arXiv subjects

S. Gopalakrishnan

Publications and source records attributed to S. Gopalakrishnan.

At least 19 recordsLinked to original sources

arXiv2025

UNCA: A Neutrosophic-Based Framework for Robust Clustering and Enhanced Data Interpretation

Accurately representing the complex linkages and inherent uncertainties included in huge datasets is still a major difficulty in the field of data clustering. We address these issues with our proposed Unified Neutrosophic Clustering Algorithm (UNCA), which combines a multifaceted strategy with Neutrosophic logic to improve clustering performance. UNCA starts with a full-fledged similarity examination via a {\lambda}-cutting matrix that filters meaningful relationships between each two points of data. Then, we initialize centroids for Neutrosophic K-Means clustering, where the membership values are based on their degrees of truth, indeterminacy and falsity. The algorithm then integrates with a dynamic network visualization and MST (Minimum Spanning Tree) so that a visual interpretation of the relationships between the clusters can be clearly represented. UNCA employs SingleValued Neutrosophic Sets (SVNSs) to refine cluster assignments, and after fuzzifying similarity measures, guarantees a precise clustering result. The final step involves solidifying the clustering results through defuzzification methods, offering definitive cluster assignments. According to the performance evaluation results, UNCA outperforms conventional approaches in several metrics: it achieved a Silhouette Score of 0.89 on the Iris Dataset, a Davies-Bouldin Index of 0.59 on the Wine Dataset, an Adjusted Rand Index (ARI) of 0.76 on the Digits Dataset, and a Normalized Mutual Information (NMI) of 0.80 on the Customer Segmentation Dataset. These results demonstrate how UNCA enhances interpretability and resilience in addition to improving clustering accuracy when contrasted with Fuzzy C-Means (FCM), Neutrosophic C-Means (NCM), as well as Kernel Neutrosophic C-Means (KNCM). This makes UNCA a useful tool for complex data processing tasks

cs.LG↗

arXiv2024

Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems

We consider one dimensional many-particle systems that exhibit kinematically protected single-particle excitations over their ground states. We show that momentum and time-resolved 4-point functions of operators that create such excitations diverge linearly in particular time differences. This behaviour can be understood by means of a simple semiclassical analysis based on the kinematics and scattering of wave packets of quasiparticles. We verify that our wave packet analysis correctly predicts the long-time limit of the four-point function in the transverse field Ising model through a form factor expansion. We present evidence in favour of the same behaviour in integrable quantum field theories. In addition, we extend our discussion to experimental protocols where two times of the four-point function coincide, e.g. 2D coherent spectroscopy and pump-probe experiments. Finally, focusing on the Ising model, we discuss subleading corrections that grow as the square root of time differences. We show that the subleading corrections can be correctly accounted for by the same semiclassical analysis, but also taking into account wave packet spreading.

cond-mat.str-el↗

arXiv2023

Bayesian optimized physics-informed neural network for estimating wave propagation velocities

In this paper, we propose a novel inverse parameter estimation approach called Bayesian optimized physics-informed neural network (BOPINN). In this study, a PINN solves the partial differential equation (PDE), whereas Bayesian optimization (BO) estimates its parameter. The proposed BOPINN estimates wave velocity associated with wave propagation PDE using a single snapshot observation. An objective function for BO is defined as the mean squared error (MSE) between the surrogate displacement field and snapshot observation. The inverse estimation capability of the proposed approach is tested in three different isotropic media with different wave velocities. From the obtained results, we have observed that BOPINN can accurately estimate wave velocities with lower MSE, even in the presence of noisy conditions. The proposed algorithm shows robust predictions in limited iterations across different runs.

eess.SP↗

arXiv2023

IoT-Based Environmental Control System for Fish Farms with Sensor Integration and Machine Learning Decision Support

In response to the burgeoning global demand for seafood and the challenges of managing fish farms, we introduce an innovative IoT based environmental control system that integrates sensor technology and advanced machine learning decision support. Deploying a network of wireless sensors within the fish farm, we continuously collect real-time data on crucial environmental parameters, including water temperature, pH levels, humidity, and fish behavior. This data undergoes meticulous preprocessing to ensure its reliability, including imputation, outlier detection, feature engineering, and synchronization. At the heart of our system are four distinct machine learning algorithms: Random Forests predict and optimize water temperature and pH levels for the fish, fostering their health and growth; Support Vector Machines (SVMs) function as an early warning system, promptly detecting diseases and parasites in fish; Gradient Boosting Machines (GBMs) dynamically fine-tune the feeding schedule based on real-time environmental conditions, promoting resource efficiency and fish productivity; Neural Networks manage the operation of critical equipment like water pumps and heaters to maintain the desired environmental conditions within the farm. These machine learning algorithms collaboratively make real-time decisions to ensure that the fish farm's environmental conditions align with predefined specifications, leading to improved fish health and productivity while simultaneously reducing resource wastage, thereby contributing to increased profitability and sustainability. This research article showcases the power of data-driven decision support in fish farming, promising to meet the growing demand for seafood while emphasizing environmental responsibility and economic viability, thus revolutionizing the future of fish farming.

