An Accurate Incremental Bekker Equation for Computational Tire-Soil Modeling

2002 ◽  
Author(s):  
Ray P. S. Han ◽  
S. G. Mao
Keyword(s):  
Computational Model ◽  
Static Analysis ◽  
Traditional Approach ◽  
Nonlinear Relationship ◽  
Iterative Approach ◽  
Numerical Examples ◽  
Nonlinear Complementarity ◽  
Loading And Unloading ◽  
Incremental Form ◽  
Interaction Problem

In this paper, an accurate computational model for analyzing tire-soil interaction is presented. In the traditional approach, Bekker equation is written in a global form and a quasi-static analysis is done to iteratively model the interaction of the tire and soil. This is due to the nonlinear relationship between soil sinkage and pressure and the unknown loading and unloading status of soil as they are dependent on past loading histories. In this work, an incremental form of Bekker model is proposed. The resulting tire-soil interaction problem is described by a set of nonlinear complementarity equations, which are easier to solve compared to the iterative approach required in the traditional Bekker model. Two numerical examples are presented to demonstrate the effectiveness of the algorithm presented in this work.

scholarly journals Nonparametric Tests for Convexity/Monotonicity/Positivity of Multivariate Functions with Noisy Observations

2017 ◽  
Vol 6 (5) ◽  
pp. 18
Author(s):  
Eunji Lim ◽  
Elizabeth Tavarez
Keyword(s):  
Traditional Approach ◽  
Test Procedure ◽  
Positive Function ◽  
Nonparametric Tests ◽  
Multivariate Functions ◽  
Data Set ◽  
Numerical Examples ◽  
Shape Characteristic ◽  
Finite Set ◽  
Traditional Approaches

We propose a new method of testing for a function's convexity, monotonicity, or positivity, based on some noisy observations of the function made over a finite set $\mathcal{T}$ of points in the domain, where the observations can be made multiple times at each point in $\mathcal{T}$. One of the traditional approaches to the test of a function's shape characteristic is to fit a convex, a monotone, or a positive function, depending on the shape characteristic we wish to test for, to the data set minimizing the sum of squared errors, and to compute the sum of squared differences (SSD) between the fit and the data set. While the traditional approach proceeds by observing the SSD as the number of points in $\mathcal{T}$ increases to infinity, we propose observing the SSD as $r$, the number of observations taken at each point in $\mathcal{T}$, increases to infinity. This new way of observing the asymptotic behavior of the SSD leads to a test procedure that does not require the estimation of any additional parameters, and hence, is easy to implement. The proposed test procedure is proven to achieve a prescribed power as $r \rightarrow \infty$. Numerical examples illustrate that the proposed test successfully detects the convexity/monotonicity/positivity of a function, as well as the non-convexity/non-monotonicity/non-positivity of a function.

Condition Monitoring of Fatigue Cracks in Machinery Blades

2005 ◽  
Vol 36 (11) ◽  
pp. 18-23
Author(s):  
L. Gelman
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Crack Detection ◽  
Traditional Approach ◽  
Fatigue Cracks ◽  
Diagnostic Features ◽  
New Approach ◽  
Numerical Examples ◽  
Power Spectral ◽  
The Fourier Transform

A novel generic approach to fatigue crack diagnostics in machinery blades is proposed and employed. The approach consists of simultaneously using two new diagnostic features: the real and imaginary parts of the Fourier transform of vibroacoustical signal generated from a blade. This approach is more generic than traditional approach based on the power spectral density; the power spectral density is a particular case of the proposed approach. Numerical examples are given based on the processing of signals generated using a nonlinear model of a blade. The signals generated are the resonant vibroacoustical oscillations of cracked and uncracked blades under narrowband vibration excitation. The numerical examples show that the crack detection is more effective when using the new approach than when using the power spectral density approach. The presented experimental results are matched with the numerical results. The proposed approach offers an effectiveness improvement over the traditional approach based on power spectral density.

On the Inverse Multiplicative Eigenvalue Problem With an Engineering Application

1995 ◽  
Author(s):  
Dmitri D. Sivan ◽  
Yitshak M. Ram
Keyword(s):  
Eigenvalue Problem ◽  
Closed Form ◽  
Engineering Application ◽  
Iterative Approach ◽  
Numerical Examples ◽  
Practical Applications ◽  
Spring System ◽  
The Masses ◽  
Three Degree Of Freedom ◽  
Mass Spring

Abstract The problem of determining the masses of a mass-spring system is an inverse multiplicative eigenvalue problem. Generally, the solutions of this problem are not yet fully characterised. Since all known methods of solution follow an iterative approach, the possibility of developing a closed-form algorithm is examined. Although such method is found for the two and three degree-of-freedom systems, it appears to be impractical for higher order systems. Two well known existing algorithms are then examined numerically. Both converge locally at a quadratic rate. However, for practical applications, a globally converging algorithm may be more effective. In this paper a new, linearly converging algorithm is advised. The three methods are then tested on some selected numerical examples, and their performances compared.

