This paper presents a novel dimension-adaptive numerical integration method for dynamic analysis of structures with stochastic parameters subjected to deterministic excitations. First, an efficient dimension-adaptive algorithm is proposed to detect the importance of each random parameter involved in the structural model, based on which the quadrature nodes used for numerical integration can be collocated more reasonably. Then, the Gaussian quadrature formulas are used to evaluate the structural response statistics. To further improve the robustness and efficiency of the proposed method, the dimension-adaptive integration is only used to calculate the structural displacement response statistics. The velocity and acceleration response statistics are further evaluated using the finite difference formulas based on the concept of stochastic difference. Such a strategy is especially attractive when evaluating the response statistics of the derivative processes requires more quadrature nodes than that of the original process. Finally, two numerical examples encountered in civil engineering, including a shear frame with stochastic parameters subjected to a seismic ground motion and an Euler beam with unidimensional stochastic field of material properties (discretized via the Karhunen–Loève expansion) subjected to a moving load are studied to illustrate the performance of the proposed method. Via the numerical results, the accuracy and efficiency of the proposed method are verified.

中文翻译：

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一种用于不确定参数结构随机动力分析的高效维数自适应数值积分方法

本文提出了一种新颖的尺寸自适应数值积分方法，用于对具有确定性激励的随机参数的结构进行动态分析。首先，提出了一种高效的维度自适应算法来检测结构模型中涉及的每个随机参数的重要性，在此基础上可以更合理地配置用于数值积分的正交节点。然后，使用高斯求积公式来评估结构响应统计量。为了进一步提高所提方法的鲁棒性和效率，维度自适应积分仅用于计算结构位移响应统计量。使用基于随机差分概念的有限差分公式进一步评估速度和加速度响应统计。当评估衍生过程的响应统计需要比原始过程更多的正交节点时，这种策略特别有吸引力。最后，研究了土木工程中遇到的两个数值例子，包括具有随机参数的剪切框架受到地震动的影响和具有材料特性的一维随机场（通过 Karhunen-Loève 展开离散）的欧拉梁受到移动载荷的影响。来说明所提出方法的性能。通过数值结果验证了所提方法的准确性和有效性。在土木工程中遇到的两个数值例子，包括一个具有随机参数的剪切框架受到地震地面运动和一个欧拉梁的材料特性的一维随机场（通过 Karhunen-Loève 展开离散）受到移动载荷的研究，以说明所提出方法的性能。通过数值结果验证了所提方法的准确性和有效性。在土木工程中遇到的两个数值例子，包括一个具有随机参数的剪切框架受到地震地面运动和一个欧拉梁的材料特性的一维随机场（通过 Karhunen-Loève 展开离散）受到移动载荷的研究，以说明所提出方法的性能。通过数值结果验证了所提方法的准确性和有效性。