Model parameters of the nonlinear stiffness of the vibrator-ground contact determined by inversion of vibrator accelerometer data

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. H25-H32 ◽  
Author(s):  
Andrey V. Lebedev ◽  
Igor A. Beresnev ◽  
Pieter L. Vermeer
Keyword(s):  
Inverse Problem ◽  
Harmonic Distortion ◽  
Source Model ◽  
Coupled Systems ◽  
Equivalent Model ◽  
Model Parameters ◽  
Accelerometer Data ◽  
Ground Contact ◽  
Force Signal ◽  
Using Data

Analysis of vibroseis data shows that harmonic distortion in the ground-force signal may exceed the primary distortions in the hydraulic system. This can be explained by the baseplate-ground contact nonlinearity created by the deformations of the contact roughness. We separated the nonlinear distortion generated in the hydraulics from that generated at the contact. We then formulated an inverse problem for resolving the parameters of the nonlinear contact rigidity, based on the equivalent model of the nonlinear source and the comparison of predicted and observed harmonic levels. The inverse problem was solved for models of bilinear contact and the contact with the rigidity smoothly varying between two asymptotic values, using data obtained on sandy soil. Rigidities changing between approximately [Formula: see text] in compression and [Formula: see text] in tension were resolved from the inversion for both models, although the smooth nonlinear-rigidity model is a better approximation. The analysis shows the adequacy of the equivalent mechanical source model used for the description of nolinear distortions in real soil-baseplate coupled systems.

Crosswell electromagnetic inversion using integral and differential equations

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 899-911 ◽  
Author(s):  
Gregory Newman
Keyword(s):  
Inverse Problem ◽  
Field Data ◽  
Green's Functions ◽  
Green’S Functions ◽  
Salt Water ◽  
Single Frequency ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Before And After ◽  
Using Data

The crosswell electromagnetic (EM) inverse problem is solved with an integral‐equation (IE) formulation using successive Born approximations in the frequency domain. Because the inverse problem is nonlinear, the predicted fields and Green’s functions are continually updated. Updating the fields and Green’s functions relates small changes in the predicted data to small changes in the model parameters through Fréchet kernels. These fields and Green functions are calculated with an efficient 3-D finite‐difference solver. Since the resistivity is invariant along strike, the 3-D fields are integrated along strike so the 2-D kernels can be assembled. At the early stages of the inversion, smoothing of the electrical conductivity stabilizes the inverse solution when it is far from convergence. As the solution converges, this smoothing is relaxed and more effort is made to reduce the data misfit. Bounds on the conductivity are included in the solution to eliminate unrealistic estimates. The robustness of the inversion scheme has been demonstrated with synthetic and field data that are underdetermined from the standpoint of the smooth models being sought. Two synthetic examples with added Gaussian noise were considered, including data arising from an IE solver. This IE solver is different from the one embedded in the inversion algorithm and has provided a stronger check on the scheme. The synthetic examples show it is more difficult to reconstruct a target’s conductivity than its geometry at a single frequency. The inversion scheme has been successfully tested using data collected at the Richmond‐field site near Berkeley, California, where it has imaged a salt water plume injected into the interwell region. The data in this experiment consisted of two sets of measurements, taken before and after the injection of 50 000 gallons of 1 Ωm salt water. Findings show that underdetermined inversion using small amounts of field data can be sufficient to produce useful, but smoothed, maps of the conductivity. The data in this instance need be only single frequency and single component.

Reflection of a longitudinal travelling wave from the notch in a rod plunged into viscous liquid

2010 ◽  
Vol 7 ◽  
pp. 129-142
Author(s):  
M.A. Ilgamov ◽  
A.G. Khakimov
Keyword(s):  
Inverse Problem ◽  
Viscous Liquid ◽  
Travelling Wave ◽  
Observation Point ◽  
Reflected Waves ◽  
Damping Characteristics ◽  
Deformed State ◽  
Using Data ◽  
Surrounding Liquid

The article investigates the reflection of a longitudinal damped travelling wave from the transverse notch and its movement along an infinite rod plunged into viscous liquid. The simplest model for the stress deformed state in the notch zone is applied. The solution is found to depend on the parameters of the liquid and damping characteristics in the material of the rod and the surrounding liquid. The solution to the inverse problem makes it possible to define the coordinate of the notch and the parameter that contains its depth and length using data on both the incident and reflected waves at the observation point.

