arXiv subjects

Shabbir Ahmed

Publications and source records attributed to Shabbir Ahmed.

At least 19 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

Learning Structural Eigenmodes with Modal Operator Network (ModalONet)

Neural operators such as the deep operator network (DeepONet) and the Laplace neural operator (LNO) are effective surrogates, but they are almost exclusively trained to reproduce the forward response of a system rather than its intrinsic structure, such as the modal properties of a structural system. We introduce ModalONet, which puts operator learning to a different use, such as recovering the modal basis, namely: mode shapes, natural frequencies, and damping ratios of a dynamical system directly from its response field, with no eigensolver and no labeled modes. Our key observation is that the DeepONet branch-trunk factorization is itself a learnable form of modal superposition: the trunk supplies continuous, mesh-free mode shapes, while an LNO branch supplies the modal coordinates in pole-residue form, so that each learned pole yields a natural frequency and a damping ratio. Training uses the response field alone, under a composite loss of reconstruction, orthonormality, and temporal projection consistency. The degenerate (equal-frequency) modes are resolved by a separable trunk and a shared frequency parameter, with post-hoc log-envelope regression improves the damping ratio estimates. Across four structural systems, namely: simply supported and cantilever Euler-Bernoulli beams and rectangular and (degenerate) square Kirchhoff plates, the ModalONet recovers the analytical modal basis with modal assurance criterion (MAC) values of at least 0.998 for every mode shape, natural frequency errors within 5%, and damping ratio errors within 7%, demonstrating the potential of neural operators as accurate and interpretable tools for modal 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

Vision-Based Structural Damage Identification in Vibrating Beams via Dynamic Mode Decomposition

Structural damage detection using non-contact sensing remains a challenging problem in structural health monitoring. This study presents a data-driven framework based on Dynamic Mode Decomposition (DMD) for extracting structural dynamics directly from high-speed video recordings of vibrating structures. Within this approach, the underlying dynamics are approximated by a linear operator, whose spectral decomposition yields modal frequencies and corresponding spatial mode shapes, enabling a physically interpretable representation of the system response. The proposed methodology is evaluated through both numerical and experimental investigations. First, a cantilever beam model is simulated in ANSYS under healthy and damaged conditions. DMD is applied to partial observation data to reconstruct and predict the system response, while the extracted modal features are analyzed to characterize damage-induced variations. Second, high-speed video recordings of the beam are processed into spatiotemporal snapshot matrices, allowing DMD to recover full-field dynamic behavior without contact sensors. To enable quantitative assessment, a damage index is formulated based on DMD-derived modal features, capturing deviations in both frequency content and spatial characteristics. The results demonstrate consistent and distinguishable patterns between healthy and damaged states across both simulation and experiments, highlighting the capability of DMD as a robust and interpretable tool for non-contact damage detection using video data.

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 ($\mathbfϕ$) 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↗

arXiv2024

Adaptive Two-stage Stochastic Programming with an Analysis on Capacity Expansion Planning Problem

Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the decision maker may need to commit to a set of actions for a number of planning periods. Two-stage stochastic programming might be better suited to such settings, where the decisions for all periods are made here-and-now and do not adapt to the uncertainty realized. In this paper, we propose a novel alternative approach, where the stages are not predetermined but part of the optimization problem. Each component of the decision policy has an associated revision point, a period prior to which the decision is predetermined and after which it is revised to adjust to the uncertainty realized thus far. We motivate this setting using the multi-period newsvendor problem by deriving an optimal adaptive policy. We label the proposed approach as adaptive two-stage stochastic programming and provide a generic mixed-integer programming formulation for finite stochastic processes. We show that adaptive two-stage stochastic programming is NP-hard in general. Next, we derive bounds on the value of adaptive two-stage programming in comparison to the two-stage and multi-stage approaches for a specific problem structure inspired by the capacity expansion planning problem. Since directly solving the mixed-integer linear program associated with the adaptive two-stage approach might be very costly for large instances, we propose several heuristic solution algorithms based on the bound analysis. We provide approximation guarantees for these heuristics. Finally, we present an extensive computational study on an electricity generation capacity expansion planning problem and demonstrate the computational and practical impacts of the proposed approach from various perspectives.

