arXiv subjects

Joshua R. Tempelman

Publications and source records attributed to Joshua R. Tempelman.

9 recordsLinked to original sources

arXiv2025

Machine Learning-Based Ultrasonic Weld Characterization Using Hierarchical Wave Modeling and Diffusion-Driven Distribution Alignment

Automated ultrasonic weld inspection remains a significant challenge in the nondestructive evaluation (NDE) community to factors such as limited training data (due to the complexity of curating experimental specimens or high-fidelity simulations) and environmental volatility of many industrial settings (resulting in the corruption of on-the-fly measurements). Thus, an end-to-end machine learning (ML) workflow for acoustic weld inspection in realistic (i.e., industrial) settings has remained an elusive goal. This work addresses the challenges of data curation and signal corruption by proposing workflow consisting of a reduced-order modeling scheme, diffusion based distribution alignment, and U-Net-based segmentation and inversion. A reduced-order Helmholtz model based on Lamb wave theory is used to generate a comprehensive dataset over varying weld heterogeneity and crack defects. The relatively inexpensive low-order solutions provide a robust training dateset for inversion models which are refined through a transfer learning stage using a limited set of full 3D elastodynamic simulations. To handle out-of-distribution (OOD) real-world measurements with varying and unpredictable noise distributions, i.e., Laser Doppler Vibrometry scans, guided diffusion produces in-distribution representations of OOD experimental LDV scans which are subsequently processed by the inversion models. This integrated framework provides an end-to-end solution for automated weld inspection on real data.

cs.LG↗

arXiv2025

Spectral Characterization of Wave Scattering at a Granular-Elastic Solid Interface: From Hyperbolic Wave Propagation to Near-Parabolic Diffusion

We present a method based on acoustic wavenumber imaging algorithms to quantify the spectral content of strongly nonlinear energy scattering of a propagating wavefront across the discrete-continuum interface of a 2D hybrid system composed of an ordered granular layer in contact with a thin elastic plate. We consider snapshots of the transmitted wavefront at given time instants, which are filtered across the wavenumber domain by applying the spatial Fourier Transform (FT), and then the filtered wavefields are transformed back to the spatial domain by inverse spatial FT. This yields a spectral decomposition of the given snapshots at varying center wavenumbers. Based on this postprocessing method, the scattering of the kinetic energy in the receiving medium (plate) can be studied in the wavenumber-time domain, proving a quantitative measure of the nonlinear scattering of the transmitted wavefront by the strongly nonlinear 2D granular layer. This postprocessing method enables the detailed quantitative study of the scattering and spectral energy redistribution of propagating wavepackets in elastic media with embedded linear or nonlinear layers or inclusions. In addition, we show that the spectral evolution of receiving plate with a granular interface exhibits diffusion-like behavior in the wavenumber domain, drawing an analogy between parabolic heat diffusion and classical hyperbolic elsatodynamic energy transport.

cond-mat.stat-mech↗

arXiv2025

Probabilistic Emissivity Retrieval from Hyperspectral Data via Physics-Guided Variational Inference

Recent research has proven neural networks to be a powerful tool for performing hyperspectral imaging (HSI) target identification. However, many deep learning frameworks deliver a single material class prediction and operate on a per-pixel basis; such approaches are limited in their interpretability and restricted to predicting materials that are accessible in available training libraries. In this work, we present an inverse modeling approach in the form of a physics-conditioned generative model.A probabilistic latent-variable model learns the underlying distribution of HSI radiance measurements and produces the conditional distribution of the emissivity spectrum. Moreover, estimates of the HSI scene's atmosphere and background are used as a physically relevant conditioning mechanism to contextualize a given radiance measurement during the encoding and decoding processes. Furthermore, we employ an in-the-loop augmentation scheme and physics-based loss criteria to avoid bias towards a predefined training material set and to encourage the model to learn physically consistent inverse mappings. Monte-Carlo sampling of the model's conditioned posterior delivers a sought emissivity distribution and allows for interpretable uncertainty quantification. Moreover, a distribution-based material matching scheme is presented to return a set of likely material matches for an inferred emissivity distribution. Hence, we present a strategy to incorporate contextual information about a given HSI scene, capture the possible variation of underlying material spectra, and provide interpretable probability measures of a candidate material accounting for given remotely-sensed radiance measurement.