Reflection of a longitudinal travelling wave from the notch in a rod

2007 ◽  
Vol 5 ◽  
pp. 212-220 ◽  
Author(s):  
M.A. Ilgamov ◽  
A.G. Khakimov
Keyword(s):  
Inverse Problem ◽  
Longitudinal Wave ◽  
Travelling Wave ◽  
Observation Point ◽  
Reflected Waves ◽  
Reflected Wave ◽  
Using Data

This article investigates the reflection of a longitudinal wave from the transverse notch and its movement along an infinite rod. The dependence is obtained between the reflected wave and parameters of the notch. The statement of the inverse problem allows defining the coordinate of the notch and the parameter that contains its depth and length using data on both the incident and reflected waves at the observation point.

scholarly journals Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 910
Author(s):  
Andrey Kovtanyuk ◽  
Alexander Chebotarev ◽  
Varvara Turova ◽  
Irina Sidorenko ◽  
Renée Lampe
Keyword(s):  
Inverse Problem ◽  
Oxygen Transport ◽  
Model Parameters ◽  
Cerebral Oxygen ◽  
System Of Equations ◽  
Blood Oxygen ◽  
Stationary Model ◽  
Average Oxygen Concentration ◽  
The Right ◽  
The Brain

An inverse problem for a system of equations modeling oxygen transport in the brain is studied. The problem consists of finding the right-hand side of the equation for the blood oxygen transport, which is a linear combination of given functionals describing the average oxygen concentration in the neighborhoods of the ends of arterioles and venules. The overdetermination condition is determined by the values of these functionals evaluated on the solution. The unique solvability of the problem is proven without any smallness assumptions on the model parameters.

scholarly journals Bayesian Reconstruction through Adaptive Image Notion

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 21
Author(s):  
Fabrizia Guglielmetti ◽  
Eric Villard ◽  
Ed Fomalont
Keyword(s):  
Inverse Problem ◽  
Image Plane ◽  
Source Distribution ◽  
Bayesian Probability ◽  
Model Parameters ◽  
Uncertain Information ◽  
Source Detection ◽  
Component Mixture ◽  
Ill Posed ◽  
Image Planes

A stable and unique solution to the ill-posed inverse problem in radio synthesis image analysis is sought employing Bayesian probability theory combined with a probabilistic two-component mixture model. The solution of the ill-posed inverse problem is given by inferring the values of model parameters defined to describe completely the physical system arised by the data. The analysed data are calibrated visibilities, Fourier transformed from the ( u , v ) to image planes. Adaptive splines are explored to model the cumbersome background model corrupted by the largely varying dirty beam in the image plane. The de-convolution process of the dirty image from the dirty beam is tackled in probability space. Probability maps in source detection at several resolution values quantify the acquired knowledge on the celestial source distribution from a given state of information. The information available are data constrains, prior knowledge and uncertain information. The novel algorithm has the aim to provide an alternative imaging task for the use of the Atacama Large Millimeter/Submillimeter Array (ALMA) in support of the widely used Common Astronomy Software Applications (CASA) enhancing the capabilities in source detection.

Predicting the longitudinal modulus of elasticity of Sitka spruce from cellulose orientation and abundance

Holzforschung ◽  
2010 ◽  
Vol 64 (4) ◽  
Author(s):  
J. Paul McLean ◽  
Robert Evans ◽  
John R. Moore
Keyword(s):  
Bulk Density ◽  
Modulus Of Elasticity ◽  
Microfibril Angle ◽  
Sitka Spruce ◽  
Picea Sitchensis ◽  
Model Parameters ◽  
Bending Tests ◽  
Wood Stiffness ◽  
Using Data ◽  
Longitudinal Modulus

