scholarly journals Towards an improved description of ocean uncertainties: effect of local anamorphic transformations on spatial correlations

2011 ◽  
Vol 8 (5) ◽  
pp. 2147-2195 ◽  
Author(s):  
J.-M. Brankart ◽  
C.-E. Testut ◽  
D. Béal ◽  
M. Doron ◽  
C. Fontana ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Correlation Radius ◽  
Correlation Structure ◽  
General Tendency ◽  
Spatial Correlations ◽  
Parameter Uncertainties ◽  
Large Size ◽  
Observation Network ◽  
Spatial Correlation Structure

Abstract. The objective of this paper is to investigate if the description of ocean uncertainties can be significantly improved by applying a local anamorphic transformation to each model variable, and by making the assumption of joint Gaussianity for the transformed variables, rather than for the original variables. For that purpose, it is first argued that a significant improvement can already be obtained by deriving the local transformations from a simple histogram description of the marginal distributions. Two distinctive advantages of this solution for large size applications are the conciseness and the numerical efficiency of the description. Second, various oceanographic examples are used to evaluate the effect of the resulting piecewise linear local anamorphic transformations on the spatial correlation structure. These examples include (i) stochastic ensemble descriptions of the effect of atmospheric uncertainties on the ocean mixed layer, and of wind uncertainties or parameter uncertainties on the ecosystem, and (ii) non-stochastic ensemble descriptions of forecast uncertainties in current sea ice and ecosystem pre-operational developments. The results indicate that (i) the transformation is accurate enough to faithfully preserve the correlation structure if the joint distribution is already close to Gaussian, and (ii) the transformation has the general tendency of increasing the correlation radius as soon as the spatial dependence between random variables becomes nonlinear, with the important consequence of reducing the number of degrees of freedom in the uncertainties, and thus increasing the benefit that can be expected from a given observation network.

scholarly journals Towards an improved description of ocean uncertainties: effect of local anamorphic transformations on spatial correlations

Ocean Science ◽  
2012 ◽  
Vol 8 (2) ◽  
pp. 121-142 ◽  
Author(s):  
J.-M. Brankart ◽  
C.-E. Testut ◽  
D. Béal ◽  
M. Doron ◽  
C. Fontana ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Correlation Radius ◽  
Correlation Structure ◽  
General Tendency ◽  
Spatial Correlations ◽  
Parameter Uncertainties ◽  
Large Size ◽  
Observation Network ◽  
Spatial Correlation Structure

Abstract. The objective of this paper is to investigate if the description of ocean uncertainties can be significantly improved by applying a local anamorphic transformation to each model variable, and by making the assumption of joint Gaussianity for the transformed variables, rather than for the original variables. For that purpose, it is first argued that a significant improvement can already be obtained by deriving the local transformations from a simple histogram description of the marginal distributions. Two distinctive advantages of this solution for large size applications are the conciseness and the numerical efficiency of the description. Second, various oceanographic examples are used to evaluate the effect of the resulting piecewise linear local anamorphic transformations on the spatial correlation structure. These examples include (i) stochastic ensemble descriptions of the effect of atmospheric uncertainties on the ocean mixed layer, and of wind uncertainties or parameter uncertainties on the ecosystem, and (ii) non-stochastic ensemble descriptions of forecast uncertainties in current sea ice and ecosystem pre-operational developments. The results indicate that (i) the transformation is accurate enough to faithfully preserve the correlation structure if the joint distribution is already close to Gaussian, and (ii) the transformation has the general tendency of increasing the correlation radius as soon as the spatial dependence between random variables becomes nonlinear, with the important consequence of reducing the number of degrees of freedom in the uncertainties, and thus increasing the benefit that can be expected from a given observation network.

Nonlinear Dynamics of One-Way Clutches in Belt-Pulley Systems

2003 ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Second Primary ◽  
Arc Length ◽  
The One

One-way clutches are frequently used in the serpentine belt accessory drives of automobiles and heavy vehicles. The clutch plays a role similar to a vibration absorber in order to reduce belt/pulley vibration and noise and increase belt life. This paper analyzes a two-pulley system where the driven pulley has a one-way clutch between the pulley and accessory shaft that engages only for positive relative displacement between these components. The belt is modeled with linear springs that transmit torque from the driving pulley to the accessory pulley. The one-way clutch is modeled as a piecewise linear spring with discontinuous stiffness that separates the driven pulley into two degrees of freedom (DOF). The harmonic balance method (HBM) combined with arc-length continuation is employed to illustrate the nonlinear dynamic behavior of the one-way clutch. HBM with arc-length continuation yields the stable and unstable periodic solutions for given parameters. These solutions are examined across a range of excitation frequencies. The results are confirmed by numerical integration and the widely used bifurcation software AUTO. At the first primary resonance, most of the responses are aperiodic, including quasiperiodic and chaotic solutions. At the second primary resonance, the peak bends to the left with classical softening nonlinearity because clutch disengagement decouples the pulley and the accessory over portions of the response period. The dependence on system parameters such as clutch stiffness, excitation amplitude, and inertia ratio between the pulley and accessory is studied to characterize the nonlinear dynamics across a range of conditions.

