arXiv subjects

Vikram Pakrashi

Publications and source records attributed to Vikram Pakrashi.

13 recordsLinked to original sources

arXiv2026

Interplay of Nonsmoothness, Time Delay, and Stochasticity in Turning Dynamics

The stochastic dynamics of orthogonal metal cutting with both regenerative and nonsmooth frictional effects are investigated numerically in this paper. The shortcomings of neglecting nonsmoothness in frictional and stochastic effects in modeling the dynamics of such a machining process are demonstrated. Dynamics of the tool motion is observed to exhibit rich nonlinear phenomena such as stick-slip during chatter, with stochastic perturbations in cutting forces adding further complexity, leading to the occurrence of stochastic P and D bifurcations. Measures of entropy are found to be effective in quantifying the dynamical transitions occurring in the dynamics of the tool. Subsequently, basin stability analyses, modified to account for stochasticity and time-delays, are carried out to systematically investigate the dynamics of the cutting tool across multiple surface roughness profiles of the workpiece. Basin stability analyses indicate that chatter can be controlled by restricting initial tool displacement and controlling initial workpiece surface roughness, suggesting practical strategies to improve machining outcomes for precision manufacturing.

nlin.CD↗

arXiv2026

A finite volume Simo-Reissner beam method for moored floating body dynamics

This paper presents a novel finite volume mooring line model based on the geometrically exact Simo-Reissner beam model for analysing the interaction between a floating rigid body and its mooring lines. The coupled numerical model is implemented entirely within a finite volume-based discretisation framework using a popular computational fluid dynamics C++ toolbox, OpenFOAM. Unlike existing methods for modelling mooring lines, which rely on lumped mass models or finite element-based approaches, this work simulates the mooring cables using non-linear beam models implemented in a finite volume framework to account for bending, tensile, and torsional loading. This advancement makes the current work particularly valuable for simulating extreme sea conditions. The coupled model developed in this study has been validated and verified using experimental and numerical data for a floating box moored with four catenary mooring lines under regular wave conditions featuring different wave heights and periods. The results demonstrate strong agreement with both experimental and numerical data, highlighting the model's accuracy in capturing mooring dynamics and floating body motion.

math.NA↗

arXiv2025

Bellman Memory Units: A neuromorphic framework for synaptic reinforcement learning with an evolving network topology

Application of neuromorphic edge devices for control is limited by the constraints on gradient-free online learning and scalability of the hardware across control problems. This paper introduces a synaptic Q-learning algorithm for the control of the classical Cartpole, where the Bellman equations are incorporated at the synaptic level. This formulation enables the iterative evolution of the network topology, represented as a directed graph, throughout the training process. This is followed by a similar approach called neuromorphic Bellman Memory Units (BMU(s)), which are implemented with the Neural Engineering Framework on Intel's Loihi neuromorphic chip. Topology evolution, in conjunction with mixed-signal computation, leverages the optimization of the number of neurons and synapses that could be used to design spike-based reinforcement learning accelerators. The proposed architecture can potentially reduce resource utilization on board, aiding the manufacturing of compact application-specific neuromorphic ICs. Moreover, the on-chip learning introduced in this work and implemented on a neuromorphic chip can enable adaptation to unseen control scenarios.

eess.SY↗

arXiv2025

Neuromorphic computing for anomaly detection in a laser powder bed fusion process

This study is the first application of spiking neural networks (SNNs) for anomaly detection in the Laser Powder Bed Fusion (LPBF) additive manufacturing process. The neural networks were used to identify print processing anomalies generated by dropping of laser energy during the printing of individual layers in a Ti-6Al-4V alloy lattice structures. Associated changes in the laser generated melt pool were observed using an in-process photodiode monitoring technique. photodiode sensors capturing plasma and infrared radiations reflected from the print bed of the metal 3D printer were utilized to detect sudden changes caused by anomalies during the printing process. The algorithm is first implemented on non-neuromorphic hardware including a central processing unit (CPU), on Field Programmable Gate Arrays (FPGA) and then on neuromorphic Intel's Loihi chip. Improved detection of anomalies is achieved by adjusting the spike latency of the neural network, which reduces masking of information by noise within the monitored temporal signal. The work demonstrates the possibility of using low-power neuromorphic chips within an edge framework for anomaly detection in additive manufacturing and creates a framework for the process.

eess.SP↗

arXiv2025

Improved Stability Estimates and Flight Time Predictions Using Higher-Order Transverse Discontinuity Mapping in Hybrid Dynamical Systems

