Academic literature on the topic 'Nonlinear time warping'

The problem of estimating relative time (or depth) shifts between two seismic images is ubiquitous in seismic data processing. This problem is especially difficult where shifts are large and vary rapidly with time and space, and where images are contaminated with noise or for other reasons are not shifted versions of one another. A new solution to this problem requires only simple extensions of a classic dynamic time warping algorithm for speech recognition. A key component of that classic algorithm is a nonlinear accumulation of alignment errors. By applying the same nonlinear accumulator repeatedly in all directions along all sampled axes of a multidimensional image, I obtain a new and effective method for dynamic image warping (DIW). In tests where known shifts vary rapidly, this new method is more accurate than methods based on crosscorrelations of windowed images. DIW also aligns seismic reflectors well in examples where shifts are unknown, for images with differences not limited to time shifts.

Mapping PS-wave data to the PP-wave time domain is a critical step before joint PP- and PS-wave data interpretation and inversion. Registration techniques are often constrained by having access to a known [Formula: see text] ratio. When an accurate [Formula: see text] ratio is not provided, one can solve the problem of seismic data registration by minimizing the difference between the PP-wave and the warped PS-wave data with a smoothing constraint applied on the warping function. To avoid undesirable foldings or rapid changes in the warped PS-wave image, we require a warping function that is monotonic and smooth. We invert the [Formula: see text] ratio directly from PP- and PS-wave data instead of estimating it from the warping function. Seismic data registration is posed as a constrained nonlinear optimization problem. Furthermore, we represent the [Formula: see text] ratio by spline functions and adopt a parameterization that guarantees monotonic warping functions. Our parameterization in terms of splines significantly reduces the number of unknowns of our problem, and the convergence to a smooth monotonic solution is guaranteed.

Time series forecasting based on pattern matching has received a lot of interest in the recent years due to its simplicity and the ability to predict complex nonlinear behavior. In this paper, we investigate into the predictive potential of the method using k-NN algorithm based on R*-tree under dynamic time warping (DTW) measure. The experimental results on four real datasets showed that this approach could produce promising results in terms of prediction accuracy on time series forecasting when comparing to the similar method under Euclidean distance.

Dynamic Time Warping (DTW) is a common technique widely used for nonlinear time normalization of different utterances in many speech recognition systems. Two major problems are usually encountered when the DTW is applied for recognizing speech utterances: (i) the normalization factors used in a warping path; and (ii) finding the K-best warping paths. Although DTW is modified to compute multiple warping paths by using the Tree-Trellis Search (TTS) algorithm, the use of actual normalization factor still remains a major problem for the DTW. In this paper, a Parallel Genetic Time Warping (PGTW) is proposed to solve the above said problems. A database extracted from the TIMIT speech database of 95 isolated words is set up for evaluating the performance of the PGTW. In the database, each of the first 15 words had 70 different utterances, and the remaining 80 words had only one utterance. For each of the 15 words, one utterance is arbitrarily selected as the test template for recognition. Distance measure for each test template to the utterances of the same word and to those of the 80 words is calculated with three different time warping algorithms: TTS, PGTW and Sequential Genetic Time Warping (SGTW). A Normal Distribution Model based on Rabiner23 is used to evaluate the performance of the three algorithms analytically. The analyzed results showed that the PGTW had performed better than the TTS. It also showed that the PGTW had very similar results as the SGTW, but about 30% CPU time is saved in the single processor system.

A new general dynamical systems approach to data analysis is presented that allows one to track slowly evolving variables responsible for non-stationarity in a fast subsystem. The method is based on the idea of phase space warping , which refers to the small distortions in the fast subsystem's phase space that results from the slow drift, and uses short-time reference model prediction error as its primary measurement of this phenomenon. The basic theory is presented and the issues associated with its implementation in a practical algorithm are discussed. A vector-tracking version of the procedure, based on smooth orthogonal decomposition analysis, is applied to the study of a nonlinear vibrating beam experiment in which a crack propagates to complete fracture. Our method shows that the damage evolution is governed by a scalar process, and we are able to give real-time estimates of the current damage state and identify the governing damage evolution model. Using a final recursive estimation step based on this model, the time to failure is continuously and accurately predicted well in advance of actual failure.

