Sliding window envelope averaging for trend removal in time-domain acceleration integration

Dynamic displacement plays a pivotal role in structural health monitoring (SHM) and fault diagnosis. In many practical engineering applications, direct high-precision measurement is often challenging, necessitating indirect acquisition through acceleration integration. This study conducts a comparative analysis of frequency-domain integration (sensitive to low-frequency signals) and time-domain integration (susceptible to trend-term interference). To achieve precise displacement reconstruction, the generation mechanism of trend terms in time-domain integration is analyzed in depth, leading to the proposal of a novel trend extraction algorithm: the sliding window envelope averaging (SWEA). Through parameter sensitivity analysis, scientific guidance for SWEA parameter configuration is provided. Physical shaking table tests, utilizing the simulated responses of both linear and nonlinear structural models as excitation inputs, validate the effectiveness of the proposed algorithm. The evaluation of physically measured sensor data fully demonstrates the robustness of SWEA in correcting time-domain integration results under complex dynamic conditions. Compared with frequency-domain integration (FDI), the least squares method (LSM), and empirical mode decomposition (EMD), SWEA exhibits distinct advantages, achieving substantial reductions in reconstruction errors. Specifically, under nonlinear excitation, it reduces the average relative peak error (e p ) by 15%-83% compared to EMD and by 11%-17% compared to FDI. Additionally, it decreases the average relative error (e d ) by 4%-50% and 1%-26% relative to EMD and FDI, respectively, while bypassing the empirical parameter dependency inherent to LSM. Furthermore, the impacts of natural frequencies and noise frequency bands on reconstruction accuracy are explored using a finite element model (FEM) of an actual structure. Results indicate that the accuracy of SWEA-reconstructed displacement does not fluctuate significantly with variations in noise frequency bands, fully demonstrating its broad applicability in engineering practice.