保结构数据驱动的端口-哈密顿微分代数系统辨识
Structure-Preserving Data-Driven Identification of Port-Hamiltonian Differential-Algebraic Systems
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中文总结 AI 辅助
本文提出一种保结构数据驱动方法，通过输入输出数据辨识线性指标1微分代数端口-哈密顿系统，利用隐式中点离散化和伴随梯度优化，实现准确替代建模与降阶，并验证预测能力。
中文摘要 AI 辅助
我们提出了一种基于输入输出测量的数据驱动方法，用于辨识线性指标1微分代数端口-哈密顿系统（pH-DAEs）。与端口-哈密顿（pH）系统的辨识相比，代数约束和指标条件带来了额外的挑战。首先，我们建立了所考虑的pH-DAE类别的保结构表述，并推导了一种隐式中点离散化方法，该方法保持代数约束和离散耗散不等式。我们将辨识问题表述为受pH-DAE动力学约束的正则化最小二乘最小化问题。利用指标1结构，我们将约束问题简化为关于系统参数的无约束优化问题，同时保持端口-哈密顿结构。接下来，我们推导了一种基于伴随的公式，以高效评估所得简化代价函数的梯度。这使我们能够使用基于梯度的优化方法进行参数估计。在关于允许参数集的适当假设下，证明了极小值的存在性。数值实验表明，所提出的方法能够辨识出准确再现参考系统输入输出行为的替代pH-DAE系统。进一步的研究显示了该方法在辨识降阶替代模型方面的潜力。使用独立输入信号的交叉验证确认了所辨识模型的预测能力。
英文摘要
We present a data-driven approach to identifying linear index-1 differential-algebraic pH systems (pH-DAEs) based on input-output measurements. In comparison to the identification of port-Hamiltonian (pH) systems, the algebraic constraint and the index condition pose additional challenges. First, we establish a structure-preserving formulation of the considered pH-DAE class and derive an implicit midpoint discretization that preserves the algebraic constraints and discrete dissipation inequality. We formulate the identification problem as a regularized least-squares minimization problem subject to the pH-DAE dynamics. Exploiting the index-1 structure, we reduce the constrained problem to an unconstrained optimization problem over the system parameters while preserving the port-Hamiltonian structure. Next, we derive an adjoint-based formulation to efficiently evaluate the gradient of the resulting reduced cost functional. This enables us to use gradient-based optimization methods for parameter estimation. Under suitable assumptions on the admissible parameter set, the existence of a minimizer is established. Numerical experiments demonstrate that the proposed approach can identify surrogate pH-DAE systems that accurately reproduce the input-output behavior of reference systems. Further investigations show the approach's potential for identifying reduced-order surrogate models. Cross-validation with independent input signals confirms the predictive capability of the identified models.
发表机构
- University of Wuppertal（伍珀塔尔大学）
机构由 AI 辅助整理，请以论文原文为准。