A model for 3D laminated composite beams, that is, beams that can vibrate in space and experience longitudinal and torsional deformations, is derived. The model is based on Timoshenko’s theory for bending and assumes that, under torsion, the cross section rotates as a rigid body but can deform longitudinally due to warping. The warping function, which is essential for correct torsional deformations, is computed preliminarily by the finite element method. Geometrical nonlinearity is taken into account by considering Green’s strain tensor. The equation of motion is derived by the principle of virtual work and discretized by thep-version finite element method. The laminates are assumed to be of orthotropic materials. The influence of the angle of orientation of the laminates on the natural frequencies and on the nonlinear modes of vibration is presented. It is shown that, due to asymmetric laminates, there exist bending-longitudinal and bending-torsional coupling in linear analysis. Dynamic responses in time domain are presented and couplings between transverse displacements and torsion are investigated.

Normal-moveout (NMO) correction is one of the most important routines in seismic processing. NMO is usually implemented by a sample-by-sample procedure; unfortunately, such implementation not only decreases the frequency content but also distorts the amplitude of seismic waveforms resulting from the well-known stretch. The degree of stretch increases with increasing offset. To minimize severe stretch associated with far offset, we use a dynamic time warping (DTW) algorithm to achieve an automatic dynamic matching NMO nonstretch correction, which does not handle crossing events and convoluted events such as thin layers. Our algorithm minimizes the stretch through an automatic static temporal correction of seismic wavelets. The local static time shifts are obtained using a DTW algorithm, which is a nonlinear optimization method. To mitigate the influence of noise, we evaluated a multitrace window strategy to improve the signal-to-noise ratio of seismic data by obtaining a more precise moveout correction at far-offset traces. To illustrate the effectiveness of our algorithm, we first applied our method to synthetic data and then to field seismic data. Both tests illustrate that our algorithm minimizes the stretch associated with far offsets, and the method preserves the amplitude fidelity.

This paper considers a dynamical system subjected to damage evolution in variable operating conditions to illustrate the reconstruction of slow-time (damage) dynamics using fast-time (vibration) measurements. Working in the reconstructed fast-time phase space, phase space warping-based feature vectors are constructed for slow-time damage identification. A subspace of the feature space corresponding to the changes in the operating conditions is identified by applying smooth orthogonal decomposition (SOD) to the initial set of feature vectors. Damage trajectory is then reconstructed by applying SOD to the feature subspace not related to the changes in the operating conditions. The theory is validated experimentally using a vibrating beam, with a variable nonlinear potential field, subjected to fatigue damage. It is shown that the changes in the operating condition (or the potential field) can be successfully separated from the changes caused by damage (or fatigue) accumulation and SOD can identify the slow-time damage trajectory.

