This paper deals with the numerical application of the Probabilistic Learning on Manifold (PLoM) method to construct a statistical surrogate model consistent with a small and incomplete target dataset. The structure under consideration is a three-dimensional engine nozzle, made up of a homogenized elastic material and subjected to random internal pressure excitation. The dynamical model assumes large displacements. A target dataset is assumed to be given, which is constituted of a subset of the normal displacements located in the nozzle exit, and expressed in the frequency domain. These random frequency response functions form a subset of the Quantities of Interest (QoI) that will beconsidered as the model outputs. A parameterized Stochastic NonLinear Computational Model (SNLCM) representing the nozzle dynamics is constructed. Its control parameters describe the power spectral density of the stochastic excitation force. Furthermore, the elasticity matrix is homogeneous, anisotropic and random, whose mean value corresponds to an isotropic elasticity matrix. Due to the complexities of such a nonlinear computational model, the calculation of the dynamical response for a given set of parameters induces a high computational cost. First, the SNLCM is used as a prior model to generate a so-called training set, that is constituted of the QoI and associated control parameters. These control parameters belong to an admissible set, and are randomly drawn following a uniform distribution. Second, the target dataset is obtained through numerical simulations, using the SNLCM, where the elasticity matrix is taken as deterministic, as slightly stiffened with respect to the mean elasticity matrix. Also, the control parameters used for generating the target dataset belong to the same admissible set as for the training set, randomly drawn following a uniform distribution within cells of a regular grid. Once both the target dataset and the training dataset are obtained, the PLoM algorithm with constraint is used for obtaining a stastitical surrogate model that is devoted to updating the statistical prediction of the QoI with respect to the control parameters. The PLoM algorithm generates a so-called learned dataset with same format as the training dataset, that takes into account the target subset of QoI. The learned dataset yields updated QoI as model outputs, which are updated with respect to the training dataset, so as to better match the target.