arXiv subjects

Khalid Mahmud Labib

Publications and source records attributed to Khalid Mahmud Labib.

5 recordsLinked to original sources

arXiv2026

Graph-Based Characterization of Vision-Derived Dynamic Modes for Structural Damage Identification

This study presents a graph theoretic framework for characterizing damage-induced changes in the dynamics of a vibrating cantilever beam from non-contact video measurements. Within this approach, dynamics of the beam under healthy and damaged conditions with crack depths of 5, 10, and 13 mm are initially modeled using delay-embedded dynamic mode decomposition (DMD) from vision-based measurements. The resulting mode matrix from DMD is used to construct the adjacency matrix of a graph for this vibrating beam system, and its topological features such as graph connectivity, centrality, two-star statistics, and dyadic configurations are evaluated as damage-sensitive measures. Additionally, different DMD-based spectral and modal measures are evaluated to support the graph theoretic damage assessment. The results show a monotonic reduction in graph connectivity, nodal accessibility, and local organization of the graph with increasing crack depth. A parametric numerical study further validates the decreasing connectivity trend observed experimentally. The results demonstrate that the topological features of the graph derived from the DMD mode matrix provide an interpretable representation of damage-induced changes in the beam dynamics and offer a promising basis for vision-based structural damage identification.

eess.SY↗

arXiv2026

Koopman Spectral Analysis of Lithium-Ion Battery Dynamics: State of Charge as a Marginally Stable Observable

Accurate state-of-charge (SOC) estimation remains a fundamental challenge in lithium-ion battery management systems because battery dynamics are highly nonlinear, operating-condition dependent, and sensitive to parameter variations caused by aging and temperature. Conventional model-based estimators, such as equivalent circuit model (ECM) and Kalman-filter-based approaches, rely heavily on repeated parameter identification and accurate electrochemical modeling, whereas purely data-driven methods often sacrifice physical interpretability. This work proposes a Koopman-theoretic, data-driven framework for SOC estimation using Dynamic Mode Decomposition with control (DMDc) combined with Hankel time-delay embedding. Instead of explicitly identifying ECM parameters, the proposed approach reconstructs a lifted dynamical state space directly from measured terminal voltage and current obtained through Hybrid Pulse Power Characterization (HPPC) testing. Spectral decomposition of the identified DMDc operator reveals intrinsic battery dynamics in terms of Koopman modes and eigenvalues. The SOC dynamics naturally emerge as the slowest marginally stable mode whose eigenvalue lies closest to the unit circle, consistent with the integrator-type behavior of charge conservation. The corresponding modal coordinate is subsequently utilized as an SOC-sensitive observable.

eess.SY↗

arXiv2026

A Graph Theoretic Approach in Combination With Dynamic Mode Decomposition With Control (DMDc) to Analyze Battery Degradation

Accurate monitoring of lithium-ion battery (LIB) degradation is essential, yet it remains challenging due to the complex, nonlinear, and time-varying nature of electrochemical aging processes. Conventional equivalent circuit models (ECMs) provide simplified representations of battery behavior using fixed electrical components, but they cannot capture evolving internal degradation mechanisms and structural changes over time. In this study, a data-driven framework is developed by integrating dynamic mode decomposition with control (DMDc) with graph-theoretic analysis to characterize battery degradation from operational data alone. The mode matrix ($\mathbf{\phi}$) obtained from DMDc is transformed into a weighted adjacency matrix, enabling the representation of battery dynamics as an evolving network of interacting states. Graph-based measures, including connectivity and a modularity (proxy), are then used to quantify structural changes in the system across degradation stages. The results show a clear transition from a highly connected and coherent network in the healthy state to a progressively weaker and more fragmented structure as degradation advances, accompanied by increasing heterogeneity. This work demonstrates that graph-theoretic representations can effectively capture the evolving dynamics of battery degradation and provide interpretable insights into system-level aging behavior.

eess.SY↗

arXiv2026

Operator-Theoretic and physics-guided Sequence Modeling of Lithium-Ion Battery Voltage Dynamics

Lithium-ion batteries exhibit nonlinear voltage dynamics across varying operating conditions and aging states, making accurate modeling essential for estimation, control, and health monitoring. This work compares two data-driven frameworks for modeling voltage responses from hybrid pulse power characterization (HPPC) measurements: an operator-theoretic model based on Dynamic Mode Decomposition with control (DMDc), and a physics-guided transformer-based sequence model. In the DMDc framework, delay-embedded snapshots of terminal voltage and current are used to identify system matrices directly from measurement data, yielding an interpretable state-space model for recursive prediction. In parallel, a modified PatchTST architecture is developed in which terminal voltage is decomposed into an analytically computed open-circuit-voltage (OCV) component and a learned dynamic residual, with a future-current fusion pathway tailored to the prescribed HPPC current profile. Experimental results on a 30 Ah lithium-ion cell show that, although both models capture the sharp transient pulse dynamics, DMDc achieves lower prediction error and greater robustness to cell degradation under the present limited data regime, while the transformer captures qualitatively similar dynamics with greater architectural flexibility. These results highlight the advantages of operator-theoretic models in interpretability, computational efficiency, and robustness, while indicating the promise of physics-guided transformer models when larger and more diverse datasets are available.

eess.SY↗

arXiv2026

Modeling of Non-linear Dynamics of Lithium-ion Batteries via Delay-Embedded Dynamic Mode Decomposition

The complex electrochemical behavior of lithium-ion batteries results in non-linear dynamics and appropriate modeling of this non-linear dynamical system is of interest for better management and control. In this work, we proposed a family of dynamic mode decomposition (DMD)-based data-driven models that do not require detailed knowledge of the composition of the battery materials but can essentially capture the non-linear dynamics with higher computational efficiency. Only voltage and current data obtained from hybrid pulse power characterization (HPPC) tests were utilized to form the state space matrices and subsequently used for predicting the future terminal voltage at different state of charge (SoC) and aging levels. To construct the system model, 60\% of the data from a single HPPC test was utilized to generate time-delay embedded snapshots, with embedding dimension ranging from 40 to 2000. Among these, an embedding dimension of 1810 resulted in the least residual sum of squares (RSS) error of 3.86 for the dynamic mode decomposition with control (DMDc) model and 30 for the standard DMD model. For DMDc model, delay embeddings (ranging from 1 to 12) were also incorporated into the input current signals. For the input matrix, an embedding dimension of 6 resulted in a minimum RSS error of 1.74. Furthermore, the system matrices A and B, identified from the HPPC test when the cell is in its healthy state, were held fixed and used to simulate the system dynamics for aged batteries by updating only the control input. Despite the presence of nonlinear degradation effects in later cycles, the DMDc model effectively captured key inner dynamics such as voltage dips and transient responses for subsequent charge and discharge cycles.

eess.SY↗