Existing formulations of warping torsion rely on a direct approximation of the warping displacement of the cross sections, even when this approach leads to several limitations. For example, assuming ...the warping to be directly proportional to the rate of twist results in a high-order governing equation and anomalies in which the twisting components of the stress and internal torque are distorted by the restrainment of the warping. As identified recently by the author, this situation reveals the presence of a kinematic warping–twist constraint in this particular approach, whose relaxation through an independent warping field still with a fixed distribution of the section’s warping, results in non–equilibrated stresses despite its wide use in recent computational models. As an alternative, we consider in this paper a mixed treatment of the axial strain and stress appearing when warping is restrained, extending an early idea of Reissner. In fact, the paper presents a new structural mixed formulation of restrained warping, based on a non–uniform distribution of the shape of the warping on the cross sections, also controlled by an independent warping field, but crucially involving the aforementioned mixed axial kinematics. Theoretical results presented here indicate the suitability of the new formulation, resolving the aforementioned issues of existing formulations.
Dynamic time warping (DTW), which finds the minimum path by providing non-linear alignments between two time series, has been widely used as a distance measure for time series classification and ...clustering. However, DTW does not account for the relative importance regarding the phase difference between a reference point and a testing point. This may lead to misclassification especially in applications where the shape similarity between two sequences is a major consideration for an accurate recognition. Therefore, we propose a novel distance measure, called a weighted DTW (WDTW), which is a penalty-based DTW. Our approach penalizes points with higher phase difference between a reference point and a testing point in order to prevent minimum distance distortion caused by outliers. The rationale underlying the proposed distance measure is demonstrated with some illustrative examples. A new weight function, called the modified logistic weight function (MLWF), is also proposed to systematically assign weights as a function of the phase difference between a reference point and a testing point. By applying different weights to adjacent points, the proposed algorithm can enhance the detection of similarity between two time series. We show that some popular distance measures such as DTW and Euclidean distance are special cases of our proposed WDTW measure. We extend the proposed idea to other variants of DTW such as derivative dynamic time warping (DDTW) and propose the weighted version of DDTW. We have compared the performances of our proposed procedures with other popular approaches using public data sets available through the UCR Time Series Data Mining Archive for both time series classification and clustering problems. The experimental results indicate that the proposed approaches can achieve improved accuracy for time series classification and clustering problems.
•We improve DTW distance measure in multivariate time series classification.•We use derivatives to improve DTW in multivariate time series classification.•We test effectiveness on 18 real time ...series.•We present a detailed comparison of proposed methods.
Multivariate time series (MTS) data are widely used in a very broad range of fields, including medicine, finance, multimedia and engineering. In this paper a new approach for MTS classification, using a parametric derivative dynamic time warping distance, is proposed. Our approach combines two distances: the DTW distance between MTS and the DTW distance between derivatives of MTS. The new distance is used in classification with the nearest neighbor rule. Experimental results performed on 18 data sets demonstrate the effectiveness of the proposed approach for MTS classification.
Time series clustering is the act of grouping time series data without recourse to a label. Algorithms that cluster time series can be classified into two groups: those that employ a time series ...specific distance measure and those that derive features from time series. Both approaches usually rely on traditional clustering algorithms such as
k
-means. Our focus is on partitional clustering algorithms that employ elastic distance measures, i.e. distances that perform some kind of realignment whilst measuring distance. We describe nine commonly used elastic distance measures and compare their performance with
k
-means and
k
-medoids clusterer. Our findings, based on experiments using the UCR time series archive, are surprising. We find that, generally, clustering with DTW distance is not better than using Euclidean distance and that distance measures that employ editing in conjunction with warping are significantly better than other approaches. We further observe that using
k
-medoids clusterer rather than
k
-means improves the clusterings for all nine elastic distance measures. One function, the move–split–merge (MSM) distance, is the best performing algorithm of this study, with time warp edit (TWE) distance a close second. Our conclusion is that MSM or TWE with
k
-medoids clusterer should be considered as a good alternative to DTW for clustering time series with elastic distance measures. We provide implementations, extensive results and guidance on reproducing results on the associated GitHub repository.
•Torsional modes of the rectangular hollow cross-section beam are studied.•Measurement of torsional warping eigenfrequencies is done.•Semi-analytical and numerical modal analyses are ...performed.•Experimental and calculated results are compared and evaluated.
This contribution contains the results of experimental measurements and modelling of torsional warping free vibrations of beams with rectangular hollow cross-sections. The experimental results are compared with results from a semi-analytical method, proposed by the authors, and from Finite Element (FE) computations by means of a standard commercial code. In these calculations, beam, solid, and shell elements are used. The semi-analytical calculations are based on the analogy between second-order beam theory, including consideration of the shear force deformation effect, and non-uniform torsion, considering the Secondary Torsion Moment Deformation Effect (STMDE). The influence of warping and of the STMDE on the torsional eigenfrequencies and eigenforms is evaluated. The difference between the measured and calculated eigenfrequencies is investigated and quantified.