La gestion du trafic urbain est un enjeu crucial pour les villes du monde entier, en raison de l'augmentation continue du nombre de véhicules. Les méthodes classiques, telles que les caméras et les boucles de détection, s'avèrent souvent inadaptées à cause de leurs coûts élevés, de la faible résolution des capteurs, et des enjeux de protection de la vie privée. Récemment, la technologie de détection acoustique distribuée (DAS) a émergé comme une solution innovante pour la surveillance du trafic. En convertissant des câbles de fibre optique en un réseau de capteurs de vibration, la technologie DAS capte les déformations générées par les véhicules avec une haute résolution spatio-temporelle, offrant ainsi une alternative rentable et respectueuse de la vie privée. Dans cette thèse, nous développons plusieurs modèles et méthodes pour une surveillance complète du trafic à l'aide de la technologie DAS, en nous concentrant sur quatre axes : la détection des véhicules, l'estimation de la vitesse, le comptage et la classification. Nous introduisons d'abord un modèle d'alignement des données DAS auto-supervisé, permettant d'extraire des informations cruciales sur le trafic grâce à l'alignement temporel des données recueillies en divers points de mesure. Ce modèle intègre un module d'apprentissage profond et un bloc de déformation temporelle non uniforme, capable de gérer des conditions de circulation complexes et d'aligner les données DAS avec précision. Nous proposons ensuite une méthode pour la détection des véhicules et l'estimation de leur vitesse, basé sur le modèle d'alignement. La détection est formulée selon le cadre du test de rapport de vraisemblance généralisé (GLRT), permettant de localiser et de détecter les véhicules de manière fiable. L'estimation de la vitesse est réalisée sur les véhicules détectés, et nos résultats sont validés avec des capteurs dédiés. Notre méthode affiche une précision supérieure, avec une erreur inférieure à kmph{3}, surpassant de 80% les méthodes traditionnelles d'alignement temporel telles que la déformation temporelle dynamique (DTW), tout en étant 16 fois plus rapide, ce qui permet une application en temps réel. Nous développons également de nouvelles méthodes de comptage et de classification des véhicules en exploitant la technologie DAS. Une première solution, basée uniquement sur la détection des véhicules, est efficace pour le comptage des camions mais montre des limites pour le comptage des voitures en trafic dense. Pour y remédier, nous proposons un modèle d'apprentissage profond supervisé pour le comptage, entraîné sur une section spécifique de la route, utilisant les résultats du comptage de la première méthode et des étiquettes à faible résolution temporelle. Une technique de transfert de caractéristiques permet d'étendre ce modèle à d'autres segments routiers, démontrant ainsi son adaptabilité. En conclusion, cette thèse propose une solution robuste et scalable pour la surveillance du trafic à l'aide de la technologie DAS, assurant à la fois une haute précision et une exécution en temps réel. Cette approche ouvre la voie à l'extraction de diverses informations critiques, telles que la détection d'accidents, et peut être étendue à d'autres modes de transport, comme les tramways ou les trains, illustrant ainsi son large potentiel d'application
Urban traffic management poses a significant challenge for cities worldwide, intensified by the growing number of vehicles on road infrastructures. Traditional methods, such as cameras and loop detectors, are often suboptimal due to their high deployment and maintenance costs, limited sensing resolution, and privacy concerns. Recently, Distributed Acoustic Sensing (DAS) technology has emerged as a promising solution for traffic monitoring. By transforming standard fiber-optic telecommunication cables into an array of vibration sensors, DAS captures vehicle-induced subsurface deformation with high spatio-temporal resolution, providing a cost-effective and privacy-preserving alternative.In this thesis, we propose several models and frameworks for comprehensive traffic monitoring using DAS technology, focusing on four key aspects: vehicle detection, speed estimation, counting, and classification. First, we introduce a self-supervised DAS data alignment model that temporally aligns the recorded DAS data across multiple measurement points, enabling the extraction of the traffic information. Our model integrates a deep learning module with a non-uniform time warping block, making it capable of handling challenging traffic conditions and accurately aligning DAS data.Next, we present a vehicle detection and speed estimation framework built on the alignment model. Vehicle detection is formulated within the Generalized Likelihood Ratio Test (GLRT) framework, allowing for reliable detection and localization of vehicles. Speed estimation is achieved over the detected vehicles using the warps from the alignment model, and the results are validated against dedicated sensors. Our method achieves a mean error of less than kmph{3}, outperforming traditional time series alignment methods like Dynamic Time Warping (DTW) by nearly 80%. Furthermore, our model's computing time is 16 times faster than DTW, enabling real-time performance.Lastly, we introduce new vehicle counting and classification methods that leverage the DAS technology. We present a first solution, based solely on vehicle detection results, which is effective for truck counting but shows limitations in cars counting under high-traffic conditions. To address these limitations, we develop a second approach for vehicle counting using a supervised deep learning model trained on a specific road section, using the vehicle counting results of the first method and low-time-resolution labels from dedicated sensors. Through an optimal transport-based feature mapping technique, we extend the model to other road segments, demonstrating its scalability and adaptability. Using the first truck counting method along with the deep learning-based vehicle counting model results in a comprehensive vehicle counting and classification solution.Overall, this thesis presents a robust and scalable framework for road traffic monitoring using DAS technology, delivering both high accuracy and real-time performance. The framework paves the way for extracting a wide range of other crucial traffic information, such as accident detection. Moreover, this approach can be generalized to various road configurations and extended to other transportation modes, such as tramways and trains, demonstrating its broader applicability