math.OC↗

arXiv2022

Stochastic Identification-based Active Sensing Acousto-Ultrasound SHM Using Stationary Time Series Models

In this work, a probabilistic damage detection and identification scheme using stochastic time series models in the context of acousto-ultrasound guided wave-based SHM is proposed, and its performance is assessed experimentally. In order to simplify the damage detection and identification process, model parameters are modified based on the singular value decomposition (SVD) as well as the principal component analysis (PCA)-based truncation approach. The modified model parameters are then used to estimate a statistical characteristic quantity that follows a chi-squared distribution. A probabilistic threshold is used instead of a user-defined margin to facilitate automatic damage detection. The method's effectiveness is assessed via multiple experiments using both metallic and composite coupons and under various damage scenarios using damage intersecting and damage non-intersecting paths. The results of the study confirm the high potential and effectiveness of the stochastic time series methods for guided wave-based damage detection and identification in a potentially automated way.

eess.SP↗

arXiv2022

Time-varying Identification of Guided Wave Propagation under Varying Temperature via Non-Stationary Time Series Models

Modern-day civil, mechanical, and aeronautical structures are transitioning towards a continuous, online, and automated maintenance paradigm in order to ensure increased safety and reliability. The field of structural health monitoring (SHM) is playing a key role in this respect and active sensing acousto-ultrasound guided-wave based SHM techniques have shown great promise due to their potential sensitivity to small changes in the structure. However, the methods' robustness and diagnosis capability become limited in the presence of environmental and operational variability such as changing temperature. In order to circumvent this difficulty, in this paper, a novel stochastic time series-based framework was adopted to model guided wave propagation under varying temperatures. Different stochastic time-varying time series models, such as Recursive Maximum Likelihood Time-varying Auto-Regressive (RML-TAR) and Recursive Maximum Likelihood Time-varying Auto-Regressive with Exogenous Excitation (RML-TARX) models are put forward to model and capture the underlying dynamics of guided wave propagation under varying temperatures. The steps and facets of the identification procedure are presented and clearly explained. Then the identified models are used to perform one-step-ahead prediction as well as "simulation" of the guided wave signals. In order to gain insight from a physics perspective, high-fidelity finite element (FE) models were also established to model the effect of temperature variation on guided wave propagation. Finally, surrogate models are formulated through the use of stochastic time-dependent RML-TARX models and compared with the FE models under varying temperatures.

eess.SP↗

arXiv2021

Intrusion Detection and Localization for Networked Embedded Control Systems

Closed-loop control systems employ continuous sensing and actuation to maintain controlled variables within preset bounds and achieve the desired system output. Intentional disturbances in the system, such as in the case of cyberattacks, can compromise reachability of control goals, and in several cases jeopardize safety. The increasing connectivity and exposure of networked control to external networks has enabled attackers to compromise these systems by exploiting security vulnerabilities. Attacks against safety-critical control loops can not only drive the system over a trajectory different from the desired, but also cause fatal consequences to humans. In this paper we present a physics-based Intrusion Detection System (IDS) aimed at increasing the security in control systems. In addition to conventional process state estimation for intrusion detection, since the controller cannot be trusted, we introduce a controller state estimator. Additionally, we make our detector context-aware by utilizing sensor measurements from other control loops, which allows to distinguish and characterize disturbances from attacks. We introduce adaptive thresholding and adaptive filtering as means to achieve context-awareness. Together, these methodologies allow detection and localization of attacks in closed-loop controls. Finally, we demonstrate feasibility of the approach by mounting a series of attacks against a networked Direct Current (DC) motor closed-loop speed control deployed on an ECU testbed, as well as on a simulated automated lane keeping system. Among other application domains, this set of approaches is key to support security in automotive systems, and ultimately increase road and passenger safety.

