Input estimation is an involved task with wide applications in nonlinear dynamic systems. Model-based input estimation methods are not feasible solutions for problems in which the underlying behavior is not sufficiently known. Data-driven methods have recently shown promise in capturing hidden and subtle nonlinearities in problems from various domains. In this study, we introduce a machine learning approach for input estimation of nonlinear dynamic systems that is applicable for a variety of mechanical properties and system complexities. The proposed neural regression model enables uncertainty quantification in predictions for each time sample which is a novel and helpful tool to analyze the accuracy of the results. For verification, three applications are investigated: (a) a numerical quarter-car model, (b) a real-world building, and (c) a real-world vehicle suspension system. We show that the estimated input signals in a numerically modeled system and real-world dynamic systems closely follow the actual inputs. In particular, the efficacy of input estimations in real-world cases confirms the strength of the proposed approach for similar applications with significant impact. For instance, the findings of this work enables the use of motion sensors mounted inside the vehicles for bridge vibration data collection which is proposed as a scalable and inexpensive paradigm for assessment of transportation infrastructure.

输入估计是一项在非线性动态系统中具有广泛应用的复杂任务。基于模型的输入估计方法对于潜在行为不充分了解的问题不是可行的解决方案。数据驱动的方法最近在捕获来自各个领域的问题中隐藏和微妙的非线性方面显示出前景。在这项研究中，我们介绍了一种用于非线性动态系统输入估计的机器学习方法，该方法适用于各种机械特性和系统复杂性。所提出的神经回归模型能够对每个时间样本的预测进行不确定性量化，这是分析结果准确性的一种新颖且有用的工具。为了验证，研究了三个应用程序：（a）数字四分之一汽车模型，（b）真实世界的建筑物，(c) 真实世界的车辆悬架系统。我们表明，数值建模系统和现实世界动态系统中的估计输入信号与实际输入密切相关。特别是，输入估计在现实世界中的有效性证实了所提出的方法对于具有重大影响的类似应用程序的强度。例如，这项工作的发现使得可以使用安装在车辆内部的运动传感器进行桥梁振动数据收集，这是一种可扩展且成本低廉的交通基础设施评估范例。输入估计在实际案例中的有效性证实了所提出的方法对于具有重大影响的类似应用程序的强度。例如，这项工作的发现使得可以使用安装在车辆内部的运动传感器进行桥梁振动数据收集，这是一种可扩展且成本低廉的交通基础设施评估范例。输入估计在实际案例中的有效性证实了所提出的方法对于具有重大影响的类似应用程序的强度。例如，这项工作的发现使得可以使用安装在车辆内部的运动传感器进行桥梁振动数据收集，这是一种可扩展且成本低廉的交通基础设施评估范例。