Direct integration methods are widely used for dynamic response computation. However, the performance of their computational accuracy significantly degrades with increasing the time step. Although machine learning methods can address this shortcoming, they require training data for dynamic response computation. This paper proposes a novel computational method to overcome these shortcomings. The proposed approach is a data-free physics-driven estimator, which minimizes the objective function of multi-output least squares support vector machines for regression to model parameters subject to physical constraints introduced by the multi-degree of freedom system's dynamic equilibrium equations and initial conditions in the feature space, bypassing the need for training data (due to the coupled physics) and for satisfying the requirement of the time step due to the built-in optimization procedure. A new efficient step-by-step solver is developed to solve the optimization problem, and the solution is equivalent to a hyperplane satisfying the physical constraints in the feature space. The extension of the proposed approach for nonlinear dynamic response computation is also analyzed theoretically. The numerical results demonstrate that the proposed approach provides the solution with higher accuracy and efficiency and achieves the best performance for large time steps over classical integration methods.

中文翻译：

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一种用于动态响应计算的无数据、基于支持向量机的物理驱动估计器

直接积分方法广泛用于动态响应计算。然而，随着时间步长的增加，它们的计算精度性能会显着降低。虽然机器学习方法可以解决这个缺点，但它们需要训练数据来进行动态响应计算。本文提出了一种新的计算方法来克服这些缺点。所提出的方法是一种无数据物理驱动的估计器，它最小化多输出最小二乘支持向量机的目标函数，用于回归到受多自由度系统动态平衡方程和初始物理约束引入的模型参数特征空间中的条件，绕过对训练数据的需要（由于耦合物理）和满足由于内置优化程序而导致的时间步长的要求。开发了一种新的高效逐步求解器来解决优化问题，该解决方案等效于满足特征空间中物理约束的超平面。还从理论上分析了所提出的非线性动态响应计算方法的扩展。数值结果表明，所提出的方法提供了具有更高精度和效率的解决方案，并且在大时间步长上比经典积分方法实现了最佳性能。并且该解等价于特征空间中满足物理约束的超平面。还从理论上分析了所提出的非线性动态响应计算方法的扩展。数值结果表明，所提出的方法提供了具有更高精度和效率的解决方案，并且在大时间步长上比经典积分方法实现了最佳性能。并且该解等价于特征空间中满足物理约束的超平面。还从理论上分析了所提出的非线性动态响应计算方法的扩展。数值结果表明，所提出的方法提供了具有更高精度和效率的解决方案，并且在大时间步长上比经典积分方法实现了最佳性能。