eess.SY↗

arXiv2021

A K-Nearest Neighbor Heuristic for Real-Time DC Optimal Transmission Switching

While transmission switching is known to reduce power generation costs, the difficulty of solving even DC optimal transmission switching (DCOTS) has prevented optimal transmission switching from becoming commonplace in real-time power systems operation. In this paper, we present a k-nearest neighbors (KNN) heuristic for DCOTS which relies on the insight that, for routine operations on a fixed network, the DCOTS solutions for similar load profiles and generation cost profiles will likely turn off similar sets of lines. We take a data-driven approach and assume that we have DCOTS solutions for many historical instances, which is realistic given that the problem is solved every 5 minutes in practice. Given a new instance, we find a set of "close" instances from the past and return the best of their solutions for the new instance. We present a case study on 7 test networks ranging in size from 118 to 3,375 buses. We compare the proposed heuristic to DCOTS heuristics from the literature, commercial solver heuristics, and a simple greedy local search algorithm. In most cases, we find better quality solutions in less computational time. In addition, the computational time is within the limits imposed by real-time operations, even on larger networks. Last, we present an empirical study of our training data to understand why the heuristic works well.

math.OC↗

arXiv2021

Distributionally Robust Bottleneck Combinatorial Problems: Uncertainty Quantification and Robust Decision Making

This paper studies data-driven distributionally robust bottleneck combinatorial problems (DRBCP) with stochastic costs, where the probability distribution of the cost vector is contained in a ball of distributions centered at the empirical distribution specified by the Wasserstein distance. We study two distinct versions of DRBCP from different applications: (i) Motivated by the multi-hop wireless network application, we first study the uncertainty quantification of DRBCP (denoted by DRBCP-U), where decision-makers would like to have an accurate estimation of the worst-case value of DRBCP. The difficulty of DRBCP-U is to handle its max-min-max form. Fortunately, the alternative forms of the bottleneck combinatorial problems from their blockers allow us to derive equivalent deterministic reformulations, which can be computed via mixed-integer programs. In addition, by drawing the connection between DRBCP-U and its sampling average approximation counterpart under empirical distribution, we show that the Wasserstein radius can be chosen in the order of negative square root of sample size, improving the existing known results; and (ii) Next, motivated by the ride-sharing application, decision-makers choose the best service-and-passenger matching that minimizes the unfairness. This gives rise to the decision-making DRBCP (denoted by DRBCP-D). For DRBCP-D, we show that its optimal solution is also optimal to its sampling average approximation counterpart, and the Wasserstein radius can be chosen in a similar order as DRBCP-U. When the sample size is small, we propose to use the optimal value of DRBCP-D to construct an indifferent solution space and propose an alternative decision-robust model, which finds the best indifferent solution to minimize the empirical variance. We further show that the decision robust model can be recast as a mixed-integer program.

math.OC↗

arXiv2021

Two-Point Voltage Fingerprinting: Increasing Detectability of ECU Masquerading Attacks

Automotive systems continuously increase their dependency on Electronic Control Units (ECUs) and become more interconnected to improve safety, comfort and Advanced Driving Assistance Systems (ADAS) functions to passengers and drivers. As a consequence of that trend, there is an expanding attack surface which may potentially expose vehicle's critical functions to cyberattacks. It is possible for an adversary to reach the underlying Control Area Network (CAN) through a compromised node or external-facing network interface, and launch masquerading attacks that can compromise road and passenger safety. Due to lack of native authentication in the CAN protocol, an approach to detect masquerading attacks is to use ECU voltage fingerprinting schemes to verify that the messages are sent by authentic ECUs. Though effective against simple masquerading attacks, prior work is unable to detect attackers such as hardware Trojans, which can mimic ECU voltages in addition to spoofing messages. We introduce a novel Two-point ECU Fingerprinting scheme and demonstrate efficacy in a controlled lab setting and on a moving vehicle. Our results show that our proposed two-point fingerprinting scheme is capable of an overall F1-score over 99.4%. The proposed approach raises the bar for attackers trying to compromise automotive security both remotely and physically, therefore improving security and safety of autonomous vehicles.