eess.SP↗

arXiv2023

Deep generative models for unsupervised delamination detection using guided waves

With the rising demands for robust structural health monitoring procedures for aerospace structures, the scope of intelligent algorithms and learning techniques is expanding. Supervised algorithms have shown promising results in the field provided a large, balanced, and labeled amount of data for training. For some applications like aerospace, the data collection process is cumbersome, time-taking, and costly. Also, generating possible damage scenarios in a laboratory setup is challenging because of the complexity of the damage initiation and failure mechanism. Besides this, the uncertainties of the real-time operation restrict the online prediction accuracy with supervised learning. In this paper, deep generative models are proposed for unsupervised delamination prediction as an anomaly detection problem. In this one-class-based model, the deep learning network is trained to learn the distribution of baseline signals. In the testing phase, damage signals and unseen baseline signals are fed into the trained network to predict the state of the structure, i.e., healthy or unhealthy (delamination). It is seen that the proposed method can successfully predict the delamination with high accuracy.

eess.SP↗

arXiv2022

Towards deep generation of guided wave representations for composite materials

Laminated composite materials are widely used in most fields of engineering. Wave propagation analysis plays an essential role in understanding the short-duration transient response of composite structures. The forward physics-based models are utilized to map from elastic properties space to wave propagation behavior in a laminated composite material. Due to the high-frequency, multi-modal, and dispersive nature of the guided waves, the physics-based simulations are computationally demanding. It makes property prediction, generation, and material design problems more challenging. In this work, a forward physics-based simulator such as the stiffness matrix method is utilized to collect group velocities of guided waves for a set of composite materials. A variational autoencoder (VAE)-based deep generative model is proposed for the generation of new and realistic polar group velocity representations. It is observed that the deep generator is able to reconstruct unseen representations with very low mean square reconstruction error. Global Monte Carlo and directional equally-spaced samplers are used to sample the continuous, complete and organized low-dimensional latent space of VAE. The sampled point is fed into the trained decoder to generate new polar representations. The network has shown exceptional generation capabilities. It is also seen that the latent space forms a conceptual space where different directions and regions show inherent patterns related to the generated representations and their corresponding material properties.

eess.SP↗

arXiv2022

Real-time rapid leakage estimation for deep space habitats using exponentially-weighted adaptively-refined search

The recent accelerated growth in space-related research and development activities makes the near-term need for long-term extraterrestrial habitats evident. Such habitats must operate under continuous disruptive conditions arising from extreme environments like meteoroid impacts, extreme temperature fluctuations, galactic cosmic rays, destructive dust, and seismic events. Loss of air or atmospheric leakage from a habitat poses safety challenges that demand proper attention. Such leakage may arise from micro-meteoroid impacts, crack growth, bolt/rivet loosening, and seal deterioration. In this paper, leakage estimation in deep space habitats is posed as an inverse problem. A forward pressure-based dynamical model is formulated for atmospheric leakage. Experiments are performed on a small-scaled pressure chamber where different leakage scenarios are emulated and corresponding pressure values are measured. An exponentially-weighted adaptively-refined search (EWARS) algorithm is developed and validated for the inverse problem of real-time leakage estimation. It is demonstrated that the proposed methodology can achieve real-time estimation and tracking of constant and variable leaks with accuracy.

eess.SP↗

arXiv2022

Computing Anti-Derivatives using Deep Neural Networks

This paper presents a novel algorithm to obtain the closed-form anti-derivative of a function using Deep Neural Network architecture. In the past, mathematicians have developed several numerical techniques to approximate the values of definite integrals, but primitives or indefinite integrals are often non-elementary. Anti-derivatives are necessarily required when there are several parameters in an integrand and the integral obtained is a function of those parameters. There is no theoretical method that can do this for any given function. Some existing ways to get around this are primarily based on either curve fitting or infinite series approximation of the integrand, which is then integrated theoretically. Curve fitting approximations are inaccurate for highly non-linear functions and require a different approach for every problem. On the other hand, the infinite series approach does not give a closed-form solution, and their truncated forms are often inaccurate. We claim that using a single method for all integrals, our algorithm can approximate anti-derivatives to any required accuracy. We have used this algorithm to obtain the anti-derivatives of several functions, including non-elementary and oscillatory integrals. This paper also shows the applications of our method to get the closed-form expressions of elliptic integrals, Fermi-Dirac integrals, and cumulative distribution functions and decrease the computation time of the Galerkin method for differential equations.

