Uncorrelated Components Research Articles

A persistence‐based Wold‐type decomposition for stationary time series

This paper shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. In particular, we provide an Extended Wold Decomposition based on an isometric scaling operator that makes averages of process innovations. Thanks to the uncorrelatedness of components, our representation of a time series naturally induces a persistence‐based variance decomposition of any weakly stationary process. We provide two applications to show how the tools developed in this paper can shed new light on the determinants of the variability of economic and financial time series.

Nonconvex Group Sparsity Signal Decomposition via Convex Optimization for Bearing Fault Diagnosis

Bearing fault diagnosis is critical for rotating machinery condition monitoring since it is a key component of rotating machines. One of the challenges for bearing fault diagnosis is to accurately realize fault feature extraction from original vibration signals. To tackle this problem, the novel group sparsity signal decomposition method is proposed in this article. For the sparsity within and across groups’ property of the bearing vibration signals, the nonconvex group separable penalty is introduced to construct the objective function, leading to that the noise between the adjacent impulses can be eliminated and the impulses can be effectively extracted. Furthermore, since the penalty function is nonconvex, the convexity condition of the corresponding objective function to the global minimum is discussed. In addition, to improve the efficiency of parameter selection, this article presents an adaptive regularization parameter selection strategy. Simulation and experimental studies show that compared with the traditional method, the proposed method can better preserve the target components and reducing uncorrelated interference components for bearing fault diagnosis.

Transverse uncorrelated emittance diagnostic for magnetized electron beams

The study of magnetized electron beam has become a high priority for its use in ion beam cooling as part of electron ion colliders and the potential of easily forming flat beams for various applications. In this paper, a purpose-specific diagnostic is described with the intention of studying transverse magnetized beam properties. The device is a modification to the classic pepper-pot, used in this context to measure the uncorrelated components of transverse emittance in addition to the typical effective emittance. The limitations of traditional methods are discussed, and simulated demonstrations of the new technique shown.

An investigation of the component of response spectrum uncorrelated with input

Abstract For a linear system, by definition, the response spectrum is related to the input spectrum through a linear transformation. An investigation of the component of the response spectrum disobeying such a correlation gives way to a non-parametric algorithm which can help detect nonlinearities in the system being tested. The uncorrelated component thus obtained contains information pertinent to both structural nonlinearities and any lack of linearity resulting from the digital signal processing (DSP) techniques employed. The current paper discusses an approach that combines cyclic averaging with the aforementioned detection scheme to help segregate the uncorrelated response components based on leakage from those due to the dynamic characteristics of the system. This scheme is then shown to be successful on numerical and experimental data sets with representative examples for both linear and nonlinear systems.

Independent component analysis for reservoir geomorphology and unsupervised seismic facies classification in the Taranaki Basin, New Zealand

During the past two decades, the number of volumetric seismic attributes has increased to the point at which interpreters are overwhelmed and cannot analyze all of the information that is available. Principal component analysis (PCA) is one of the best-known multivariate analysis techniques that decompose the input data into second-order statistics by maximizing the variance, thus obtaining mathematically uncorrelated components. Unfortunately, projecting the information in the multiple input data volumes onto an orthogonal basis often mixes rather than separates geologic features of interest. To address this issue, we have implemented and evaluated a relatively new unsupervised multiattribute analysis technique called independent component analysis (ICA), which is based on higher order statistics. We evaluate our algorithm to study the internal architecture of turbiditic channel complexes present in the Moki A sands Formation, Taranaki Basin, New Zealand. We input 12 spectral magnitude components ranging from 25 to 80 Hz into the ICA algorithm and we plot 3 of the resulting independent components against a red-green-blue color scheme to generate a single volume in which the colored independent components correspond to different seismic facies. The results obtained using ICA proved to be superior to those obtained using PCA. Specifically, ICA provides improved resolution and separates geologic features from noise. Moreover, with ICA, we can geologically analyze the different seismic facies and relate them to sand- and mud-prone seismic facies associated with axial and off-axis deposition and cut-and-fill architectures.

Dental development and craniofacial morphology in school-age children.