Comparison of Statistical Methods for Assessing Spatial Correlations Between Maps of Different Arterial Properties

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Ethan M. Rowland ◽  
Yumnah Mohamied ◽  
K. Yean Chooi ◽  
Emma L. Bailey ◽  
Peter D. Weinberg
Keyword(s):  
Wavelet Transforms ◽  
Degrees Of Freedom ◽  
Arterial Wall ◽  
Atherosclerotic Lesion ◽  
Null Distribution ◽  
Correlation Coefficients ◽  
Spatial Correlations ◽  
Aggregated Data ◽  
Anatomical Correlation ◽  
Lesion Frequency

Assessing the anatomical correlation of atherosclerosis with biomechanical localizing factors is hindered by spatial autocorrelation (SA), wherein neighboring arterial regions tend to have similar properties rather than being independent, and by the use of aggregated data, which artificially inflates correlation coefficients. Resampling data at lower resolution or reducing degrees-of-freedom in significance tests negated effects of SA but only in artificial situations where it occurred at a single length scale. Using Fourier or wavelet transforms to generate autocorrelation-preserving surrogate datasets, and thus to compute the null distribution, avoided this problem. Bootstrap methods additionally circumvented the errors caused by aggregating data. The bootstrap technique showed that wall shear stress (WSS) was significantly correlated with atherosclerotic lesion frequency and endothelial nuclear elongation, but not with the permeability of the arterial wall to albumin, in immature rabbits.

scholarly journals Empirical estimate of the signal content of Holocene temperature proxy records

2019 ◽  
Vol 15 (2) ◽  
pp. 521-537 ◽  
Author(s):  
Maria Reschke ◽  
Kira Rehfeld ◽  
Thomas Laepple
Keyword(s):  
Time Series ◽  
Climate Models ◽  
Climate Model ◽  
Model Simulation ◽  
Correlation Structure ◽  
Past Climate ◽  
Time Uncertainty ◽  
Proxy Records ◽  
Spatial Correlation Structure ◽  
Temperature Proxy

Abstract. Proxy records from climate archives provide evidence about past climate changes, but the recorded signal is affected by non-climate-related effects as well as time uncertainty. As proxy-based climate reconstructions are frequently used to test climate models and to quantitatively infer past climate, we need to improve our understanding of the proxy record signal content as well as the uncertainties involved. In this study, we empirically estimate signal-to-noise ratios (SNRs) of temperature proxy records used in global compilations of the middle to late Holocene (last 6000 years). This is achieved through a comparison of the correlation of proxy time series from nearby sites of three compilations and model time series extracted at the proxy sites from two transient climate model simulations: a Holocene simulation of the ECHAM5/MPI-OM model and the Holocene part of the TraCE-21ka simulation. In all comparisons, we found the mean correlations of the proxy time series on centennial to millennial timescales to be low (R<0.2), even for nearby sites, which resulted in low SNR estimates. The estimated SNRs depend on the assumed time uncertainty of the proxy records, the timescale analysed, and the model simulation used. Using the spatial correlation structure of the ECHAM5/MPI-OM simulation, the estimated SNRs on centennial timescales ranged from 0.05 – assuming no time uncertainty – to 0.5 for a time uncertainty of 400 years. On millennial timescales, the estimated SNRs were generally higher. Use of the TraCE-21ka correlation structure generally resulted in lower SNR estimates than for ECHAM5/MPI-OM. As the number of available high-resolution proxy records continues to grow, a more detailed analysis of the signal content of specific proxy types should become feasible in the near future. The estimated low signal content of Holocene temperature compilations should caution against over-interpretation of these multi-proxy and multisite syntheses until further studies are able to facilitate a better characterisation of the signal content in paleoclimate records.

scholarly journals Statistical Beamforming for Massive MIMO Systems with Distinct Spatial Correlations

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6255
Author(s):  
Taehyoung Kim ◽  
Sangjoon Park
Keyword(s):  
Massive Mimo ◽  
Degrees Of Freedom ◽  
Mimo Systems ◽  
Mimo System ◽  
Multiple Input Multiple Output ◽  
High Signal ◽  
Spatial Correlations ◽  
Channel Correlation ◽  
Low Correlation ◽  
Noise Ratio