math.NA↗

arXiv2022

Inverse characterization of composites using guided waves and convolutional neural networks with dual-branch feature fusion

In this work, ultrasonic guided waves and a dual-branch version of convolutional neural networks are used to solve two different but related inverse problems, i.e., finding layup sequence type and identifying material properties. In the forward problem, polar group velocity representations are obtained for two fundamental Lamb wave modes using the stiffness matrix method. For the inverse problems, a supervised classification-based network is implemented to classify the polar representations into different layup sequence types (inverse problem - 1) and a regression-based network is utilized to identify the material properties (inverse problem - 2)

eess.SP↗

arXiv2022

Delamination prediction in composite panels using unsupervised-feature learning methods with wavelet-enhanced guided wave representations

With the introduction of damage tolerance-based design philosophies, the demand for reliable and robust structural health monitoring (SHM) procedures for aerospace composite structures is increasing rapidly. The performance of supervised learning algorithms for SHM depends on the amount of labeled and balanced datasets. Apart from this, collecting datasets accommodating all possible damage scenarios is cumbersome, costly, and inaccessible for aerospace applications. In this paper, we have proposed two different unsupervised-feature learning approaches where the algorithms are trained only on the baseline scenarios to learn the distribution of baseline signals. The trained unsupervised feature learner is used for delamination prediction with an anomaly detection philosophy. In the first approach, we have combined dimensionality reduction techniques (principal component analysis and independent component analysis) with a one-class support vector machine. In another approach, we have utilized deep learning-based deep convolutional autoencoders (CAE). These state-of-the-art algorithms are applied on three different guided wave-based experimental datasets. The raw guided wave signals present in the datasets are converted into wavelet-enhanced higher-order representations for training unsupervised feature-learning algorithms. We have also compared different techniques, and it is seen that CAE generates better reconstructions with lower mean squared error and can provide higher accuracy on all the datasets.

eess.SP↗

arXiv2020

Direct measurement of non-local interactions in the many-body localized phase

The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modification of the dynamics, making their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two qubit density matrices allowed us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here measure affirmative correlations and allow us to exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter.

cond-mat.dis-nn↗

arXiv2019

Distinguishing localization from chaos: challenges in finite-size systems

We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models for which rigorous results are available, we find that these measures can be particularly adversely affected by the strong finite-size effects observed in nearly all numerical studies of many-body localization. This severely impacts their utility in probing the transition and the localized phase. In light of this analysis, we argue that a recent study [Šuntajs et al., arXiv:1905.06345] of the behavior of the Thouless energy and level repulsion in disordered spin chains likely reaches misleading conclusions, in particular as to the absence of MBL as a true phase of matter.

cond-mat.str-el↗

arXiv2018

Differential quadrature element for second strain gradient beam theory

In this paper, first we present the variational formulation for a second strain gradient Euler-Bernoulli beam theory for the first time. The governing equation and associated classical and non-classical boundary conditions are obtained. Later, we propose a novel and efficient differential quadrature element based on Lagrange interpolation to solve the eight order partial differential equation associated with the second strain gradient Euler-Bernoulli beam theory. The second strain gradient theory has displacement, slope, curvature and triple displacement derivative as degrees of freedom. A generalize scheme is proposed herein to implement these multi-degrees of freedom in a simplified and efficient way. The proposed element is based on the strong form of governing equation and has displacement as the only degree of freedom in the domain, whereas, at the boundaries it has displacement, slope, curvature and triple derivative of displacement. A novel DQ framework is presented to incorporate the classical and non-classical boundary conditions by modifying the conventional weighting coefficients. The accuracy and efficiency of the proposed element is demonstrated through numerical examples on static, free vibration and stability analysis of second strain gradient elastic beams for different boundary conditions and intrinsic length scale values.

cs.CE↗

arXiv2018

Novel weak form quadrature elements for second strain gradient Euler-Bernoulli beam theory

Two novel version of weak form quadrature elements are proposed based on Lagrange and Hermite interpolations, respectively, for a sec- ond strain gradient Euler-Bernoulli beam theory. The second strain gradient theory is governed by eighth order partial differential equa- tion with displacement, slope, curvature and triple derivative of dis- placement as degrees of freedom. A simple and efficient differential quadrature frame work is proposed herein to implement these classi- cal and non-classical degrees of freedom. A novel procedure to com- pute the modified weighting coefficient matrices for the beam element is presented. The proposed elements have displacement as the only degree of freedom in the element domain and displacement, slope, cur- vature and triple derivative of displacement at the boundaries. The Gauss-Lobatto-Legender quadrature points are assumed as element nodes and also used for numerical integration of the element matrices. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed beam element.

cs.CE↗

arXiv2018

Novel differential quadrature element method for higher order strain gradient elasticity theory

