For UMDA, three methods, i.e., the first order interval Taylor expansion method, the interval vertex theorem, the direct optimization approach are formulated.
Based on the first-order Neumann series and random interval moment method, the interval bounds of the probabilistic characteristics of the uncertain temperature field are calculated effectively.
To implement sensitivity analysis based on this method, the interval ranges of the responses of the vibro-acoustic system with interval parameters should first be obtained.
Unlike normal sensitivity analysis method, the interval analysis method obtains informations on the response of structures with structural parameters (or design variables) changing and without any partial differential operation.
In the proposed method, the interval random matrix and vector are expanded by the first-order Taylor series and the sound pressure response vector is obtained by the matrix perturbation technique.
[ 36] Bayesian method, the interval estimate is from 82.15 to 95.27.
These solutions were computed numerically with the Milstein method on the interval ([0,20]).
However given the method used, the interval defining QTL 1.2 was not established and our work helps defining a small interval containing NIS1 (Figure 4A).
Figure 7 shows the exact solution and approximate solutions obtained by NHPM and our method in the interval ([0,10]).
The experimental and numerical case studies are given to illustrate and verify the proposed method in the interval identification of structural parameters.
Notice that these membership functions are similar to the previous method; however, the interval of definition is adjusted by experts to get the best algorithm's performance.