scholarly journals Rapid migrations and dynamics of citizen response

2019 ◽  
Vol 6 (3) ◽  
pp. 181864
Author(s):  
Anand Sahasranaman ◽  
Henrik Jeldtoft Jensen
Keyword(s):  
Computational Model ◽  
Sharp Increase ◽  
Inverse Relationship ◽  
Analytical Approximation ◽  
Nonlinear Relationship ◽  
Rapid Rise ◽  
Resident Population ◽  
Social Concerns ◽  
Citizen Response

One of the pressing social concerns of our time is the need for meaningful responses to migrants and refugees fleeing conflict and environmental catastrophe. We develop a computational model to model the influx of migrants into a city, varying the rates of entry, and find a nonlinear inverse relationship between the fraction of resident population whose tolerance levels are breached due to migrant entry and the average time to such tolerance breach. Essentially, beyond a certain rate of migrant entry, there is a rapid rise in the fraction of residents whose tolerances are breached, even as the average time to breach decreases. We also model an analytical approximation of the computational model and find qualitative correspondence in the observed phenomenology, with caveats. The sharp increase in the fraction of residents with tolerance breach could potentially underpin the intensity of resident responses to bursts of migrant entry into their cities. Given this nonlinear relationship, it is perhaps essential that responses to refugee situations are multi-country or global efforts so that sharp spikes of refugee migrations are equitably distributed among nations, potentially enabling all participating countries to avoid impacting resident tolerances beyond limits that are socially sustainable.

scholarly journals Detecting and learning from unknown by extremely weak supervision: exploratory classifier (xClass)

2021 ◽  
Author(s):  
Plamen Angelov ◽  
Eduardo Soares
Keyword(s):  
Data Base ◽  
Traditional Approach ◽  
Data Distribution ◽  
Autonomous Driving ◽  
Single Class ◽  
Weak Supervision ◽  
Numerical Examples ◽  
Data Density ◽  
Interpretable Models ◽  
Self Learning

AbstractIn this paper, we break with the traditional approach to classification, which is regarded as a form of supervised learning. We offer a method and algorithm, which make possible fully autonomous (unsupervised) detection of new classes, and learning following a very parsimonious training priming (few labeled data samples only). Moreover, new unknown classes may appear at a later stage and the proposed xClass method and algorithm are able to successfully discover this and learn from the data autonomously. Furthermore, the features (inputs to the classifier) are automatically sub-selected by the algorithm based on the accumulated data density per feature per class. In addition, the automatically generated model is easy to interpret and is locally generative and based on prototypes which define the modes of the data distribution. As a result, a highly efficient, lean, human-understandable, autonomously self-learning model (which only needs an extremely parsimonious priming) emerges from the data. To validate our proposal, we approbated it on four challenging problems, including imbalanced Faces-1999 data base, Caltech-101 dataset, vehicles dataset, and iRoads dataset, which is a dataset of images of autonomous driving scenarios. Not only we achieved higher precision (in one of the problems outperforming by 25% all other methods), but, more significantly, we only used a single class beforehand, while other methods used all the available classes and we generated interpretable models with smaller number of features used, through extremely weak and weak supervision. We demonstrated the ability to detect and learn new classes for both images and numerical examples.

scholarly journals Comparative analysis of stability criteria for polynomials

2020 ◽  
pp. 31-54
Author(s):  
M. M. Chernyavsky
Keyword(s):  
Comparative Analysis ◽  
Algebraic Equation ◽  
Nonlinear Relationship ◽  
Stability Criteria ◽  
Fourth Degree ◽  
Numerical Examples ◽  
Analysis Of Stability ◽  
The Relationship

The article provides a comparative analysis of two stability criteria for polynomials. They do not require obtaining any information about the roots, but allow us to judge stability directly by the coefficients of the polynomial. On specific numerical examples, the features of their application are considered. The article also provides symbolic expressions of the relationship between the coefficients of sixth and fourth degree polynomials for cases where there is a linear or definite nonlinear relationship between the roots of these polynomials. In these cases, an algebraic equation of the sixth degree can be solved in radicals.

scholarly journals An Iterative Approach for the Parameter Estimation of Shear-Rate and Temperature-Dependent Rheological Models for Polymeric Liquids

Polymers ◽  
2021 ◽  
Vol 13 (23) ◽  
pp. 4185
Author(s):  
Medeu Amangeldi ◽  
Yanwei Wang ◽  
Asma Perveen ◽  
Dichuan Zhang ◽  
Dongming Wei
Keyword(s):  
Experimental Data ◽  
Iterative Algorithm ◽  
Newtonian Fluid ◽  
Traditional Approach ◽  
Fluid Model ◽  
Polymer Processing ◽  
Iterative Approach ◽  
Temperature Dependent ◽  
Small Amplitude Oscillatory Shear ◽  
Flow Simulations