This article emphasizes on inconsistencies in the dynamical estimates obtained by first-order transverse discontinuity mapping (TDM) and direct numerical observations for hybrid dynamical systems. Pitfalls of locally linearizing hybrid nonlinear dynamical systems near discontinuity boundaries are demonstrated along with examples of how such linearization could lead to incorrect estimates of impact occurrences for transverse interactions with a rigid barrier. A higher-order TDM is proposed to overcome this shortcoming, allowing for better analytical estimation of impact occurrence times, state transitions, and, consequently, the evolution of trajectories. The difference in flight times of two closely initiated trajectories in the local neighbourhood of a discontinuity boundary is estimated up to $\mathcal{O}(2)$. The resulting quadratic equation implies that the orbits local to the impacting state, corresponding to a negative discriminant, won't reach the discontinuity boundary. Further, the $\mathcal{O}(2)$ correction terms to the analytical expression of the TDM ensure that the flight time estimates do not diverge for low-velocity impacts near grazing, thereby avoiding overestimation of the mapped state. A numerical method is subsequently developed to estimate a saltation matrix incorporating the proposed higher-order TDM to avoid incorrect impact occurrences. Modifications to the existing algorithms used to numerically quantify local stability, namely the Lyapunov spectra and Floquet multipliers, are proposed. Stability analyses using the proposed higher-order approach are carried out for representative cases of a hard impact oscillator and a pair impact oscillator, with results consistent with numerically obtained bifurcation diagrams.

nlin.CD↗

arXiv2025

Explaining Optomechanical Libration Spectra: A Stochastic Simulation Approach

We present a practical and computationally effective Ito-Taylor expansion based stochastic simulation framework for modeling rotational optomechanics experiments. By developing a model using this framework, we could capture the nonlinear orientation dynamics of an optically levitated, nearly cylindrically symmetric nanodumbbell. It successfully reproduces and explains shoulder-like features observed in the power spectral density of libration, which we show arising from the interplay between confined libration and thermally driven rotation around the particle symmetry axis.

physics.comp-ph↗

arXiv2025

Benchmarking Spiking Neurons for Linear Quadratic Regulator Control of Multi-linked Pole on a Cart: from Single Neuron to Ensemble

The emerging field of neuromorphic computing for edge control applications poses the need to quantitatively estimate and limit the number of spiking neurons, to reduce network complexity and optimize the number of neurons per core and hence, the chip size, in an application-specific neuromorphic hardware. While rate-encoding for spiking neurons provides a robust way to encode signals with the same number of neurons as an ANN, it often lacks precision. To achieve the desired accuracy, a population of neurons is often needed to encode the complete range of input signals. However, using population encoding immensely increases the total number of neurons required for a particular application, thus increasing the power consumption and on-board resource utilization. A transition from two neurons to a population of neurons for the LQR control of a cartpole is shown in this work. The near-linear behavior of a Leaky-Integrate-and-Fire neuron can be exploited to achieve the Linear Quadratic Regulator (LQR) control of a cartpole system. This has been shown in simulation, followed by a demonstration on a single-neuron hardware, known as Lu.i. The improvement in control performance is then demonstrated by using a population of varying numbers of neurons for similar control in the Nengo Neural Engineering Framework, on CPU and on Intel's Loihi neuromorphic chip. Finally, linear control is demonstrated for four multi-linked pendula on cart systems, using a population of neurons in Nengo, followed by an implementation of the same on Loihi. This study compares LQR control in the NEF using $7$ control and $7$ neuromorphic performance metrics, followed by a comparison with other conventional spiking and non-spiking controllers.

eess.SY↗

arXiv2025

Higher-Order Transverse Discontinuity Mapping in Filippov Systems: Analysis and Experimental Validation using an Electronic Circuit

This paper shows that linearizing the transverse discontinuity mapping (TDM) in Filippov systems can produce inaccurate predictions of the dynamics in impact oscillators operating near a pre-stressed soft barrier. This discrepancy arises from the limitations of the linearized saltation matrix, which inaccurately predicts impacts in the local neighborhood of the discontinuity boundary. To address this issue, a higher-order approximation of the TDM is derived, which accurately captures the onset of impacts and closely matches the results obtained from both numerical simulations and electronic experiments. The proposed higher-order TDM results in a quadratic estimation of flight time for impacts. Geometrically, real-valued impact events are only feasible when the discriminant of this quadratic equation is positive. The differences in the predicted higher-order flight times and mapping estimates become more pronounced for low-velocity impacts close to grazing. Subsequently, a numerical approximation of the higher-order saltation matrix and its consequent Floquet multipliers and Lyapunov exponents for stability analysis is proposed and demonstrated on a pre-stressed, forced, damped, soft impact oscillator. To validate the numerically observed discontinuity-induced bifurcations, an analog electronic circuit is proposed that models a soft mechanical prestressed oscillator. This inductor-less circuit overcomes the limitations of typical LCR-based circuits, which are used to design such oscillators but cannot accommodate low stiffness ratios. The experimentally obtained limit cycles, finger-shaped Poincaré sections, and bifurcation diagrams match the predictions of the higher-order TDM, validating that the proposed circuit accurately models the soft-impact oscillator for both low and high stiffness ratios.

