The present research deals with a computational application of a methodology that consists in identifying a statistical surrogate model with respect to a small incomplete target dataset [1]. The investigated structure is a three-dimensional engine nozzle, made of an elastic homogenized material and subjected to an internal stochastic pressure jet. It is assumed to undergo large displacements. A small target dataset consisting in a subset of normal accelerations located at the exit of the nozzle and expressed in the frequency domain is assumed to be available. % A parameterized stochastic nonlinear computational model (SNLCM) of the nozzle dynamics for which controlled parameters describe the isotropic part of the elastic material and the spectrum dispersion of the stochastic load and for which uncontrolled parameters describe the anisotropic part of the material is constructed. Given the complexity of such highly nonlinear SNLCM, high computational costs are needed to get one response for a given set of parameters. % First, a rough grid of controlled parameters is generated and the SNLCM is used without uncontrolled parameters to get the quantities of interests (QoI) corresponding to the small incomplete target dataset. The parameterized SNLCM is also used with random values of controlled and uncontrolled parameters for constructing a small training dataset. This latter one describes the realizations of the controlled parameters, of the corresponding random responses located at the exit of the nozzle and of the corresponding QoI related to the target. % Then, the PLoM algorithm, which is based on a purely probabilistic approach [2] is used and adapted to the constraint of an existing incomplet target data et [1] in order to construct a surrogate computational model whose learning set is constituted of realizations of controlled parameters and of the corresponding QoI. The updating of such surrogate computational model allows then to match for the best with the available incomplete target data set. [1] Soize, C. and Ghanem, R., Probabilistic-learning-based stochastic surrogate model from small incomplete datasets, Computer Methods in Applied Mechanics and Engineering, Vol.418, paper 116498, 2024. [2] Soize, C. and Ghanem, R.,Data-driven probability concentration and sampling on manifold, Journal of Computational Physics, Vol. 321, pp. 242--258, 2016.