The dynamic analysis of multibody systems with uncertain parameters using interval method

The theoretical and computational aspects of interval methodology based on Chebyshev polynomials for modeling multibody dynamic systems in the presence of parametric uncertainties are proposed, where the uncertain parameters are modeled by uncertain-but-bounded interval variables which only need the bounds of uncertain parameters, not necessarily knowing the probabilistic distribution. The Chebyshev inclusion function which employs the truncated Chevbyshev series expansion to approximate the original function is proposed. Based on Chebyshev inclusion function, the algorithm for solving the nonlinear equations with interval parameters is proposed. Combining the HHT-I3 method, this algorithm is used to calculate the multibody systems dynamic response which is governed by differential algebraic equations (DAEs). A numerical example that is a slider-crank with uncertain parameters is presented, which shows that the novel methodology can control the overestimation effectively and is computationally faster than the scanning method.