Multi-source uncertainty-oriented dynamic force reconstruction framework based on adaptive fitting precise integration and optimized wavelet denoising.

This study advances dynamic force reconstruction in the time domain through the precise integration method (PIM), particularly effective for matrix exponential numerical solutions. Traditional PIM approaches, typically reliant on linear or step function assumptions within integration time steps, face limitations in handling large integration time step loads. Addressing this, our research introduces an innovative method employing velocity and displacement sensors in simple and complex structures, significantly enhancing load fitting accuracy, especially for nonlinear loads. We propose a refined version of PIM: the Chebyshev polynomial integration method (CPIM) and the adaptive precise integration method (APIM) based on wavelets. These methods are designed to fit force functions of varying orders across different time steps, thereby bolstering signal reconstruction robustness. The efficacy of these approaches is validated given adequate measurement response data. Furthermore, recognizing the growing emphasis on uncertainty in engineering, our work incorporates the collocation method for uncertainty quantification in load identification. To counteract the erratic results from polynomial fitting, particle swarm optimization (PSO) thresholding is employed to eliminate high-frequency noise, thus enhancing the Signal-to-Noise Ratio and minimizing signal distortion. Notably, we demonstrate that the Shannon wavelet surpasses the Chebyshev polynomial in fitting ability due to its tighter branch, rendering APIM more suitable for engineering applications compared to CPIM. APIM adeptly minimizes errors related to acquisition frequency by adaptively adjusting the number of discretization points and wavelet convergence levels to fulfill convergence criteria and matrix norm requisites. This paper proposes a multi-source uncertainty-oriented dynamic Force Reconstruction Framework, integrating adaptive fitting precise integration with PSO. Our numerical examples illustrate that APIM, as discussed herein, offers broader applications and is more time efficient than CPIM. [ABSTRACT FROM AUTHOR]