cs.LG↗

arXiv2024

Subwavelength topological interface modes in a multilayered vibroacoustic metamaterial

We present a systematic and rigorous analytical approach, based on the transfer matrix methodology, to study the existence, evolution, and robustness of subwavelength topological interface states in practical multilayered vibroacoustic phononic lattices. These lattices, composed of membrane-air cavity unit cells, exhibit complex band structures with various bandgaps, including Bragg, band-splitting induced, local resonance, and plasma bandgaps. Focusing on the challenging low-frequency range and assuming axisymmetric modes, we show that topological interface states are confined to Bragg-like band-splitting induced bandgaps. Unlike the Su-Schrieffer-Heeger model, the vibroacoustic lattice exhibits diverse topological phase transitions across infinite bands, enabling broadband, multi-frequency vibroacoustics in the subwavelength regime. We establish three criteria for the existence of these states: the Zak phase, surface impedance, and a new reflection coefficient concept, all derived from transfer matrix components. Notably, we provide an explicit expression for the exact location of topological interface states within the band structure, offering insight for their predictive implementation. We confirm the robustness of these states against structural variations and identify delocalization as bandgaps narrow. Our work provides a complete and exact analytical characterization of topological interface states, demonstrating the effectiveness of the transfer matrix method. Beyond its analytical depth, our approach provides a useful framework and design tool for topological phononic lattices, advancing applications such as efficient sound filters, waveguides, noise control, and acoustic sensors in the subwavelength regime. Its versatility extends beyond the vibroacoustic systems, encompassing a broader range of phononic and photonic crystals with repetitive inversion-symmetric unit cells.

physics.app-ph↗

arXiv2024

Physics-Informed Machine Learning for the Inverse Design of Wave Scattering Clusters

Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward scattering problem may be readily analyzed, the inverse problem is very challenging as it is ill-posed, high-dimensional, and known to admit non-unique solutions. Therefore, the inverse design of multiple scattering fields and remote sensing of scattering elements remains a topic of great interest. Motivated by recent advances in physics-informed machine learning, we develop a deep neural network that is capable of predicting the locations of scatterers by evaluating the patterns of a target wavefield. We present a modeling and training formulation to optimize the multi-functional nature of our network in the context of inverse design, remote sensing, and wavefield engineering. Namely, we develop a multi-stage training routine with customized physics-based loss functions to optimize models to detect the locations of scatterers and predict cluster configurations that are physically consistent with the target wavefield. We demonstrate the efficacy of our model as a remote sensing and inverse design tool for three scattering problem types, and we subsequently applicability for designing clusters that direct waves along preferred paths or localize wave energy. Hence, we present an effective model for multiple scattering inverse design which may have diverse applications such as wavefield imaging or passive wave energy control.

eess.SP↗

arXiv2023

A Topological Framework for Identifying Phenomenological Bifurcations in Stochastic Dynamical Systems

Changes in the parameters of dynamical systems can cause the state of the system to shift between different qualitative regimes. These shifts, known as bifurcations, are critical to study as they can indicate when the system is about to undergo harmful changes in its behavior. In stochastic dynamical systems, there is particular interest in P-type (phenomenological) bifurcations, which can include transitions from a mono-stable state to multi-stable states, the appearance of stochastic limit cycles, and other features in the probability density function (PDF) of the system's state. Current practices are limited to systems with small state spaces, cannot detect all possible behaviours of the PDFs, and mandate human intervention for visually identifying the change in the PDF. In contrast, this study presents a new approach based on Topological Data Analysis (TDA) that uses superlevel persistence to mathematically quantify P-type bifurcations in stochastic systems through a "homological bifurcation plot'' -- which shows the changing ranks of 0th and 1st homology groups. Using these plots, we demonstrate the successful detection of P-bifurcations on the stochastic Duffing, Raleigh-Vander Pol and Quintic Oscillators given their analytical PDFs, and elaborate on how to generate an estimated homological bifurcation plot given a kernel density estimate (KDE) of these systems by employing a tool for finding topological consistency between PDFs and KDEs.

