This paper presents an inverse Algebraic Wavenumber Identification (AWI) technique for multi-modal 1D-periodic structures, which can extract complex wavenumbers from steady-state vibration measurements under stochastic conditions. These wave dispersion characteristics provide valuable vibroacoustic indicators for model updating, damage monitoring in operational conditions, or metamaterial design. Wavenumber extraction techniques are highly sensitive to noisy measurements, nonuniform sampling points, or geometrical uncertainties. The proposed formulation relies on algebraic parameters identification to enable the extraction of complex wavenumbers in four scenarios: (a) low Signal Noise Ratio; (b) small perturbation caused by uncertainties on sampling points' coordinates; (c) unknown structural periodicity; (d) nonuniform sampling. This AWI is compared with Inhomogeneous Wave Correlation (IWC) method and INverse COnvolution MEthod (INCOME) to assess the robustness and accuracy of the method.