To address the challenge of measuring the response of jacket platform structures beneath the water surface and to address the limitations of existing non-modal response reconstruction methods that lack structural feature constraints, a novel global response reconstruction method is proposed. Taking the structural strain response as an example, the optimal scaling orthogonal basis between the finite and global measurement points is derived from the structure's impulse response. Global strain reconstruction of the structure under service loads is achieved by using this orthogonal basis in conjunction with the measured response. To validate the feasibility of this approach, a numerical model of a jacket platform is established and parameter-corrected based on a physical jacket platform model. Using this model, the global strain response reconstruction under multi-harmonic load excitation and noise robustness analysis are conducted with RE, TRAC and FRAC as response accuracy evaluation indicators, combined with a genetic algorithm. Numerical analyses indicate that the average error using the proposed method is 1.81% at each validation node, with TRAC and FRAC both above 0.9997. Compared to the fixed basis function reconstruction, the strain error is reduced by 8.67%, and the curve trend and shape are more consistent with the calculated response curve. Moreover, the proposed method exhibits satisfactory robustness against noise interference. The results of this research provide a technical reference for fatigue monitoring of offshore jacket platforms.