Numerical flow simulations play an important role in polymer processing. One of the essential prerequisites for accurate and precise flow simulations is to obtain accurate materials functions. In the framework of the generalized Newtonian fluid model, one needs to obtain shear viscosity as a function of the rate-of-shear and temperature—as determined by rheometry—and then fitted to a mathematical model. Often, many subjectively perform the fitting without paying attention to the relative quality of the estimated parameters. This paper proposes a unique iterative algorithm for fitting the rate-of-shear and temperature-dependent viscosity model under the time–temperature superposition (TTS) principle. Proof-of-concept demonstrations are shown using the five-parameter Carreau–Yasuda model and experimental data from small-amplitude oscillatory shear (SAOS) measurements. It is shown that the newly proposed iterative algorithm leads to a more accurate representation of the experimental data compared to the traditional approach. We compare their performance in studies of the steady isothermal flow of a Carreau–Yasuda model fluid in a straight, circular tube. The two sets of parameters, one from the traditional approach and the other from the newly proposed iterative approach, show considerable differences in flow simulation. The percentage difference between the two predictions can be as large as 10% or more. Furthermore, even in cases where prior knowledge of the TTS shifting factors is not available, the newly proposed iterative approach can still yield a good fit to the experimental data, resulting in both the shifting factors and parameters for the non-Newtonian fluid model.

Application of an Absorbing Boundary Condition in a Wave-Structure Interaction Problem

2012 ◽  
Author(s):  
Bulent Duz ◽  
Rene H. M. Huijsmans ◽  
Mart J. A. Borsboom ◽  
Peter R. Wellens ◽  
Arthur E. P. Veldman
Keyword(s):  
Boundary Condition ◽  
Traditional Approach ◽  
Wave Structure ◽  
Offshore Structures ◽  
Absorbing Boundary Condition ◽  
Design Stage ◽  
Absorbing Boundary ◽  
Structure Interaction ◽  
Interaction Problem ◽  
Wave Structure Interaction

For the design of offshore structures, an accurate assessment of the ability of the structure to survive in extreme sea conditions is of prime importance. Next to scaled model tests on the structure in waves, also CFD capabilities are at the disposal of the designer. However even with the fastest computers available, it is still a challenge to use CFD in the design stage because of the large computational resources they require. In this study we focus our attention on the implementation of an absorbing boundary condition (ABC) in a wave-structure interaction problem. Unlike the traditional approach where the boundaries are located far from the object to avoid reflection, we gradually locate them closer while at the same time observing the influence of the absorbing boundary condition on the solution. Numerical calculations are performed using the CFD simulation tool ComFLOW which is a volume-of-fluid (VOF) based Navier-Stokes solver. Comparisons with experimental results are also provided and the performance of the ABC is discussed.

Analysis on the Straight-End Problem in Thin-Plate Three-Roll Bending

2011 ◽  
Vol 80-81 ◽  
pp. 585-590 ◽  
Author(s):  
Zhong Yr Cai ◽  
Ying Wu Lan
Keyword(s):  
Theoretical Analysis ◽  
Thin Plate ◽  
Analytical Solutions ◽  
Numerical Examples ◽  
Roll Bending ◽  
Bending Process ◽  
Bending Behavior ◽  
Loading And Unloading ◽  
Set Up

The analytical solutions for the deformations of straight-ends in three-roll bending process of thin-plate were presented. Based on the theoretical analysis on the loading and unloading during roll-bending, the curvature equations governing the bending behavior of thin-plate were set up and then solved by integration. Numerical examples were given to illustrate the application of the solutions. The curvature and deflection distributions on straight-ends were shown in graphically and discussed.

scholarly journals Numerical Study of Mach Reflection and Detonation by Using a Second-Order CE/SE Method

2010 ◽  
Vol 26 (4) ◽  
pp. 465-472
Author(s):  
Deliang Zhang ◽  
S.-M. Liang
Keyword(s):  
Fluid Dynamics ◽  
Shock Waves ◽  
Present Method ◽  
Numerical Study ◽  
Mach Reflection ◽  
Second Order ◽  
Improved Method ◽  
Numerical Examples ◽  
Interaction Problem ◽  
Good Agreement

ABSTRACTAn improved method of space-time conservation element and solution element (CE/SE) is developed to solve the equations of conservation laws in fluid dynamics. The present method substantially differs in both concept and methodology from the traditional CE/SE method. In this paper the improved second-order CE/SE method is presented in a hexahedral grid. Furthermore, the present CE/SE method was successfully applied to solve the interaction problem of shock waves and detonation. Several numerical examples were also given. Numerical results have compared with the results of experiments and other computational methods. The compared results have shown a good agreement. The improved CE/SE method has higher accuracy and becomes a more prospective scheme.

Sign in / Sign up

Export Citation Format

Share Document