For many applications first-principles nonlinear dynamic models are preferred by practitioners. Parameter estimation for these models is often a non-trivial and time consuming task. The use of optimally designed dynamic inputs can reduce the experimental burden and increase the accuracy of the estimated parameters. Traditionally, piecewise polynomial input sequences are exploited for this purpose. In contrast, this paper proposes optimal experiment design with the use of random phase multisine inputs, which are typically used for black box model identification. The main motivations are (i) the practical requirement that the inputs have to be concentrated around an operating point, and (ii) the fact that fast dynamics have to be included in the input profile without introducing a large number of discretization parameters. Moreover, multisines can be designed to excite exclusively a specific frequency band of interest. As an illustration, optimal inputs are designed and validated experimentally for estimating the parameters important for the dynamical behaviour of a Diesel engine airpath model.