Predictive maintenance plays a crucial role in the field of intelligent machinery fault diagnosis, which improves the efficiency of maintenance. This paper focuses on the extraction of real-time ...damage feature and the prediction of remaining useful life (RUL) in predictive maintenance of rolling bearings. Some RUL prediction approaches lack dynamic foundations and require large amounts of data and prior knowledge. This paper proposes the algorithm of segmented relative phase space warping (SRPSW) and a strategy combining double exponential model (DEM) and particle filter (PF) to predict the RUL. SRPSW provides a dynamic basis for real-time RUL prediction in different stages. The DEM-based PF reduces the need for prior knowledge and improves accuracy. The analysis results from normal and accelerated degradation experiments show that the proposed SRPSW overcomes the failure of the original PSW in depicting the later operating stage of bearings. Further, the relative damage indicators (RDIs) extracted by SRPSW are more accurately than commonly used indicators. The predicted results show that the DEM-based PF does not require professional and prior information whilst ensuring the accuracy of RUL prediction. The proposed approach in this paper provides a new avenue for predictive maintenance of bearings.
Dynamic Time Warping (DTW) is probably the most popular distance measure for time series data, because it captures flexible similarities under time distortions. However, DTW has long been suffering ...from the pathological alignment problem, and most existing solutions, which essentially impose rigid constraints on the warping path, are likely to miss the correct alignments. A crucial observation on pathological alignment is that it always leads to an abnormally large number of links between two sequences. Based on this new observation, we propose a novel variant of DTW called LDTW, which limits the total number of links during the optimization process of DTW. LDTW not only oppresses the pathological alignment effectively, but also allows more flexibilities when measuring similarities. It is a softer constraint because we still let the optimization process of DTW decide how many links to allocate to each data point and where to put these links. In this paper, we introduce the motivation and algorithm of LDTW and we conduct a nearest neighbor classification experiment on UCR time series archive to show its performance.
Neural volumes Lombardi, Stephen; Simon, Tomas; Saragih, Jason ...
ACM transactions on graphics,
07/2019, Volume:
38, Issue:
4
Journal Article
Peer reviewed
Modeling and rendering of dynamic scenes is challenging, as natural scenes often contain complex phenomena such as thin structures, evolving topology, translucency, scattering, occlusion, and ...biological motion. Mesh-based reconstruction and tracking often fail in these cases, and other approaches (e.g., light field video) typically rely on constrained viewing conditions, which limit interactivity. We circumvent these difficulties by presenting a learning-based approach to representing dynamic objects inspired by the integral projection model used in tomographic imaging. The approach is supervised directly from 2D images in a multi-view capture setting and does not require explicit reconstruction or tracking of the object. Our method has two primary components: an encoder-decoder network that transforms input images into a 3D volume representation, and a differentiable ray-marching operation that enables end-to-end training. By virtue of its 3D representation, our construction extrapolates better to novel viewpoints compared to screen-space rendering techniques. The encoder-decoder architecture learns a latent representation of a dynamic scene that enables us to produce novel content sequences not seen during training. To overcome memory limitations of voxel-based representations, we learn a dynamic irregular grid structure implemented with a warp field during ray-marching. This structure greatly improves the apparent resolution and reduces grid-like artifacts and jagged motion. Finally, we demonstrate how to incorporate surface-based representations into our volumetric-learning framework for applications where the highest resolution is required, using facial performance capture as a case in point.
Dynamic time warping under limited warping path length (LDTW) is a state-of-the-art time series similarity evaluation method. However, it suffers from high space-time complexity, which makes some ...large-scale series evaluations impossible. In this paper, an alternating matrix with a concise structure is proposed to replace the complex three-dimensional matrix in LDTW and reduce the high complexity. Furthermore, an evolutionary chain tree is proposed to represent the warping paths and ensure an effective retrieval of the optimal one. Experiments using the benchmark platform offered by the University of California-Riverside show that our method uses 1.33% of the space, 82.7% of the time used by LDTW on average, which proves the efficiency of the proposed method.
The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: ...infinite-dimensionality of function spaces, observation noise, and so on. However, there is another interesting phenomena that creates problems in FDA. The functional data often comes with lateral displacements/deformations in curves, a phenomenon which is different from the height or amplitude variability and is termed phase variation. The presence of phase variability artificially often inflates data variance, blurs underlying data structures, and distorts principal components. While the separation and/or removal of phase from amplitude data is desirable, this is a difficult problem. In particular, a commonly used alignment procedure, based on minimizing the 𝕃2 norm between functions, does not provide satisfactory results. In this paper we motivate the importance of dealing with the phase variability and summarize several current ideas for separating phase and amplitude components. These approaches differ in the following: (1) the definition and mathematical representation of phase variability, (2) the objective functions that are used in functional data alignment, and (3) the algorithmic tools for solving estimation/optimization problems. We use simple examples to illustrate various approaches and to provide useful contrast between them.
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