Accurately obtaining the dynamic load of a structure is crucial for structural design, optimization, and maintenance. However, dynamic methods based on classical mechanics systems often introduce artificial dissipation and other flaws. This paper presents a novel time-domain centralized load identification method to address structural dynamic load problems, leveraging Birkhoffian system dynamics and its symplectic integrators. State variables are first introduced, and Birkhoffian functions are constructed to reformulate the structural dynamic problem into dynamic equations under the Birkhoffian system. Based on the discretized Birkhoffian equations, a symplectic difference scheme is then established for a time-domain load-solving algorithm within the Birkhoffian framework. To tackle large-scale engineering problems and noise pollution encountered in practice, preprocessing methods based on modal decomposition and post-processing methods based on the Savitzky-Golay filter are also proposed. Compared to traditional numerical algorithms, the symplectic algorithms based on the Birkhoffian dynamics framework do not introduce algorithmic dissipation, offering better stability and accuracy. Finally, three numerical examples and one experimental case demonstrate the effectiveness and precision of the proposed method. The results show that, in terms of overall error and peak error metrics, the proposed method offers high accuracy and improved stability under noisy input conditions.

中文翻译：

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一种基于离散变分符号积分器的新型 Birkhoffian 系统结构动载荷重构方法


准确获取结构的动态载荷对于结构设计、优化和维护至关重要。然而，基于经典力学系统的动力学方法经常会引入人为耗散和其他缺陷。本文提出了一种新的时域集中载荷识别方法，利用 Birkhoffian 系统动力学及其对称积分器来解决结构动态载荷问题。首先引入了状态变量，并构建了 Birkhoffian 函数，以将结构动力学问题重新表述为 Birkhoffian 系统下的动力学方程。基于离散的 Birkhoffian 方程，然后为 Birkhoffian 框架内的时域载荷求解算法建立了对称差分方案。针对实践中遇到的大规模工程问题和噪声污染问题，该文还提出了基于模态分解的预处理方法和基于 Savitzky-Golay 滤波器的后处理方法。与传统数值算法相比，基于 Birkhoffian 动力学框架的符号算法没有引入算法耗散，提供了更好的稳定性和准确性。最后，3个数值算例和一个实验实例验证了所提方法的有效性和精度。结果表明，在总体误差和峰值误差指标方面，所提方法在噪声输入条件下具有较高的精度和更高的稳定性。