scholarly journals Uncertainty of model parameters in stream pollution using fuzzy arithmetic

2008 ◽  
Vol 10 (3) ◽  
pp. 189-200 ◽  
Author(s):  
H. Mpimpas ◽  
P. Anagnostopoulos ◽  
J. Ganoulis
Keyword(s):  
Dispersion Equation ◽  
Fuzzy Numbers ◽  
Quality Parameters ◽  
Quality Parameter ◽  
Fuzzy Arithmetic ◽  
Model Parameters ◽  
Water Stream ◽  
Stream Pollution ◽  
Advection Dispersion ◽  
The One

Fuzzy arithmetic is employed for the analysis of uncertainties in water-stream pollution, when the various model parameters involved are imprecise. The one-dimensional advection–dispersion equation, for both a conservative and a non-conservative substance, was solved analytically for point and Gaussian-hill input loads of pollution, considering the dispersion and decay coefficients involved as fuzzy numbers. The solution of the advection–dispersion equation was also conducted numerically for the same input loads with the finite-difference method, employing a Lagrangian–Eulerian scheme. The good agreement between analytical and numerical results presented in the form of fuzzy numbers confirms the reliability of the numerical scheme. The advection–dispersion equation of a non-conservative substance was then solved numerically for ten different water quality parameters, in order to study the water pollution in a water stream. The dispersion coefficient, the source terms and the input loads were expressed as fuzzy numbers, and the concentration of each quality parameter was obtained in fuzzy-number form. With fuzzy modeling, imprecise data can be represented and imprecise output produced, with minimal input data requirements and without the need of a large number of computations.

Advection-dispersion modelling tools: what about numerical dispersion?

2005 ◽  
Vol 52 (3) ◽  
pp. 19-27 ◽  
Author(s):  
R. Bouteligier ◽  
G. Vaes ◽  
J. Berlamont ◽  
C. Flamink ◽  
J.G. Langeveld ◽  
...  
Keyword(s):  
Dispersion Equation ◽  
Model Calibration ◽  
Suspended Particles ◽  
Numerical Dispersion ◽  
Model Parameters ◽  
One Dimensional ◽  
Advection Dispersion ◽  
The One ◽  
Calibration Tool ◽  
Tracer Experiments

In general the transport of dissolved substances and fine suspended particles is governed by the one-dimensional advection-dispersion equation. In order to model the transport of dissolved substances and fine suspended particles, the advection-dispersion equation is incorporated into commonly used urban drainage modelling tools such as InfoWorks CS (Wallingford Software, United Kingdom) and MOUSE (DHI Software, Denmark). Two examples show the use of InfoWorks CS and MOUSE using standard model settings. Modelling results using tracer experiments show that numerical model parameters need to be altered in order to calibrate the model. Using tracer experiments as a model calibration tool, it is shown that a non-negligible amount of dispersion is generated by InfoWorks CS and MOUSE and that it is in fact the numerical dispersion that is calibrated.

scholarly journals Fuzzy Arithmetical Analysis of Multibody Systems with Uncertainties

2013 ◽  
Vol 60 (1) ◽  
pp. 109-125 ◽  
Author(s):  
Nico-Philipp Walz ◽  
Michael Hanss
Keyword(s):  
Multibody Systems ◽  
System Analysis ◽  
Fuzzy Numbers ◽  
Considerable Proportion ◽  
Fuzzy Arithmetic ◽  
Model Parameters ◽  
Modeling And Analysis ◽  
Simulation Techniques ◽  
Parameter Values ◽  
Random Nature

