A bivariate Chebyshev polynomials method for nonlinear dynamic systems with interval uncertainties

A bivariate Chebyshev polynomials approach is proposed to estimate the dynamic response bounds of nonlinear systems with interval uncertainties. The existing collocation method directly searches maximum and minimum values surrogate model in entire space by scanning (SM). presence too many uncertain parameters will lead expansive computational cost. To overcome this shortcoming, decomposed a function decomposition (BFD), established based on high-order Taylor expansion, into sum multiple univariate functions. above functions are fitted using polynomials, polynomial coefficients obtained through one-dimensional (1D) two-dimensional (2D) interpolation points. Thus, solution can be transformed that extremum low-dimensional found SM, then acquired arithmetic. Since SM for extreme only 1D 2D domains, amount calculation reduced compared searching whole space. efficiency, practicability effectiveness uncertainty analysis proved three examples.