In this paper, we propose a novel and efficient differential quadrature element based on Lagrange interpolation to solve a sixth order partial differential equations encountered in non-classical beam theories. These non-classical theories render displacement, slope and curvature as degrees of freedom for an Euler-Bernoulli beam. A generalize scheme is presented herein to implementation the multi-degrees degrees of freedom associated with these non-classical theories in a simplified and efficient way. The proposed element has displacement as the only degree of freedom in the domain, whereas, at the boundaries it has displacement, slope and curvature. Further, we extend this methodology and formulate two novel versions of plate element for gradient elasticity theory. In the first version, Lagrange interpolation is assumed in $x$ and $y$ directions and the second version is based on mixed interpolation, with Lagrange interpolation in $x$ direction and Hermite interpolation in $y$ direction. The procedure to compute the modified weighting coefficients by incorporating the classical and non-classical boundary conditions is explained. The efficiency of the proposed elements is demonstrated through numerical examples on static analysis of gradient elastic beams and plates for different boundary conditions.

cs.CE↗

arXiv2018

Novel weak form quadrature elements for non-classical higher order beam and plate theories

Based on Lagrange and Hermite interpolation two novel versions of weak form quadrature element are proposed for a non-classical Euler-Bernoulli beam theory. By extending these concept two new plate elements are formulated using Lagrange-Lagrange and mixed Lagrange-Hermite interpolations for a non-classical Kirchhoff plate theory. The non-classical theories are governed by sixth order partial differential equation and have deflection, slope and curvature as de- grees of freedom. A novel and generalize way is proposed herein to implement these degrees of freedom in a simple and efficient manner. A new procedure to compute the modified weighting coefficient matri- ces for beam and plate elements is presented. The proposed elements have displacement as the only degree of freedom in the element do- main and displacement, slope and curvature at the boundaries. The Gauss-Lobatto-Legender quadrature points are considered as element nodes and also used for numerical integration of the element matrices. The framework for computing the stiffness matrices at the integra- tion points is analogous to the conventional finite element method. Numerical examples on free vibration analysis of gradient beams and plates are presented to demonstrate the efficiency and accuracy of the proposed elements.

cs.CE↗

arXiv2017

Unified nonlocal rational continuum models developed from discrete atomistic equations

In this paper, a unified nonlocal rational continuum enrichment technique is presented for improving the dispersive characteristics of some well known classical continuum equations on the basis of atomistic dispersion relations. This type of enrichment can be useful in a wide range of mechanical problems such as localization of strain and damage in many quasibrittle structures, size effects in microscale elastoplasticity, and multiscale modeling of materials. A novel technique of transforming a discrete differential expression into an exact equivalent rational continuum derivative form is developed considering the Taylor's series transformation of the continuous field variables and traveling wave type of solutions for both the discrete and continuum field variables. An exact equivalent continuum rod representation of the 1D harmonic lattice with the non-nearest neighbor interactions is developed considering the lattice details. Using similar enrichment technique in the variational framework, other useful higher-order equations, namely nonlocal rational Mindlin-Herrmann rod and nonlocal rational Timoshenko beam equations, are developed to explore their nonlocal properties in general. Some analytical and numerical studies on the high frequency dynamic behavior of these novel nonlocal rational continuum models are presented with their comparison with the atomistic solutions for the respective physical systems. These enriched rational continuum equations have crucial use in studying high-frequency dynamics of many nano-electro-mechanical sensors and devices, dynamics of phononic metamaterials, and wave propagation in composite structures.

cond-mat.mtrl-sci↗

arXiv2015

Phononic band structure of honeycomb lattice with defects, using spectrally formulated finite element method

A spectrally formulated finite element analysis based methodology has been proposed to calculate phononic band structure of reticulated honeycomb lattices having translationally invariant repetitive elements called unit cells. Bloch formulation captures dynamics of infinite structure through that of a unit cell. While conventional FEM is generally used for analyzing dynamics of such unit systems, here, constituent structural members are treated as 1D waveguide and modeled as Timoshenko beam frame element, enabling application of spectral FEM, suitable for accurately analyzing the dynamics, particularly efficient at very high frequencies. Using exact solutions as shape functions spares dense meshing. Resulting eigenvalue problem is solved by Wittrick-Williams method, an iterative scheme. Subsequently, band structures are obtained for supercells- units comprising multiple elemental unit cells; compared and reconciled with those obtained using elemental cell (termed primitive unit cell to distinguish from supercell). Primitive cell band structures are reconstructed from Supercell band structures. Supercell band structures show some spurious bands, which are explained in terms of band folding in the primitive cell band structure. Supercell allows treatment of defects as a periodic feature with certain defect density. Of particular observation in such band structures is the separation of bands, known as degeneracy breaking.

cond-mat.mtrl-sci↗