Jointed structures in engineering naturally perform with some of nonlinearity and uncertainty, which significantly affect the dynamic characteristics of the structural system. In this paper, the method of Bayesian uncertainty identification of model parameters for the jointed structures with local nonlinearity is proposed. Firstly, the nonlinear stiffness and damping of the joints under the random excitation are represented with functions of excitation magnitude in terms of the equivalent linearization. The process of uncertainty identification is separated from the representation of local nonlinearity. In this way, the dynamic behavior of the joints is penetratingly characterized instead of ascribing the nonlinearity to uncertainty. Secondly, a variable-expanded Bayesian (VEB) method is originally proposed to identify the mixed of aleatory and epistemic uncertainties of model parameters. Different from traditional Bayesian identification, the aleatory uncertainties of model parameters are identified as one of the most important parts rather than only measurement noise of output. Notablely, a series of intermediate variables are introduced to expand the parameter with aleatory uncertainty in order to overcome the difficulty of establishing the likelihood function. Moreover, a 3-DOF numerical example is illustrated with case studies to verify the proposed method. The influence of observed sample size and prior distribution selection on the identification results is tested. Furthermore, an engineering example of the jointed structure with rubber isolators is performed to show the practicability of the proposed method. It is indicated that the computational model updated with the accurately identified parameters with both nonlinearity and uncertainty has shown the excellent predictive capability.

中文翻译：

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非线性连接结构模型参数的贝叶斯不确定性辨识

工程中的节点结构自然具有一些非线性和不确定性，这对结构系统的动力特性有显着影响。本文提出了具有局部非线性的节点结构模型参数的贝叶斯不确定性辨识方法。首先，随机激励下关节的非线性刚度和阻尼用等效线性化的激励幅度函数表示。不确定性识别的过程与局部非线性的表示分离。通过这种方式，关节的动态行为被深入地表征，而不是将非线性归因于不确定性。其次，最初提出了一种可变扩展贝叶斯 (VEB) 方法来识别模型参数的随机和认知不确定性的混合。与传统的贝叶斯识别不同，模型参数的偶然不确定性被识别为最重要的部分之一，而不仅仅是输出的测量噪声。值得注意的是，为了克服建立似然函数的困难，引入了一系列中间变量来扩展具有随机不确定性的参数。此外，还通过案例研究说明了一个 3-DOF 数值示例，以验证所提出的方法。测试了观察到的样本大小和先验分布选择对识别结果的影响。此外，一个带有橡胶隔振器的连接结构的工程实例被用来展示所提出方法的实用性。结果表明，用准确识别的具有非线性和不确定性的参数更新的计算模型显示出优异的预测能力。