The consideration of uncertainties in numerical simulation is generally reasonable and is often indicated in order to provide reliable results, and thus is gaining attraction in various fields of simulation technology. However, in multibody system analysis uncertainties have only been accounted for quite sporadically compared to other areas. The term uncertainties is frequently associated with those of random nature, i.e. aleatory uncertainties, which are successfully handled by the use of probability theory. Actually, a considerable proportion of uncertainties incorporated into dynamical systems, in general, or multibody systems, in particular, is attributed to so-called epistemic uncertainties, which include, amongst others, uncertainties due to a lack of knowledge, due to subjectivity in numerical implementation, and due to simplification or idealization. Hence, for the modeling of epistemic uncertainties in multibody systems an appropriate theory is required, which still remains a challenging topic. Against this background, a methodology will be presented which allows for the inclusion of epistemic uncertainties in modeling and analysis of multibody systems. This approach is based on fuzzy arithmetic, a special field of fuzzy set theory, where the uncertain values of the model parameters are represented by socalled fuzzy numbers, reflecting in a rather intuitive and plausible way the blurred range of possible parameter values. As a result of this advanced modeling technique, more comprehensive system models can be derived which outperform the conventional, crisp-parameterized models by providing simulation results that reflect both the system dynamics and the effect of the uncertainties. The methodology is illustrated by an exemplary application of multibody dynamics which reveals that advanced modeling and simulation techniques using some well-thought-out inclusion of the presumably limiting uncertainties can provide significant additional benefit.

scholarly journals A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Silvia Jerez ◽  
Ivan Dzib
Keyword(s):  
Numerical Simulation ◽  
Analytical Solution ◽  
Fractional Derivative ◽  
Dispersion Equation ◽  
Numerical Algorithm ◽  
Initial Condition ◽  
Discrete Method ◽  
One Dimensional ◽  
Advection Dispersion ◽  
The One

We obtain a numerical algorithm by using the space-time conservation element and solution element (CE-SE) method for the fractional advection-dispersion equation. The fractional derivative is defined by the Riemann-Liouville formula. We prove that the CE-SE approximation is conditionally stable under mild requirements. A numerical simulation is performed for the one-dimensional case by considering a benchmark with a discontinuous initial condition in order to compare the results with the analytical solution.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

scholarly journals Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling

2021 ◽  
Author(s):  
Sebastian Brandstaeter ◽  
Sebastian L. Fuchs ◽  
Jonas Biehler ◽  
Roland C. Aydin ◽  
Wolfgang A. Wall ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Computational Studies ◽  
Growth And Remodeling ◽  
Global Sensitivity ◽  
Output Variability ◽  
Constrained Mixture ◽  
The One ◽  
Influential Parameters

AbstractGrowth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

scholarly journals More about solar g modes

2018 ◽  
Vol 612 ◽  
pp. L1 ◽  
Author(s):  
E. Fossat ◽  
F. X. Schmider
Keyword(s):  
Cross Correlation ◽  
Previous Analysis ◽  
Model Parameters ◽  
Real Spectrum ◽  
Space Observatory ◽  
Correlation Peak ◽  
Similar Frequency ◽  
Precise Estimation ◽  
The One ◽  
Additional Constraints

Context. The detection of asymptotic solar g-mode parameters was the main goal of the GOLF instrument onboard the SOHO space observatory. This detection has recently been reported and has identified a rapid mean rotation of the solar core, with a one-week period, nearly four times faster than all the rest of the solar body, from the surface to the bottom of the radiative zone. Aim. We present here the detection of more g modes of higher degree, and a more precise estimation of all their parameters, which will have to be exploited as additional constraints in modeling the solar core. Methods. Having identified the period equidistance and the splitting of a large number of asymptotic g modes of degrees 1 and 2, we test a model of frequencies of these modes by a cross-correlation with the power spectrum from which they have been detected. It shows a high correlation peak at lag zero, showing that the model is hidden but present in the real spectrum. The model parameters can then be adjusted to optimize the position (at exactly zero lag) and the height of this correlation peak. The same method is then extended to the search for modes of degrees 3 and 4, which were not detected in the previous analysis.Results. g-mode parameters are optimally measured in similar-frequency bandwidths, ranging from 7 to 8 μHz at one end and all close to 30 μHz at the other end, for the degrees 1 to 4. They include the four asymptotic period equidistances, the slight departure from equidistance of the detected periods for l = 1 and l = 2, the measured amplitudes, functions of the degree and the tesseral order, and the splittings that will possibly constrain the estimated sharpness of the transition between the one-week mean rotation of the core and the almost four-week rotation of the radiative envelope. The g-mode periods themselves are crucial inputs in the solar core structure helioseismic investigation.

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