Jinhui Jiang

Accurate and efficient identification of distributed dynamic loads is a critical task in inverse dynamics and structural vibration analysis. However, online identification in continuous structures remains challenging when the initial conditions of each identification window are unknown, since inaccurate initial-state estimation may introduce significant boundary errors in segment-wise time-domain reconstruction. This paper proposes a finite-memory time-domain method for online identification of distributed dynamic loads in continuous structures under unknown initial conditions. Based on the Newmark- integration scheme, the mapping relationship between structural responses and modal loads is established in the time domain. Unlike conventional segment-wise identification methods, the proposed approach truncates the historical memory of the dynamic system to a finite length, thereby replacing the explicit contribution of the unknown initial state in each sliding window with an equivalent finite-history load contribution. This strategy effectively alleviates the adverse influence of unknown initial conditions and enables sliding-window-based online identification. To reduce the dimensionality of the inverse problem, the distributed dynamic load is represented by Legendre orthogonal polynomials. A generalized Tikhonov regularization scheme with temporal difference constraints is further introduced to enhance the stability and noise robustness of the inverse solution. Numerical simulations on a simply supported beam and a simply supported plate are conducted under distributed periodic, impact, and random loads. The results demonstrate that the proposed method can accurately reconstruct distributed dynamic loads under different noise levels, while the computational time remains considerably shorter than the identification duration. Compared with the standard Newmark-β method, the proposed method exhibits a significant accuracy advantage in the presence of nonzero initial conditions. Experimental validation on a cantilever plate subjected to a loudspeaker-induced sinusoidal distributed load further confirms the accuracy, efficiency, and engineering applicability of the proposed method.

As an essential component of dynamic loads, traditional time-domain identification methods exhibit notably insufficient accuracy when dealing with distributed dynamic load identification under unknown initial conditions. This paper explores a novel and effective methodology, utilizing the Bayesian framework and orthogonal polynomials fitting, to reconstruct the distributed dynamic loads of thin plate structures over any arbitrary time period under unknown initial conditions. The forced vibration under the orthogonal basis function loads and the free decay vibration after the removal of basis function loads are used to characterize the forced vibration induced by the identified distributed dynamic load and the decay vibration caused by unknown initial conditions, respectively. By integrating structural dynamic responses within a multi-layer Bayesian framework, the time history and spatial distribution of the load over any arbitrary time period are identified. The innovation of this methodology is that the contribution of the initial conditions to the response is independently characterized by the free decay response caused by the removal of the basis function loads, which effectively resolves the issue of insufficient identification accuracy in existing traditional time-domain methods due to unknown initial conditions. Consequently, the accuracy and reliability of the distributed dynamic load identification is significantly enhanced, which provides a new solution for distributed dynamic load identification under unknown initial conditions. Additionally, simulation cases involving various load conditions and noise levels are discussed under unknown initial conditions over arbitrary time periods. The results demonstrate that the proposed method achieves favorable identification accuracy and robustness under unknown initial conditions.

Accurate and efficient identification of distributed dynamic loads is a critical task in inverse dynamics and structural vibration analysis. However, online identification in continuous structures remains challenging when the initial conditions of each identification window are unknown, since inaccurate initial-state estimation may introduce significant boundary errors in segment-wise time-domain reconstruction. This paper proposes a finite-memory time-domain method for online identification of distributed dynamic loads in continuous structures under unknown initial conditions. Based on the Newmark- integration scheme, the mapping relationship between structural responses and modal loads is established in the time domain. Unlike conventional segment-wise identification methods, the proposed approach truncates the historical memory of the dynamic system to a finite length, thereby replacing the explicit contribution of the unknown initial state in each sliding window with an equivalent finite-history load contribution. This strategy effectively alleviates the adverse influence of unknown initial conditions and enables sliding-window-based online identification. To reduce the dimensionality of the inverse problem, the distributed dynamic load is represented by Legendre orthogonal polynomials. A generalized Tikhonov regularization scheme with temporal difference constraints is further introduced to enhance the stability and noise robustness of the inverse solution. Numerical simulations on a simply supported beam and a simply supported plate are conducted under distributed periodic, impact, and random loads. The results demonstrate that the proposed method can accurately reconstruct distributed dynamic loads under different noise levels, while the computational time remains considerably shorter than the identification duration. Compared with the standard Newmark-β method, the proposed method exhibits a significant accuracy advantage in the presence of nonzero initial conditions. Experimental validation on a cantilever plate subjected to a loudspeaker-induced sinusoidal distributed load further confirms the accuracy, efficiency, and engineering applicability of the proposed method.

The identification of dynamic loads on structures relies on an accurate finite element model. For structures under certain complex working conditions, it is difficult to determine the specific structural constraints, posing challenges to the study of the structure’s dynamic characteristics. To accurately conduct dynamic load identification research on structures under such conditions, a high-precision finite element model is required. This paper introduces existing finite element model correction methods, as well as the current status of dynamic load identification research, and proposes a model correction method based on sensitivity correction to adjust finite element models of structures with unknown constraint conditions. The constraint stiffness of the model is set as a design parameter, and adjusting the constraint stiffness is used to modify the model’s modal frequencies and frequency response functions. The errors in the first two modal frequencies after correction are 0.2%. Dynamic load identification studies are conducted on the corrected model and structure under typical loads, such as concentrated loads. The experimental identification results meet the working condition standards, with errors all below 10%. After the model correction, the dynamic load identification results are more accurate.

This paper proposes a novel dynamic response reconstruction method based on the Kalman filter which can simultaneously identifies external excitation and reconstructs dynamic responses at unmeasured positions. The weighted least squares method determines the load weighting matrix for excitation identification, while minimum variance unbiased estimation determines the Kalman filter gain. The excitation prediction Kalman filter is constructed through time, excitation, and measurement updates. Subsequently, the response at the target point is reconstructed using the state vector, observation matrix, and excitation influence matrix obtained through the excitation prediction Kalman filter algorithm. An algorithm for reconstructing responses in Continuous System using the excitation prediction Kalman filtering algorithm in modal space is derived. The proposed structural dynamic response reconstruction method evaluates response reconstruction and load identification performance under various load types and errors through simulation examples. Finally, a test system for structural dynamic response reconstruction on simply supported beams is constructed and tested. Results demonstrate accurate excitation identification under different load conditions and simultaneous reconstruction of target point responses, verifying the feasibility and reliability of the method.