Principal force pattern and impulse response mode for structural equivalent force estimation and full-field response reconstruction

An impulse response mode-based approach is proposed in this study to estimate the equivalent force and achieve full-field monitoring under complex loading conditions. The structural impulse responses to quasi-static and dynamic forces are decomposed as the superposition of a set of predefined representative basis to provide the low-rank property of responses. The principal impulse response modes are calculated from the correlation matrix of the impulse responses in a time step using the principal component analysis. The principal relative force pattern is the eigenvector of the correlation matrix, and the truncation number is determined by the distribution of the eigenvalues. The equivalent force is subsequently defined and solved by the dynamic stiffness method. The full-field responses are then reconstructed by calculating the model responses to the estimated equivalent force. The systematic uncertainty is also quantified by an error propagation method for sensor placement optimization. Numerical examples and experimental tests demonstrate that the proposed methodology can estimate the equivalent force and reconstruct the structural responses accurately under various load scenarios.