In this paper, we propose a novel statistical beamforming (SBF) method called the partial-nulling-based SBF (PN-SBF) to serve a number of users that are undergoing distinct degrees of spatial channel correlations in massive multiple-input multiple-output (MIMO) systems. We consider a massive MIMO system with two user groups. The first group experiences a low spatial channel correlation, whereas the second group has a high spatial channel correlation, which can happen in massive MIMO systems that are based on fifth-generation networks. By analyzing the statistical signal-to-interference-plus-noise ratio, it can be observed that the statistical beamforming vector for the low-correlation group should be designed as the orthogonal complement for the space spanned by the aggregated channel covariance matrices of the high-correlation group. Meanwhile, the spatial degrees of freedom for the high-correlation group should be preserved without cancelling the interference to the low-correlation group. Accordingly, a group-common pre-beamforming matrix is applied to the low-correlation group to cancel the interference to the high-correlation group. In addition, to deal with the intra-group interference in each group, the post-beamforming vector for each group is designed in the manner of maximizing the signal-to-leakage-and-noise ratio, which yields additional performance improvements for the PN-SBF. The simulation results verify that the proposed PN-SBF outperforms the conventional SBF schemes in terms of the ergodic sum rate for the massive MIMO systems with distinct spatial correlations, without the rate ceiling effect in the high signal-to-noise ratio region unlike conventional SBF schemes.

Extracting Articulation Models from CAD Models of Parts With Curved Surfaces

2001 ◽  
Vol 124 (1) ◽  
pp. 106-114 ◽  
Author(s):  
Rajarishi Sinha ◽  
Satyandra K. Gupta ◽  
Christiaan J. J. Paredis ◽  
Pradeep K. Khosla
Keyword(s):  
Contact Mechanics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Curved Surfaces ◽  
Global Motion ◽  
Intended Behavior ◽  
Cad Models ◽  
Constraint Method ◽  
Motion Behavior ◽  
Algebraic Constraint

In an assembly, degrees of freedom are realized by creating mating features that permit relative motion between parts. In complex assemblies, interactions between individual degrees of freedom may result in a behavior different from the intended behavior. In addition, current methods perform assembly reasoning by approximating curved surfaces as piecewise linear surfaces. Therefore, it is important to be able to reason about assemblies using exact representations of curved surfaces; verify global motion behavior of parts in the assembly; and create motion simulations of the assembly by examination of the geometry and material properties. In this paper, we present a linear algebraic constraint method to automatically construct the space of allowed instantaneous motions of an assembly from the geometry of its constituent parts. Our work builds on previous work on linear contact mechanics and curved surface contact mechanics. We enumerate the conditions under which general curved surfaces can be represented using a finite number of constraints that are linear in the instantaneous velocities. We compose such constraints to build a space of allowed instantaneous velocities for the assembly. The space is then described as a set-theoretic sum of contact-preserving and contact-breaking subspaces. Analysis of each subspace provides feedback to the designer, which we demonstrate through the use of an example assembly—a 4-part mechanism. Finally, the results of the analysis of a 4-bar linkage are compared to those from mechanism theory.

Sky-Cover Correlation within a Sky Dome

1991 ◽  
Vol 30 (7) ◽  
pp. 1037-1039 ◽  
Author(s):  
James H. Willand ◽  
Julia Steeves
Keyword(s):  
Spatial Correlation ◽  
Cloud Cover ◽  
Correlation Structure ◽  
National Weather Service ◽  
Structural Pattern ◽  
The Earth ◽  
Spatial Correlation Structure ◽  
Sky Conditions ◽  
Very High ◽  
Weather Service

Abstract A new utility for the use of whole-sky photographs has been developed through an effort to discern the structural pattern of correlations of cloud cover within an observer's sky dome. The photographs were taken from the National Weather Service observing site at Columbia, Missouri, and were originally assembled for the purpose of estimating probabilities of cloud-free lines of sight from the earth through the atmosphere. The procedure for determining the spatial correlation structure of sky cover within the sky dome starts with the defining and tabulating of a dichotomous sky-cover condition over small sectors of the sky dome, and then calculating the correlation associated with the tabulated sky conditions in each sector. This note shows that correlation of sky-cover conditions over a sky dome are very high, and that they are less degrading in the winter than in the summer. The results of this study can be applied to the estimation of cloud-free lines of sight to multiple satellites.

Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

2006 ◽  
Author(s):  
Brian M. Korte ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Shape Change ◽  
Piecewise Linear ◽  
Single Chain ◽  
Open Chain ◽  
Revolute Joints ◽  
Planar Shape ◽  
Rigid Body Displacement ◽  
Planar Linkages

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves” differ from each other by a combination of rigid-body displacement and shape change. Rigid link geometry is determined through analysis of piecewise linear curves to achieve shape-change approximation, and increasing the number of links improves the approximation. A mechanism is determined through connecting the rigid links into a single chain and adding dyads to eliminate degrees of freedom. The procedure is applied to two open-chain examples.

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