cs.CR↗

arXiv2021

Consensus-Based Dantzig-Wolfe Decomposition

Dantzig-Wolfe decomposition (DWD) is a classical algorithm for solving large-scale linear programs whose constraint matrix involves a set of independent blocks coupled with a set of linking rows. The algorithm decomposes such a model into a master problem and a set of independent subproblems that can be solved in a distributed manner. In a typical implementation, the master problem is solved centrally. In certain settings, solving the master problem centrally is undesirable or infeasible, such as in the case of decentralized storage of data, or when independent agents who are responsible for the subproblems desire privacy of information. In this paper, we propose a fully distributed DWD algorithm which relies on solving the master problem using a consensus-based Alternating Direction Method of Multipliers (ADMM) method. We derive error bounds on the optimality gap and feasibility violation of the proposed approach. We provide preliminary computational results for our algorithm using a Message Passing Interface (MPI) implementation on cutting stock instances from the literature and synthetic instances where we obtain high quality solutions.

math.OC↗

arXiv2020

Efficient Algorithms for Distributionally Robust Stochastic Optimization with Discrete Scenario Support

Recently, there has been a growing interest in distributionally robust optimization (DRO) as a principled approach to data-driven decision making. In this paper, we consider a distributionally robust two-stage stochastic optimization problem with discrete scenario support. While much research effort has been devoted to tractable reformulations for DRO problems, especially those with continuous scenario support, few efficient numerical algorithms were developed, and most of them can neither handle the non-smooth second-stage cost function nor the large number of scenarios $K$ effectively. We fill the gap by reformulating the DRO problem as a trilinear min-max-max saddle point problem and developing novel algorithms that can achieve an $\mathcal{O}(1/ε)$ iteration complexity which only mildly depends on $K$. The major computations involved in each iteration of these algorithms can be conducted in parallel if necessary. Besides, for solving an important class of DRO problems with the Kantorovich ball ambiguity set, we propose a slight modification of our algorithms to avoid the expensive computation of the probability vector projection at the price of an $\mathcal{O}(\sqrt{K})$ times more iterations. Finally, preliminary numerical experiments are conducted to demonstrate the empirical advantages of the proposed algorithms.

math.OC↗

arXiv2020

A Simulated Annealing Algorithm for the Directed Steiner Tree Problem

In \cite{siebert2019linear} the authors present a set of integer programs (IPs) for the Steiner tree problem, which can be used for both, the directed and the undirected setting of the problem. Each IP finds an optimal Steiner tree with a specific structure. A solution with the lowest cost, corresponds to an optimal solution to the entire problem. The authors show that the linear programming relaxation of each IP is integral and, also, that each IP is polynomial in the size of the instance, consequently, they can be solved in polynomial time. The main issue is that the number of IPs to solve grows exponentially with the number of terminal nodes, which makes this approach impractical for large instances. In this paper, we propose a local search procedure to solve the directed Steiner tree problem using the approach presented in \cite{siebert2019linear}. In order to do this, we present a dynamic programming algorithm to solve each IP efficiently. Then we provide a characterization of the neighborhood of each tree structure. Finally, we use the proposed algorithm and the neighborhood characterization to solve the problem using a simulated annealing framework. Computational experiments show that the quality of the solutions delivered by our approach is better than the ones presented in the literature for the directed Steiner tree problem.

math.CO↗

arXiv2020

Distributionally Robust Facility Location Problem under Decision-dependent Stochastic Demand

Facility location decisions significantly impact customer behavior and consequently the resulting demand in a wide range of businesses. Furthermore, sequentially realized uncertain demand enforces strategically determining locations under partial information. To address these issues, we study a facility location problem where the distribution of customer demand is dependent on location decisions. We represent moment information of stochastic demand as a piecewise linear function of facility-location decisions. Then, we propose a decision-dependent distributionally robust optimization model, and develop its exact mixed-integer linear programming reformulation. We further derive valid inequalities to strengthen the formulation. We conduct an extensive computational study, in which we compare our model with the existing (decision-independent) stochastic and robust models. Our results demonstrate superior performance of the proposed approach with remarkable improvement in profit and quality of service by extensively testing problem characteristics, in addition to computational speed-ups due to the formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.

math.OC↗