Search results for: sobol

Authors: A. B. M. Rezaul Islam, Ernur Karadogan

Abstract:

Shape memory alloys (SMAs) are known for their shape memory effect and pseudoelasticity behavior. Their thermomechanical behaviors are modeled by numerous researchers using microscopic thermodynamic and macroscopic phenomenological point of view. Tanaka, Liang-Rogers and Ivshin-Pence models are some of the most popular SMA macroscopic phenomenological constitutive models. They describe SMA behavior in terms of stress, strain and temperature. These models involve material parameters and they have associated uncertainty present in them. At different operating temperatures, the uncertainty propagates to the output when the material is subjected to loading followed by unloading. The propagation of uncertainty while utilizing these models in real-life application can result in performance discrepancies or failure at extreme conditions. To resolve this, we used probabilistic approach to perform the sensitivity and uncertainty analysis of Tanaka, Liang-Rogers, and Ivshin-Pence models. Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods have been used to perform the sensitivity analysis for simulated isothermal loading/unloading at various operating temperatures. As per the results, it is evident that the models vary due to the change in operating temperature and loading condition. The average and stress-dependent sensitivity indices present the most significant parameters at several temperatures. This work highlights the sensitivity and uncertainty analysis results and shows comparison of them at different temperatures and loading conditions for all these models. The analysis presented will aid in designing engineering applications by eliminating the probability of model failure due to the uncertainty in the input parameters. Thus, it is recommended to have a proper understanding of sensitive parameters and the uncertainty propagation at several operating temperatures and loading conditions as per Tanaka, Liang-Rogers, and Ivshin-Pence model.

Keywords: constitutive models, FAST sensitivity analysis, sensitivity analysis, sobol, shape memory alloy, uncertainty analysis

Procedia PDF Downloads 102

Authors: Soha Saad, Jean Bigeon, Florence Ossart, Etienne Sourdille

Abstract:

Developing better solutions for train rescheduling problems has been drawing the attention of researchers for decades. Most researches in this field deal with minor incidents that affect a large number of trains due to cascading effects. They focus on timetables, rolling stock and crew duties, but do not take into account infrastructure limits. The present work addresses electric infrastructure incidents that limit the power available for train traction, and hence the transportation capacity of the railway system. Rescheduling is needed in order to optimally share the available power among the different trains. We propose a rescheduling process based on dynamic multiphysics railway simulations that include the mechanical and electrical properties of all the system components and calculate physical quantities such as the train speed profiles, voltage along the catenary lines, temperatures, etc. The optimization problem to solve has a large number of continuous and discrete variables, several output constraints due to physical limitations of the system, and a high computation cost. Our approach includes a phase of sensitivity analysis in order to analyze the behavior of the system and help the decision making process and/or more precise optimization. This approach is a quantitative method based on simulation statistics of the dynamic railway system, considering a predefined range of variation of the input parameters. Three important settings are defined. Factor prioritization detects the input variables that contribute the most to the outputs variation. Then, factor fixing allows calibrating the input variables which do not influence the outputs. Lastly, factor mapping is used to study which ranges of input values lead to model realizations that correspond to feasible solutions according to defined criteria or objectives. Generalized Sobol indexes are used for factor prioritization and factor fixing. The approach is tested in the case of a simple railway system, with a nominal traffic running on a single track line. The considered incident is the loss of a feeding power substation, which limits the power available and the train speed. Rescheduling is needed and the variables to be adjusted are the trains departure times, train speed reduction at a given position and the number of trains (cancellation of some trains if needed). The results show that the spacing between train departure times is the most critical variable, contributing to more than 50% of the variation of the model outputs. In addition, we identify the reduced range of variation of this variable which guarantees that the output constraints are respected. Optimal solutions are extracted, according to different potential objectives: minimizing the traveling time, the train delays, the traction energy, etc. Pareto front is also built.