nlin.CD↗

arXiv2024

Wake-induced response of vibro-impacting systems

The stability and bifurcation behaviour of a wake-induced vibro-impacting oscillator is studied. The effects of a discontinuity on the stability of the structure while it is undergoing phase-locked motions due to the surrounding fluid-structure interactions (FSI) are examined. The primary structure and the near wake dynamics are modelled as a harmonic oscillator and a Van der Pol oscillator, respectively, and are weakly coupled to each other via acceleration coupling. Qualitative changes in the dynamical behaviour of this system are investigated in the context of discontinuity-induced bifurcations (DIBs) that result from the interaction of fluid flow and non-smoothness from the primary structure. Phenomenological behaviours like the co-existence of attractors and period-adding cascades of limit cycles separated by chaotic orbits are observed. The existence of these phenomena is demonstrated via stability analysis using Floquet theory and the associated Lyapunov spectra. In addition, the behaviour of orbits in the local neighbourhood of the barrier is defined using a higher-order transverse discontinuity map. This mapping is implemented to obtain the respective Lyapunov exponents. Solutions obtained using this modified algorithm are demonstrated to accurately predict both stable and chaotic regimes, as observed from the corresponding bifurcation diagrams.

nlin.CD↗

arXiv2023

Exploring Chaos and Ergodic behavior of an Inductorless Circuit driven by Stochastic Parameters

There exist extensive studies on periodic and random perturbations of various continuous maps investigating their dynamics. This paper presents a random piecewise smooth map derived from a simple inductor-less switching circuit. The bifurcation parameter is bounded and randomly selected from a stationary distribution. Due to the stochasticity inherent in either the parameter values or the state variable, the time evolution of the state variable cannot be predicted at a specific time instant. We observe that the state variable exhibits completely ergodic behavior when the minimum value of the parameter is 2.0. However, the ensemble average of the state variable converges to a fixed value. For parameter values ranging from 2.0 to 3.5, the system demonstrates nonchaotic behavior, and the absolute value of the Lyapunov exponent increases monotonically with the asymmetry (ap) of the distribution from which the bifurcation parameter values are sampled. We determine the probability density function of the random map and verify its invariance under any initial condition. The most noteworthy result is the disappearance of chaotic behavior when the lower range of the distribution is varied while maintaining a fixed upper threshold for a particular distribution, even though the nonrandom map exhibits an array of periodic and chaotic behaviors within that range.

nlin.AO↗

arXiv2021

A cell-centred finite volume formulation of geometrically-exact Simo-Reissner beams with arbitrary initial curvatures

This paper presents a novel total Lagrangian cell-centred finite volume formulation of geometrically exact beams with arbitrary initial curvature undergoing large displacements and finite rotations. The choice of rotation parametrisation, the mathematical formulation of the beam kinematics, conjugate strain measures and the linearisation of the strong form of governing equations is described. The finite volume based discretisation of the computational domain and the governing equations for each computational volume are presented. The discretised integral form of the equilibrium equations are solved using a block-coupled Newton-Raphson solution procedure. The efficacy of the proposed methodology is presented by comparing the simulated numerical results with classic benchmark test cases available in the literature. The objectivity of strain measures for the current formulation and mesh convergence studies for both initially straight and curved beam configurations are also discussed.

math.NA↗

arXiv2019

Effective Bounds on Network-Size for Anti-phase Synchronization

We consider anti-phase synchronization of coupled oscillators using the Stuart-Landau model and explore its relative infrequency in occurrence compared to in-phase synchronization. We report effective limits in number of oscillators which can anti-phase synchronize for general configurations of real-world networks. We link anti-phase synchronization to the Ising model and consequently to combinatorial optimization problems, thereby explaining experimentally observed limits in self-organization of natural systems. We illustrate this using the Steiner-tree problem.

nlin.AO↗

arXiv2017

Extreme Value Estimates using Vibration Energy Harvesting

This paper establishes the possibility of utilising energy harvesting from mechanical vibrations to estimate extreme value responses of the host structure and demonstrates the calibration of these estimates for excitation spectra typical to natural systems. For illustrative purposes, a cantilever type energy harvester is considered for wind excitation. The extreme value estimates are established through a Generalised Pareto Distribution (GPD). Classically well-known Kaimal and Davenport spectra for wind have been considered in this paper for comparison purposes. The work also demonstrates how return levels can be mapped using energy harvesting levels and indicates that vibration energy harvesting, in its own right has the potential to be used for extreme value analysis and estimates. The work has impact on health monitoring and assessment of built infrastructure in various stages of repair or disrepair and exposed to nature throughout their lifetime.

stat.AP↗