Modified Lagrangian Formulation of Gear Tooth Crack Analysis using Combined Approach of Variable Mode Decomposition (VMD) and Time Synchronous Averaging (TSA)

Subrata Mukherjee; Vikash Kumar; Somnath Sarangi

Home/Archive/arXiv

arXiv · 2309.00641

Modified Lagrangian Formulation of Gear Tooth Crack Analysis using Combined Approach of Variable Mode Decomposition (VMD) and Time Synchronous Averaging (TSA)

Subrata Mukherjee·Vikash Kumar·Somnath Sarangi

View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper discusses the possible observation of an integrated gear tooth crack analysis procedure that employs the combined approach of variable mode decomposition (VMD) and time synchronous averaging (TSA) based on the coupled electromechanical gearbox (CEMG) system. This paper also incorporates the modified Lagrangian formulation to model the CEMG system by considering Rayleigh's dissipative potential. An analytical improved time-varying mesh stiffness (IAM-TVMS) with different levels of gear tooth crack depts is also incorporated into the CEMG system to inspect the influence of cracks on the system's dynamic behavior. Dynamic responses of the CEMG system with different tooth crack levels have been used for further investigations. For the first time, the integrated approach of variable mode decomposition (VMD) and time-synchronous averaging (TSA) has been presented to analyze the dynamic behaviour of CEMG systems at the different gear tooth cracks have been experienced as non-stationary and complex vibration signals with noise. Based on the integrated approach of VMD-TSA, two types of nonlinear features, i.e., Lyapunov Exponent (LE) and Correlation Dimension (CD), were calculated to predict the level of chaotic vibration and complexity of the CEMG system at the different levels of gear tooth cracks. Also, the LE and CD are used as chaotic behaviour features to predict the gear tooth crack propagation level. The results of the proposed approach show significant improvements in the gear tooth crack analysis based on the chaotic features. Also, this is one of the first attempts to study the CEMG system using chaotic features based on the combined approach of VMD-TSA.

Explore related subjects

eess.SY cs.LG cs.SY

Keep this discovery

BibTeX RIS

Subrata Mukherjee, Vikash Kumar, Somnath Sarangi. 2023-08-29. Modified Lagrangian Formulation of Gear Tooth Crack Analysis using Combined Approach of Variable Mode Decomposition (VMD) and Time Synchronous Averaging (TSA). https://arxiv.org/abs/2309.00641

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Structured Stochastic Representations of Integrated Dynamic Strategies

Dynamic allocation decisions couple present resource use to evolving internal conditions, delayed returns, and future costs. We represent this interaction by four probability localizations linked through regime-indexed, graph-constrained column-stochastic operators. Pre-action state or context selects a locally affine model, while action-dependent changes update subsequent regimes, yielding a causal switched representation of nonlinear evolution. We characterize operator identifiability relative to the graph, the stochastic constraints, and the sampled embedding, separating coefficient recovery from predictive equivalence on the decision domain. Decision making is then formulated through implementable return--cost acceptability regions. Finite-horizon error propagation supplies conservative classification margins, and simultaneous intervals distinguish model-relative near-optimality from certified $\epsilon$-optimality over a declared finite policy class. Regime-indexed stochastic feedback is admitted when it satisfies the same certification test. Reproducible synthetic laboratories for personal preparation, supplier participation, and customer retention illustrate exact, operator-supplied, and noisy feedback cases. Multinomial experiments show improving recovery of the feedback function and fewer unresolved decisions with increasing sample size, while unrestricted off-policy recovery remains limited. The contribution is a structure-preserving representation--identification--decision workflow, not a domain-specific physiological or commercial calibration.

eess.SY↗

arXiv2026

Fusion Estimation in Multi-sensor Systems for Data Packets with Disrupted Identities

In this paper, we explore the problem of fusion estimation for a multi-sensor system where the identity of the data packet received by each sensor may be disrupted or incorrect due to confusion in device identity allocation, communication protocol defects, or the lack of a clear sensor identifier. This can result in a random shuffle of the data components during the fusion estimation process, compromising the performance of the fusion estimation. To address this issue, we introduce the concepts of permutations and symmetry groups to describe this phenomenon as data packet permutation. We construct statistics to simplify the information set, developing two algorithms: a Bayesian approach, which performs fusion using posterior arrangement probabilities, and a greedy approach, which effectively improves estimation performance by guessing the likely data arrangement. We compare these two algorithms and demonstrate that both are expectation error-bounded. We improve algorithms for information-scarce scenarios. By employing the expectation-maximization algorithm, we fill in the prior information of data arrangement where the correct convergence is proven. Finally, we present numerical simulations to validate our results.

eess.SY↗

arXiv2026

Quantifying the Reality Gap for RL-Based UAV Placement at mmWave and Sub-THz

Reinforcement learning (RL) policies for unmanned aerial vehicle (UAV) placement in mmWave and sub-terahertz networks are typically trained on simplified analytical channels. We quantify the resulting sim-to-real gap on a real urban map of Doha, Qatar, at carriers {28, 140, 183, 300} GHz and altitudes {50, 75, 100, 125} m, evaluating three channel pipelines: an analytical model (FSPL + atmospheric absorption + cuboid LoS), full Monte-Carlo ray tracing in Sionna RT with ITU-R P.676-13 absorption, and a deterministic-LoS hybrid that reuses Sionna's mesh under a closed-form path-gain expression. We formalize the gap on the spatial SNR distribution via four metrics, namely bias, RMSE, Jensen-Shannon divergence, and optimum-deployment displacement. Three findings emerge: at 28/140 GHz, $\sim$70% of the apparent -5.6/-4.8 dB Sionna bias is Monte-Carlo undersampling and shrinks to -1.7/-1.5 dB after mitigation; at 183 GHz a -9.2 dB residual isolates the atmospheric absorption / ITU-R P.676 line-shape disagreement; at 300 GHz the stochastic ray tracer agrees with the analytical model only coincidentally, with a +3.8 dB structural offset exposed by the deterministic-LoS pipeline. Across all carriers the linear-domain regret of the analytical-trained policy stays $\geq$ 0.93, indicating practical near-optimality but with a carrier-resolved SNR bias that warrants explicit reporting.

eess.SY↗