Estimation of most of the metrics used to characterize dynamical systems’ output require fairly long time series (e.g., Lyapunov Exponents, Fractal Dimensions), or substantial computational resources (e.g., phase space warping metrics, sensitivity vector fields). In many practical applications, when there is abundance of data (e.g., in Atomic Force Microscopy) fast and simple features are needed, and when there is sparsity of data (e.g., in many Structural Health Monitoring situations) robust features are needed. Here, we propose a new class of features based on Birkhoff Ergodic Theorem, which are fast to calculate and do not require large data or computational resources. Applications of these metrics, in conjunction with the smooth orthogonal decomposition, to identifying underlying processes causing nonstationarity both in simulations and actual experiments are demonstrated.

Abstract Detailed finite element (FE) models of biological tissues and structures are typically generated from medical image data collected from one individual subject — a process which draws from an array of segmentation and mesh generation tools. The geometric model is augmented with material constitutive properties as well as natural and essential boundary conditions. This is a time consuming process which is exacerbated by the inhomogeneity and anisotropy of biological structures. Even after the model is complete its application is usually limited to a single subject owing to geometric and constitutive variations between individuals. In many cases, however, it is possible to account for geometric variations by deforming the geometry of the detailed FE model to reflect the anatomy of an individual subject. In the present work this alignment is achieved automatically by using medical image data to drive a nonlinear deformation process termed anatomical warping.

Identifying physiological fatigue is important for the development of more robust training protocols, better energy supplements, and/or reduction of muscle injuries. Current fatigue measurement technologies are usually invasive and/or impractical, and may not be realizable in out of laboratory settings. A fatigue identification methodology that only uses motion kinematics measurements has a great potential for field applications. Phase space warping (PSW) features of motion kinematic time series analyzed through smooth orthogonal decomposition (SOD) have tracked individual muscle fatigue. In this paper, the performance of a standard SOD analysis is compared to its nonlinear extension using a new experimental data set. Ten healthy right-handed subjects (27 ± 2.8 years; 1.71 ± 0.10 m height; and 69.91 ± 18.26 kg body mass) perform a sawing motion by pushing a weighted handle back and forth until voluntary exhaustion. Three sets of joint kinematic angles are measured from the elbow, wrist and shoulder as well as surface Electromyography (EMG) from ten different muscle groups. A vector-valued feature time series is generated using PSW metrics estimated from movement kinematics. Dominant SOD coordinates of these features are extracted to track the individual muscle fatigue trends as indicated by mean and median frequencies of the corresponding EMG power spectra. Cross subject variability shows that considerably fewer nonlinear SOD coordinates are needed to track EMG-based fatigue markers, and that nonlinear SOD methodology captures fatigue dynamics in a lower-dimensional subspace than its linear counterpart.

Structural elements with thin-walled open cross-sections are common in metal and composite structures. These thin-walled beams have generally a good flexural strength with respect to the axis of greatest inertia, but a low flexural stiffness in relation to the second principal axis and a low torsional stiffness. These elements generally have an instability, which leads to a flexural-flexural-torsional coupling. The same applies to the vibration modes. Many of these structures work in a nonlinear regime, and a nonlinear formulation that takes into account large displacements and the flexural-flexural-torsional coupling is required. In this work a nonlinear beam theory that takes into account large displacements, warping and shortening effects, as well as flexural-flexural-torsional coupling is adopted. The governing nonlinear equations of motion are discretized in space using the Galerkin method and the discretized equations of motion are solved by the Runge-Kutta method. Special attention is given to the nonlinear oscillations of beams with low torsional stiffness and its influence on the bifurcations and instabilities of the structure, a problem not tackled in the previous literature on this subject. Time responses, phase portraits and bifurcation diagrams are used to unveil the complex dynamic.

