标题： 基于非线性动力学特征训练的神经网络的混合自适应建模 显示英文标题

标题： Hybrid Adaptive Modeling using Neural Networks Trained with Nonlinear Dynamics Based Features

摘要： 准确的模型对于复杂工程系统的设计、性能预测、控制和诊断至关重要。基于物理的模型在设计阶段表现出色，但由于运行条件的变化、未知的相互作用、激励和参数漂移，在系统部署期间往往变得过时。虽然基于数据的模型可以捕捉复杂系统的当前状态，但它们面临重大挑战，包括过度依赖数据、对变化条件的泛化能力有限以及无法预测参数依赖性。这导致了将物理与数据结合建模的方法，称为融合物理的机器学习，通常使用基于物理模型的数值模拟。本文介绍了一种新方法，该方法不同于标准技术，通过从非线性动力学建模中提取信息并将其嵌入基于数据的模型中。目标是创建一个混合自适应建模框架，将基于数据的建模与新测量的数据和分析性非线性动力学模型相结合，以提高准确性、参数依赖性和更好的泛化能力。通过通过扰动方法显式地纳入非线性动态现象，其预测能力比从蛮力数值模拟中获得的知识更加现实和有洞察力。特别是，扰动方法被用于推导渐近解，这些解被参数化以生成频率响应。频率响应提供了关于动力学和非线性的全面见解，并被量化和提取为高质量特征。由这些特征训练的机器学习模型可以跟踪参数变化并更新不匹配的模型。结果表明，这种自适应建模方法在预测精度和计算效率方面优于数值灰箱模型。 显示英文摘要

摘要： Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing operational conditions, unknown interactions, excitations, and parametric drift. While data-based models can capture the current state of complex systems, they face significant challenges, including excessive data dependence, limited generalizability to changing conditions, and inability to predict parametric dependence. This has led to combining physics and data in modeling, termed physics-infused machine learning, often using numerical simulations from physics-based models. This paper introduces a novel approach that departs from standard techniques by uncovering information from nonlinear dynamical modeling and embedding it in data-based models. The goal is to create a hybrid adaptive modeling framework that integrates data-based modeling with newly measured data and analytical nonlinear dynamical models for enhanced accuracy, parametric dependence, and improved generalizability. By explicitly incorporating nonlinear dynamic phenomena through perturbation methods, the predictive capabilities are more realistic and insightful compared to knowledge obtained from brute-force numerical simulations. In particular, perturbation methods are utilized to derive asymptotic solutions which are parameterized to generate frequency responses. Frequency responses provide comprehensive insights into dynamics and nonlinearity which are quantified and extracted as high-quality features. A machine-learning model, trained by these features, tracks parameter variations and updates the mismatched model. The results demonstrate that this adaptive modeling method outperforms numerical gray box models in prediction accuracy and computational efficiency.