The growth of the craniofacial complex is important for establishing a balanced relationship among the teeth, jaws, and other facial structures. However, there is still a lack of information about craniofacial parameters that are affected by the rate of dental development. The aim of this study was to investigate the association between dental development and craniofacial morphology in school-age children. This study was embedded in the Generation R Study, Rotterdam, The Netherlands. In 3,896 children aged 8 to 11years, dental development was assessed from panoramic radiographs and craniofacial morphology was assessed by combining cephalometric parameters into 9 uncorrelated principal components, each representing a distinct skeletal or dental craniofacial pattern. The statistical analysis was performed using linear and nonlinear regression model. Dental development was positively associated with the bimaxillary growth (β=0.04; 95% CI 0.01 to 0.08). Children with above-average dental development had a tendency toward Class II jaw relationship (β=-0.08; 95% CI -0.13 to -0.04). Regarding dental parameters, the proclination increased for incisors and lips with advanced dental development (β=0.15 [95% CI 0.10 to 0.19] and β=0.13 [95% CI 0.09 to 0.17], respectively), but the incisor proclination remained more pronounced in children that had above-average dental development. The findings of this large population-based study show that dental development is associated with specific dental and skeletal cephalometric characteristics in school-age children. Further longitudinal studies are necessary to confirm the observed effects over time.

LISA Pathfinder micronewton cold gas thrusters: In-flight characterization

The LISA Pathfinder (LPF) mission has demonstrated the ability to limit and measure the fluctuations in acceleration between two free falling test masses down to sub-femto-g levels. One of the key elements to achieve such a level of residual acceleration is the drag free control. In this scheme the spacecraft is used as a shield against any external disturbances by adjusting its relative position to a reference test mass. The actuators used to move the spacecraft are cold gas micropropulsion thrusters. In this paper, we report in-flight characterization of these thrusters in term of noise and artefacts during science operations using all the metrology capabilities of LISA Pathfinder. Using the LISA Pathfinder test masses as an inertial reference frame, an average thruster noise of ∼0.17 μN/Hz is observed and decomposed into a common (coherent) and an uncorrelated component. The very low noise and stability of the onboard metrology system associated with the quietness of the space environment allowed the measurement of the thruster noise down to ∼20 μHz, more than an order of magnitude below any ground measurement. Spectral lines were observed around ∼1.5 mHz and its harmonics and around 55 and 70 mHz. They are associated with the cold gas system itself and possibly to a clock synchronization issue. The thruster noise-floor exhibits an excess of ∼70% compared to characterization that have been made on ground on a single unit and without the feeding system. However this small excess has no impact on the LPF mission performance and is compatible with the noise budget for the upcoming LISA gravitational wave observatory. Over the whole mission, nominal, and extension, the thrusters showed remarkable stability for both the science operations and the different maneuvers necessary to maintain LPF on its orbit around L1. It is therefore concluded that a similar cold gas system would be a viable propulsion system for the future LISA mission.

Maximum Likelihood Analysis of the Total Least Squares Problem with Correlated Errors

This paper performs a maximum likelihood analysis of the total least squares problem with Gaussian noise errors and correlated elementwise components in the design matrix. This analysis also includes a derivation of the Fisher information matrix and the error-covariance for the parameter estimates. Furthermore, the error-covariances of the associated coefficient and output estimates are also derived. These error-covariances can yield a much improved covariance approximation than would be achieved using naïve least squares. The results are compared with previously derived results for the uncorrelated elementwise component with nonequal row variance case. Simulation results using three-dimensional bearings-only localization are shown to quantify the theoretical derivations, which show that the derived error-covariances are more consistent than those given by the naïve least squares solution.

Functional data analysis by matrix completion

Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short scale fluctuations may indeed be rough relative to the global scale, but still smooth at shorter scales. These may be confounded with the global smooth components of variation by the smoothing and PCA, potentially distorting the parsimony and interpretability of the analysis. The goal of this paper is to investigate how both smooth and rough variations can be recovered on the basis of discretely observed functional data. Assuming that a functional datum arises as the sum of two uncorrelated components, one smooth and one rough, we develop identifiability conditions for the recovery of the two corresponding covariance operators. The key insight is that they should possess complementary forms of parsimony: one smooth and finite rank (large scale), and the other banded and potentially infinite rank (small scale). Our conditions elucidate the precise interplay between rank, bandwidth and grid resolution. Under these conditions, we show that the recovery problem is equivalent to rank-constrained matrix completion, and exploit this to construct estimators of the two covariances, without assuming knowledge of the true bandwidth or rank; we study their asymptotic behaviour, and then use them to recover the smooth and rough components of each functional datum by best linear prediction. As a result, we effectively produce separate functional PCAs for smooth and rough variation.