Abstract Seismic 4D analysis is a model for integrating different disciplines in the oil and gas industry, such as seismic, petrophysics, reservoir engineering, and production engineering. Two 3D seismic surveys were conducted in the studied area with low repeatability of the recordings: the baseline survey in 1994 and the monitoring survey in 2014. A full 4D seismic co-processing of the baseline and monitor surveys was performed for both surveys starting with the field tapes. The 4D seismic co-processing improved poor seismic acquisition repeatability and 4D seismic attributes such as NRMS and predictability showed that. 4D time-trace shift was also performed, using the baseline survey as a reference to measure the time shifts between the baseline survey and the monitor survey at 20-year intervals. Dynamic 4D trace warping was followed by seismic 4D inversion to compare the 4D difference in the seismic inverted data with the difference in seismic amplitude. The seismic inversion helped overcome noise, multiple contamination, and differences in dynamic amplitude range between the baseline and seismic monitoring measurements. Applications of machine learning in the geosciences are growing rapidly in both processing and seismic interpretation. We then examined the relationship between well logs and seismic volumes by predicting a volume of log properties at the well locations of the seismic volume. In this method, we computed a possibly nonlinear operator that can predict well logs based on the properties of the adjacent seismic data. We then tested the Deep Forward Neural Network (DFNN) on six wells to adequately train and validate the machine learning approach using baseline seismic inversion data and monitoring data. The objective of trying such a supervised machine learning approach was to predict the density and porosity of both the baseline seismic data and the monitoring seismic data to verify the accuracy of the 4D seismic inversion.

A ship hull is regarded as a box girder structure consisting of plates and stiffeners. When the ship hull is subjected to excessive longitudinal bending moment, buckling and yielding of plates and stiffeners take place progressively and the ultimate strength of the cross-section is attained. The ultimate longitudinal bending strength is one of the most fundamental strength of a ship hull girder. Finite element method (FEM) analysis using fine-mesh hold models has been increasingly applied to the ultimate longitudinal strength analysis of ship hull girder. However, the cost and elapsed time necessary for FEM analysis including finite element modelling are still large for the design stage. Therefore, the so-called Smith’s method [1] has been widely employed for the progressive collapse analysis of a ship hull girder under bending. Recently, there is a growing demand for a container ship, which is characterized as a hull girder with large open decks. This type of ship has a relatively small torsional stiffness compared to the ships with closed cross-section and the effect of torsion on the ultimate longitudinal strength may be significant. However, the Smith’s method above mentioned cannot consider the influence of torsion. Therefore, some of the authors developed a simplified method of the ultimate strength analysis of a hull girder under torsion as well as bending [2–4]. In this method, a hull girder is modeled by linear beam elements in the longitudinal direction, and the warping as well as bending deformation is included in the formulation. The cross-section of a beam element is divided into plate elements by the same way as the Smith’s method. Therefore, the shift of instantaneous neutral axis and shear center can be automatically considered by introducing the axial degree of freedom as well as the bending ones into the beam elements, and keeping the zero axial load condition. In this study, the average stress-average strain relationship of each element is calculated using the formulae of the Common Structural Rules (CSR) [5] and HULLST proposed by Yao et al. [6, 7] considering the effect of shear stress due to torsion on the yield strength. There had been a lot of papers [8] which discuss the importance of strength assessment to large container ships under torsion. However, there are few papers which discuss the influence of torsion on the ultimate hull girder strength. In this paper, the proposed simplified method is applied to the existing Post-Panamax class container ship. First, a torsional moment is applied to the beam model for the ship within the elastic range. Then, the ultimate bending strength of cross-sections is calculated applying the Smith’s method to a beam element considering the warping and shear stresses. On the other hand, nonlinear explicit FEM are adopted for the progressive collapse analysis of the ship by using LS-DYNA. The effectiveness of present simplified analysis method of ultimate hull girder strength under combined loads is discussed compared with the LS-DYNA analysis.