Abstract Sitka spruce (Picea sitchensis) is the most widely planted commercial tree species in the United Kingdom and Ireland. Because of the increasing use of this species for construction, the ability to predict wood stiffness is becoming more important. In this paper, a number of models are developed using data on cellulose abundance and orientation obtained from the SilviScan-3 system to predict the longitudinal modulus of elasticity (MOE) of small defect-free specimens. Longitudinal MOE was obtained from both bending tests and a sonic resonance technique. Overall, stronger relationships were found between the various measures of cellulose abundance and orientation and the dynamic MOE obtained from the sonic resonance measurements, rather than with the static MOE obtained from bending tests. There was only a moderate relationship between wood bulk density and dynamic MOE (R2=0.423), but this relationship was improved when density was divided by microfibril angle (R2=0.760). The best model for predicting both static and dynamic MOE involved the product of bulk density and the coefficient of variation in the azimuthal intensity profile (R2=0.725 and 0.862, respectively). The model parameters obtained for Sitka spruce differed from those obtained in earlier studies on Pinus radiata and Eucalyptus delegatensis, indicating that the model might require recalibration before it can be applied to different species.

scholarly journals Resource-Driven Encounters and the Induction of Disease Among Consumers

2016 ◽  
Author(s):  
Rebecca K. Borchering ◽  
Steve E. Bellan ◽  
Jason M. Flynn ◽  
Juliet R.C. Pulliam ◽  
Scott A. McKinley
Keyword(s):  
National Park ◽  
Interaction Model ◽  
Spatially Explicit ◽  
Encounter Rate ◽  
Model Parameters ◽  
Expected Number ◽  
Spatially Explicit Model ◽  
Consumer Population ◽  
Using Data ◽  
The Relationship

AbstractSubmitted Manuscript 2016. Territorial animals share a variety of common resources, which can be a major driver of conspecific encounter rates. We examine how changes in resource availability influence the rate of encounters among individuals in a consumer population by implementing a spatially explicit model for resource visitation behavior by consumers. Using data from 2009 and 2010 in Etosha National Park, we verify our model's prediction that there is a saturation effect in the expected number of jackals that visit a given carcass site as carcasses become abundant. However, this does not directly imply that the overall resource-driven encounter rate among jackals decreases. This is because the increase in available carcasses is accompanied by an increase in the number of jackals that detect and potentially visit carcasses. Using simulations and mathematical analysis of our consumer-resource interaction model, we characterize key features of the relationship between resource-driven encounter rate and model parameters. These results are used to investigate a standing hypothesis that the outbreak of a fatal disease among zebras can potentially lead to an outbreak of an entirely different disease in the jackal population, a process we refer to as indirect induction of disease.

scholarly journals Three-dimensional data-tracking simulations of sprinting using a direct collocation optimal control approach

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e10975
Author(s):  
Nicos Haralabidis ◽  
Gil Serrancolí ◽  
Steffi Colyer ◽  
Ian Bezodis ◽  
Aki Salo ◽  
...  
Keyword(s):  
Experimental Data ◽  
Reaction Force ◽  
Three Dimensional ◽  
Contact Model ◽  
Model Parameters ◽  
Ground Contact ◽  
Control Approach ◽  
Average Percentage ◽  
Data Tracking ◽  
The Individual

Biomechanical simulation and modelling approaches have the possibility to make a meaningful impact within applied sports settings, such as sprinting. However, for this to be realised, such approaches must first undergo a thorough quantitative evaluation against experimental data. We developed a musculoskeletal modelling and simulation framework for sprinting, with the objective to evaluate its ability to reproduce experimental kinematics and kinetics data for different sprinting phases. This was achieved by performing a series of data-tracking calibration (individual and simultaneous) and validation simulations, that also featured the generation of dynamically consistent simulated outputs and the determination of foot-ground contact model parameters. The simulated values from the calibration simulations were found to be in close agreement with the corresponding experimental data, particularly for the kinematics (average root mean squared differences (RMSDs) less than 1.0° and 0.2 cm for the rotational and translational kinematics, respectively) and ground reaction force (highest average percentage RMSD of 8.1%). Minimal differences in tracking performance were observed when concurrently determining the foot-ground contact model parameters from each of the individual or simultaneous calibration simulations. The validation simulation yielded results that were comparable (RMSDs less than 1.0° and 0.3 cm for the rotational and translational kinematics, respectively) to those obtained from the calibration simulations. This study demonstrated the suitability of the proposed framework for performing future predictive simulations of sprinting, and gives confidence in its use to assess the cause-effect relationships of technique modification in relation to performance. Furthermore, this is the first study to provide dynamically consistent three-dimensional muscle-driven simulations of sprinting across different phases.

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