math.DS↗

arXiv2023

Wavenumber Scattering and Inter-band Targeted Energy Transfer in Phononic Lattices with Local Vibro-Impact Nonlinearities

We propose a method for manipulating wave propagation in phononic lattices by employing local vibro-impact (VI) nonlinearities to \textit{scatter} energy across the underling linear band structure of the lattice, and \textit{transfer} energy from lower to higher optical bands.Inspired by recent developments in the field of nonlinear targeted energy transfer (TET) using \textit{non-resonant} energy exchanges, we achieve this using spatially localized VI forces that redistribute energy across the linear spectrum of the lattice in a non-resonant fashion.First, a 1-dimensional (1D), 2-band phononic lattice with embedded VI unit cells is computationally studied to demonstrate that energy is scattered in the wavenumber domain, and this nonlinear scattering mechanism depends on the energy of the propagating wave. Next, a 4-band lattice is studied with a similar technique to demonstrate the concept of inter-band targeted energy transfer (IBTET) and to establish analogous scaling relations with respect to energy. To interpret the results of IBTET, we study the nonlinear normal modes (NNMs) of a reduced order model (ROM) of the VI unit cell in the 4-band lattice, using the method of numerical continuation. Interestingly, the slope of the frequency-energy branches of the ROM corresponding to the 1:1 resonance NNM matches remarkably well with the dependence of IBTET to input energy in the 4-band lattice. Moreover, relations between the dynamics of the VI lattice and the NNMs of the underlying Hamiltonian system provide physical interpretations for the relative energy transfers.

physics.app-ph↗

arXiv2021

Topological Protection in a Strongly Nonlinear Interface Lattice

Mechanical topological insulators are well understood for linear and weakly nonlinear systems, however traditional analysis methods break down for strongly nonlinear systems since linear methods can not be applied in that case. We study one such system in the form of a one-dimensional mechanical analog of the Su-Schrieffer-Heeger interface model with strong nonlinearity of the cubic form. The frequency-energy dependence of the nonlinear bulk modes and topologically insulated mode is explored using Numerical continuation of the system's nonlinear normal modes (NNMs), and the linear stability of the NNMs are investigated using Floquet Multipliers (FMs) and Krein signature analysis. We find that the nonlinear topological lattice supports a family of topologically insulated NNMs that are parameterized by the total energy of the system and are stable within a range of frequencies. Next, it is shown that empirical calculations of the geometric Zak Phase can define an energy threshold to predict the excitability of the nonlinear topological mode, and that this threshold coincides with the energy that the topological NNM intersects the linear bulk-spectrum. These predictions are validated with numerical simulations of the nonlinear topological system. These results are also tested for parametric perturbations which preserve and break chirality in the system. Thus, we provide a new method for analyzing and predicting the existence of topologically insulated modes in a strongly nonlinear lattice based on the physical observable of band topology.

physics.app-ph↗

arXiv2020

A Look into Chaos Detection through Topological Data Analysis

Traditionally, computation of Lyapunov exponents has been the marque method for identifying chaos in a time series. Recently, new methods have emerged for systems with both known and unknown models to produce a definitive 0--1 diagnostic. However, there still lacks a method which can reliably perform an evaluation for noisy time series with no known model. In this paper, we present a new chaos detection method which utilizes tools from topological data analysis. Bi-variate density estimates of the randomly projected time series in the $p$-$q$ plane described in Gottwald and Melbourne's approach for 0--1 detection are used to generate a gray-scale image. We show that simple statistical summaries of the 0D sub-level set persistence of the images can elucidate whether or not the underlying time series is chaotic. Case studies on the Lorenz and Rossler attractors as well as the Logistic Map are used to validate this claim. We demonstrate that our test is comparable to the 0--1 correlation test for clean time series and that it is able to distinguish between periodic and chaotic dynamics even at high noise-levels. However, we show that neither our persistence based test nor the 0--1 test converge for trajectories with partially predicable chaos, i.e. trajectories with a cross-distance scaling exponent of zero and a non-zero cross correlation.

nlin.CD↗