experiment In Constrained Space And Its Engineering Application

Design of Experiment(DoE),is about how to formulate an appropriate experiment plan according to the predetermined goal so as to carry out an effective statistical analysis of the experimental results,which is normally estimated by the space-filling property and projection characteristics.In recent years,data-driven design methods such as surrogate models have gradually emerged,and good experimental design is a necessary prerequisite to ensure the validity of data-driven design methods and the reliability of results.At present,researches of DoE focus on unconstrained space is considerable but on the constrained area is sparse.Most of existing DoEs are applied to regular design space,and will be invalidated if applied to constrained design space.In this paper,an improved SLE-LHS approach for constrained design space is proposed,named as SLE-CLHS approach.The proposed SLE-CLHS is an improved algorithm of SLE-LHS,which taking into account constraints between the sample variables and can be used in the constrained space.Several engineering cases show the effectiveness and uniformity of the proposed strategy.The details are as follows:(1)In the process of design,the points that do not satisfy the constrained condition are to be eliminated,then new points are generated in the constrained space and they will iterate with a certain step until the optimal position has been attained.(2)Several numerical examples are given in this paper,and the results of regular convex constraints in 2-dimensional space and 1/8 space of sphere and irregular convex constraint in 3-D sampling constrained design space indicate that the SLE-CLHS approach performs well both in space-fillingness and in projection.(3)In this paper,SLE-CLHS method is applied to the optimization of UAV blade and to the optimization of excavator boom.In the UAV blade process,training points and testing points are generated by using SLE-CLHS algorithm to sample points of four parameters with coupling relation in feasible region.The objective of torque has been reduced by 10.53% after constructing RBF surrogate model and optimization;During the optimization of excavator boom,we establish the excavator boom optimal mathematical model based on physical model and optimize the mass,stress and fatigue life of the boom.After sampling the parameters d2 and d3 in the feasible region by SLE-CLHS algorithm,the complete six-dimensional space sampling points are generated.Later,surrogate models are constructed and optimization process is carried out,and the optimized excavator boom is got which fulfills all the constraints.The SLE-CLHS method proposed in this paper can sample in the feasible region directly.Compared with the LHS sampling points,the results show that SLE-CLHS can obtain smaller value of ?,which shows that the sample points obtained by SLE-CLHS have better spatial filling and projection performance than those obtained by random LHS,and has a profound meaning.