A Lagrangian probability-density-function model for collisional turbulent fluid–particle flows

Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These clusters, in turn, can generate and sustain turbulence in the fluid phase, which we refer to as cluster-induced turbulence (CIT). In the present work, we tackle the problem of developing a framework for the stochastic modelling of moderately dense particle-laden flows, based on a Lagrangian probability-density-function formalism. This framework includes the Eulerian approach, and hence can be useful also for the development of two-fluid models. A rigorous formalism and a general model have been put forward focusing, in particular, on the two ingredients that are key in moderately dense flows, namely, two-way coupling in the carrier phase, and the decomposition of the particle-phase velocity into its spatially correlated and uncorrelated components. Specifically, this last contribution allows us to identify in the stochastic model the contributions due to the correlated fluctuating energy and to the granular temperature of the particle phase, which determine the time scale for particle–particle collisions. The model is then validated and assessed against direct-numerical-simulation data for homogeneous configurations of increasing difficulty: (i) homogeneous isotropic turbulence, (ii) decaying and shear turbulence and (iii) CIT.

Evolutionary relationships of courtship songs in the parasitic wasp genus, Cotesia (Hymenoptera: Braconidae).

Acoustic signals play an important role in premating isolation based on sexual selection within many taxa. Many male parasitic wasps produce characteristic courtship songs used by females in mate selection. In Cotesia (Hymenoptera: Braconidae: Microgastrinae), courtship songs are generated by wing fanning with repetitive pulses in stereotypical patterns. Our objectives were to sample the diversity of courtship songs within Cotesia and to identify e underlying patterns of differentiation. We compared songs among 12 of ca. 80 Cotesia species in North America, including ten species that have not been recorded previously. For Cotesia congregata, we compared songs of wasps originating from six different host-foodplant sources, two of which are considered incipient species. Songs of emergent males from wild caterpillar hosts in five different families were recorded, and pattern, frequency, and duration of song elements analyzed. Principal component analysis converted the seven elements characterized into four uncorrelated components used in a hierarchical cluster analysis and grouped species by similarity of song structure. Species songs varied significantly in duration of repeating pulse and buzz elements and/or in fundamental frequency. Cluster analysis resolved similar species groups in agreement with the most recent molecular phylogeny for Cotesia spp., indicating the potential for using courtship songs as a predictor of genetic relatedness. Courtship song analysis may aid in identifying closely related cryptic species that overlap spatially, and provide insight into the evolution of this highly diverse and agriculturally important taxon.

Linearly uncorrelated principal component and deep convolutional image deblurring for natural images

Blind image deblurring of natural images still remains a demanding task. The traditional methods, pre-processes the uniform and non-uniform images with a deblurring algorithm and employs a low-rank prior algorithm. The rich textures do not possess enough similar patches in the deblurring process and this loss results in noisy images. Also, computational efficiency gets compromised during the performance of the succeeding process. In this study, the authors propose a novel method called, linearly uncorrelated principal component and deep convolution (LUPC-DC) for deblurring natural images. The natural images are first de-correlated with which good similar patches are extracted to generate a low-rank matrix by linearly uncorrelated principal component (PC) extraction. Then, the deep convolutional neural network model jointly extracts good similar patches and deblurs the first PCs. Eventually, good similar patches in the last PCs are suppressed using Hard Thresholding for computational efficiency. Analysis of concurrence performance of the algorithm confirms the viability of this method theoretically. In addition, simulation results and performance evaluations of image quality metrics are provided to assess the effectiveness of the proposed method. Moreover, the proposed method provides improvement in the peak-signal-to-noise ratio rate, success rate and reduction in the computation time for image deblurring.

Principal Component Analysis as a Dimensionality Reduction and Data Preprocessing Technique

Nowadays, dealing with high dimension data has become common in many fields such as network security, image processing, medical diagnosis, biometric systems, e-commerce, etc. In data base with higher dimension the direct use of data is costlier in terms of its storage, processing, mathematical computations etc. Moreover, in many applications with wireless networks, Received Signal Strength (RSS) needs to be processed to remove the redundant readings. In this paper, we discussed Principal Component Analysis (PCA) as a dimensionality reduction technique. PCA can be done either by calculating the covariance matrix or by Singular Value Decomposition (SVD). We used covariance matrix calculation due to its less complexity. Simulation results verify that the correlated input data sequence is sorted to uncorrelated principal components (PC’s) with decreasing variation and some of first PC’s can represent nearly all data sets.

