A parameter mapping technique-based interval perturbation method for predicting the uncertain acoustic field in the enclosure with nonlinear interval parameters

Classical wave-based acoustic simulation are usually conducted under the assumption that the parameters are deterministic. While in real engineering, uncertainties on environmental parameters are often unavoidable. Thus, the uncertain acoustical simulation has gradually been a research focus. Because of the effectiveness and simplicity, the interval perturbation method has attracted sustained attentions and been used in many uncertain acoustic problems in recent years. However, the commonly used first order approximation in the perturbation method would no longer be a feasible strategy due to omitting the high orders of the Taylor series when the uncertain parameters are nonlinear. To solve the uncertain problems with nonlinear interval parameters, a parameter mapping technique is proposed in this paper. This technique firstly constructs a function with respect to a nonlinear parameter. Then, by mapping the initial interval of the nonlinear parameter into the newly constructed function space, this function can be considered as a new independent parameter. Finally, the uncertain acoustical problems can be solved by the classical interval perturbation methods in which the first order approximation is capable of giving precise results. The numerical verifications demonstrate that the proposed technique is effective for uncertain acoustic field simulation with nonlinear interval parameters.