The advantage of nonparametric identification methods based on the use of approximations of the restoring forces is that they do not require the a priori knowledge of a model for the nonlinear behavior of the structure. However, the main difficulty encountered with this type of methods is the fitting of nonlinear forces in the force-state mapping fields where there are not sufficient experimental data. In this paper, an improvement of the regression technique in conjunction with the use of two-dimensional Chebyshev orthogonal polynomials by introducing an interative computation process is presented. It is shown that the proposed method can properly identify the discretized model even in the case of high cross-product displacement-velocity terms and that this method can be used for structures presenting important nonlinear modal coupling.

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