OP37 Impact On Uncertainty Of Disaggregating Cost Data

IntroductionEconomic models contain several parameters ordinarily subject to uncertainty. Unlike most other model parameters, costs can constitute numerous distinct components. For example, a surgical intervention can require a variety of disposables and reusable equipment. A micro-costing output may be disaggregated or presented as a total cost. Uncertainty could be applied to individual cost components or to total cost. We aimed to explore how disaggregation of cost data may impact on uncertainty using a case study.MethodsA set of simulations using hypothetical scenarios were developed with uncertainty set at ± 20 percent. The simulations investigated the impact of number of cost components, balance between components, and correlation between them. A cost-utility model from an assessment of robot-assisted radical prostatectomy was analyzed; procedure cost was divided into 32 individual cost components or treated as a total cost.ResultsBased on five equal cost components, uncertainty reduces from ± 20 percent for correlated variables to ± 9 percent for uncorrelated variables. With increasing numbers of uncorrelated cost components, the uncertainty in the total cost decreases markedly. The uncertainty around total robot-assisted surgery procedure equipment costs was ± 19.7 percent when components were correlated and ± 9.4 percent when uncorrelated. The impact on uncertainty in the incremental cost effectiveness ratio (ICER) was negligible but the ranking of parameters in the univariate sensitivity analysis changed.ConclusionsAnalyzing uncertainty by aggregated or disaggregated costs can have implications for presenting uncertainty in costs to decision makers. Applying uncertainty to aggregated costs essentially implies that variation in the cost of individual components is perfectly correlated. By disaggregating cost components they are being treated as uncorrelated, which can substantially reduce uncertainty in the total cost. In this case study we found that although the reduction in uncertainty could be clearly seen in the cost parameter, it had a negligible impact on uncertainty in the ICER.

Blind Audio-Visual Localization and Separation via Low-Rank and Sparsity.

The ability to localize visual objects that are associated with an audio source and at the same time to separate the audio signal is a cornerstone in audio-visual signal-processing applications. However, available methods mainly focus on localizing only the visual objects, without audio separation abilities. Besides that, these methods often rely on either laborious preprocessing steps to segment video frames into semantic regions, or additional supervisions to guide their localization. In this paper, we aim to address the problem of visual source localization and audio separation in an unsupervised manner and avoid all preprocessing or post-processing steps. To this end, we devise a novel structured matrix decomposition method that decomposes the data matrix of each modality as a superposition of three terms: 1) a low-rank matrix capturing the background information; 2) a sparse matrix capturing the correlated components among the two modalities and, hence, uncovering the sound source in visual modality and the associated sound in audio modality; and 3) a third sparse matrix accounting for uncorrelated components, such as distracting objects in visual modality and irrelevant sound in audio modality. The generality of the proposed method is demonstrated by applying it onto three applications, namely: 1) visual localization of a sound source; 2) visually assisted audio separation; and 3) active speaker detection. Experimental results indicate the effectiveness of the proposed method on these application domains.

An Integrated Machine Learning Algorithm for Separating the Long-Term Deflection Data of Prestressed Concrete Bridges

Deflection is one of the key indexes for the safety evaluation of bridge structures. In reality, due to the changing operational and environmental conditions, the deflection signals measured by structural health monitoring systems are greatly affected. These ambient changes in the system often cover subtle changes in the vibration signals caused by damage to the system. The deflection signals of prestressed concrete (PC) bridges are regarded as the superposition of different effects, including concrete shrinkage, creep, prestress loss, material deterioration, temperature effects, and live load effects. According to multiscale analysis theory of the long-term deflection signal, in this paper, an integrated machine learning algorithm that combines a Butterworth filter, ensemble empirical mode decomposition (EEMD), principle component analysis (PCA), and fast independent component analysis (FastICA) is proposed for separating the individual deflection components from a measured single channel deflection signal. The proposed algorithm consists of four stages: (1) the live load effect, which is a high-frequency signal, is separated from the raw signal by a Butterworth filter; (2) the EEMD algorithm is used to extract the intrinsic mode function (IMF) components; (3) these IMFs are utilized as input in the PCA model and some uncorrelated and dominant basis components are extracted; and (4) FastICA is applied to derive the independent deflection component. The simulated results show that each individual deflection component can be successfully separated when the noise level is under 10%. Verified by a practical application, the algorithm is feasible for extracting the structural deflection (including concrete shrinkage, creep, and prestress loss) only caused by structural damage or material deterioration.

