Surrogate model provides a promising way to reasonably approximate complex underlying relationships between system parameters. However, the expensive modeling cost, especially in large problem sizes, hinders its applications in practical problems. To overcome this issue, with the advantages of the multi-fidelity surrogate (MFS) model, this paper proposes a single-fidelity surrogate model with a hierarchical structure, named nonlinearity integrated correlation mapping surrogate (NI-CMS) model. The NI-CMS model first establishes the low-fidelity model to capture the underlying landscape of the true function, and then, based on the idea of MFS model, the established low-fidelity model is corrected by minimizing the mean square error to ensure prediction accuracy. Especially, a novel MFS model (named NI-MFS), is constructed to enhance the stability of the proposed NI-CMS model. More specifically, a nonlinear scaling term, which assumes the linear combination of the projected low-fidelity predictions in a high-dimensional space can reach the high-fidelity level, is introduced to assist the traditional scaling term. The performances of the proposed model are evaluated through a series of numerical test functions. In addition, a surrogate-based digital twin of an XY compliant parallel manipulator is used to validate the practical performance of the proposed model. The results show that compared with the existing models, the NI-CMS model provides a higher performance under the condition of a small sample set, illustrating the promising potential of this surrogate modeling technique.