Estimating the stiffness and damping coming from a joint is a major challenge. This work proposes a novel framework to estimate the unknown parameters using frequency-based substructuring and a maximum a posteriori optimization approach. The idea is to minimize the discrepancy between the measured responses of an assembled system and the responses obtained by coupling the measured responses of the individual substructures with a joint model. The system’s dynamics are assumed to be linear. However, the FRFs of the coupled system (which drive the objective function) change nonlinearly with the linear joint parameters, making it a nonlinear optimization problem. Therefore, the joint parameters are estimated iteratively using the Gauss minimization method, a well-established linearization scheme. The framework is numerically validated on simple mdof systems, and the method’s effectiveness is tested by adding noise to the generated data. To demonstrate the framework’s applicability on real structures, joint stiffness and damping of a known benchmark structure are estimated based on real measurements. Two different underlying joint models are applied. The first assumes just flexibility at the connection. The second assumes the joint is a separate substructure. The algorithm can find realistic stiffness parameters and a range for the damping parameters providing a good compromise between the measurements in both cases.

中文翻译：

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使用基于频率的子结构来估计线性螺栓接头刚度和阻尼的新型优化框架


估计关节的刚度和阻尼是一项重大挑战。这项工作提出了一种新颖的框架，使用基于频率的子结构和最大后验优化方法来估计未知参数。其想法是最大限度地减少组装系统的测量响应与通过将各个子结构的测量响应与联合模型耦合而获得的响应之间的差异。系统的动力学被假定为线性的。然而，耦合系统（驱动目标函数）的频响函数随着线性关节参数的变化而非线性变化，使其成为非线性优化问题。因此，使用高斯最小化方法（一种完善的线性化方案）迭代估计关节参数。该框架在简单的 mdof 系统上进行了数值验证，并通过向生成的数据添加噪声来测试该方法的有效性。为了证明该框架在实际结构上的适用性，根据实际测量来估计已知基准结构的接头刚度和阻尼。应用了两种不同的底层联合模型。第一个假设只是连接的灵活性。第二个假设接头是一个单独的子结构。该算法可以找到实际的刚度参数和阻尼参数的范围，从而在两种情况下的测量之间提供良好的折衷。