Uncertainty propagation through integrated quantities for radiation thermometry

Uncertainty formulae are derived for propagating both correlated and uncorrelated components of uncertainty in spectral responsivity measurements directly through the Planck integrals for the radiation thermometry range of the international temperature scale of 1990 (ITS-90) and for absolute radiometry. These formulae are compared to those obtained using the Sakuma–Hattori equation as an approximation to the Planck integrals. It is shown that for typical spectral responsivity bandwidths, the differences are negligible, confirming that the Sakuma–Hattori approximation provides an excellent model for the basis of uncertainty propagation for radiation thermometry, resulting in simpler and more intuitive uncertainty equations.

Exploitation of error correlation in a large analysis validation: GlobCurrent case study

An assessment of variance in ocean current signal and noise shared by in situ observations (drifters) and a large gridded analysis (GlobCurrent) is sought as a function of day of the year for 1993–2015 and across a broad spectrum of current speed. Regardless of the division of collocations, it is difficult to claim that any synoptic assessment can be based on independent observations. Instead, a measurement model that departs from ordinary linear regression by accommodating error correlation is proposed. The interpretation of independence is explored by applying Fuller's (1987) concept of equation and measurement error to a division of error into shared (correlated) and unshared (uncorrelated) components, respectively. The resulting division of variance in the new model favours noise. Ocean current shared (equation) error is of comparable magnitude to unshared (measurement) error and the latter is, for GlobCurrent and drifters respectively, comparable to ordinary and reverse linear regression. Although signal variance appears to be small, its utility as a measure of agreement between two variates is highlighted.Sparse collocations that sample a dense (high resolution) grid permit a first order autoregressive form of measurement model to be considered, including parameterizations of analysis-in situ error cross-correlation and analysis temporal error autocorrelation. The former (cross-correlation) is an equation error term that accommodates error shared by both GlobCurrent and drifters. The latter (autocorrelation) facilitates an identification and retrieval of all model parameters. Solutions are sought using a prescribed calibration between GlobCurrent and drifters (by variance matching). Because the true current variance of GlobCurrent and drifters is small, signal to noise ratio is near zero at best. This is particularly evident for moderate current speed and for the meridional current component.

Volatility Martingale Difference Divergence Matrix and Its Application to Dimension Reduction for Multivariate Volatility

In this article, we propose the so-called volatility martingale difference divergence matrix (VMDDM) to quantify the conditional variance dependence of a random vector given , building on the recent work on martigale difference divergence matrix (MDDM) that measures the conditional mean dependence. We further generalize VMDDM to the time series context and apply it to do dimension reduction for multivariate volatility, following the recent work by Hu and Tsay and Li et al. Unlike the latter two papers, our metric is easy to compute, can fully capture nonlinear serial dependence and involves less user-chosen numbers. Furthermore, we propose a variant of VMDDM and apply it to the estimation of conditional uncorrelated components model (Fan, Wang, and Yao 2008). Simulation and data illustration show that our method can perform well in comparison with the existing ones with less computational time, and can outperform others in cases of strong nonlinear dependence.

Grout assessment of plastic ducts in prestressed structures with an HHT-based method

This paper introduces the detection of grouting quality in plastic ducts in prestressed concrete structures based on impact-echo (IE) testing with an HHT-based method. This method takes steps to suppress unrelated signals. At first, the thickness frequency of the intact concrete whose thickness is equal to the detected concrete is calculated, then a band pass filter is conducted to filtering uncorrelated frequency component. Secondly, complementary ensemble empirical mode decomposition (CEEMD) is used to decompose the signal to intrinsic mode functions (IMFs). Thirdly, an IMF screening process is conducted on the IMFs to extract the main patterns of vibrations related to grouting. At last, the Hilbert marginal cumulative spectra are set up. This method has been verified by both simulated and laboratory models. The cumulative Hilbert marginal spectra showed that the thickness frequencies decreased gradually with the decreasing of grouting compactness. On-site IE tests verified the feasibility and practicability of the proposed method.