Keywords: optimization, rescheduling, railway system, sensitivity analysis, train timetable

Procedia PDF Downloads 371

Authors: S. Dey, T. Mukhopadhyay, S. Adhikari

Abstract:

This paper presents an exhaustive comparative investigation on sampling techniques of polynomial regression model based stochastic natural frequency of composite plates. Both individual and combined variations of input parameters are considered to map the computational time and accuracy of each modelling techniques. The finite element formulation of composites is capable to deal with both correlated and uncorrelated random input variables such as fibre parameters and material properties. The results obtained by Polynomial regression (PR) using different sampling techniques are compared. Depending on the suitability of sampling techniques such as 2k Factorial designs, Central composite design, A-Optimal design, I-Optimal, D-Optimal, Taguchi’s orthogonal array design, Box-Behnken design, Latin hypercube sampling, sobol sequence are illustrated. Statistical analysis of the first three natural frequencies is presented to compare the results and its performance.

Keywords: composite plate, natural frequency, polynomial regression model, sampling technique, uncertainty quantification

Procedia PDF Downloads 476

Authors: Wojciech Sas, Emil Soból, Katarzyna Gabryś, Andrzej Głuchowski, Alojzy Szymański

Abstract:

Depleting of natural resources is forcing the man to look for alternative construction materials. One of them is recycled concrete aggregates (RCA). RCA from the demolition of buildings and crushed to proper gradation can be a very good replacement for natural unbound granular aggregates, gravels or sands. Physical and the mechanical properties of RCA are well known in the field of basic civil engineering applications, but to proper roads and railways design dynamic characteristic is need as well. To know maximum shear modulus (GMAX) and the minimum damping ratio (DMIN) of the RCA dynamic loads in resonant column apparatus need to be performed. The paper will contain literature revive about alternative construction materials and dynamic laboratory research technique. The article will focus on dynamic properties of RCA, but early studies conducted by the authors on physical and mechanical properties of this material also will be presented. The authors will show maximum shear modulus and minimum damping ratio. Shear modulus and damping ratio degradation curves will be shown as well. From exhibited results conclusion will be drawn at the end of the article.

Keywords: recycled concrete aggregate, shear modulus, damping ratio, resonant column

Procedia PDF Downloads 364

Authors: Kai Zhang, Xi Jiang

Abstract:

Effect of fuel variabilities on premixed combustion of bio-syngas mixtures is of great importance in bio-syngas utilisation. The uncertainties of concentrations of fuel constituents such as H2, CO and CH4 may lead to unpredictable combustion performances, combustion instabilities and hot spots which may deteriorate and damage the combustion hardware. Numerical modelling and simulations can assist in understanding the behaviour of bio-syngas combustion with pre-defined species concentrations, while the evaluation of variabilities of concentrations is expensive. To be more specific, questions such as ‘what is the burning velocity of bio-syngas at specific equivalence ratio?’ have been answered either experimentally or numerically, while questions such as ‘what is the likelihood of burning velocity when precise concentrations of bio-syngas compositions are unknown, but the concentration ranges are pre-described?’ have not yet been answered. Uncertainty quantification (UQ) methods can be used to tackle such questions and assess the effects of fuel compositions. An efficient probabilistic UQ method based on Polynomial Chaos Expansion (PCE) techniques is employed in this study. The method relies on representing random variables (combustion performances) with orthogonal polynomials such as Legendre or Gaussian polynomials. The constructed PCE via Galerkin Projection provides easy access to global sensitivities such as main, joint and total Sobol indices. In this study, impacts of fuel compositions on combustion (adiabatic flame temperature and laminar flame speed) of bio-syngas fuel mixtures are presented invoking this PCE technique at several equivalence ratios. High-pressure effects on bio-syngas combustion instability are obtained using detailed chemical mechanism - the San Diego Mechanism. Guidance on reducing combustion instability from upstream biomass gasification process is provided by quantifying the significant contributions of composition variations to variance of physicochemical properties of bio-syngas combustion. It was found that flame speed is very sensitive to hydrogen variability in bio-syngas, and reducing hydrogen uncertainty from upstream biomass gasification processes can greatly reduce bio-syngas combustion instability. Variation of methane concentration, although thought to be important, has limited impacts on laminar flame instabilities especially for lean combustion. Further studies on the UQ of percentage concentration of hydrogen in bio-syngas can be conducted to guide the safer use of bio-syngas.

Keywords: bio-syngas combustion, clean energy utilisation, fuel variability, PCE, targeted uncertainty reduction, uncertainty quantification

Procedia PDF Downloads 245

Authors: Utkarsh A. Mishra, Ankit Bansal

Abstract:

At high temperature, radiative heat transfer is the dominant mode of heat transfer. It is governed by various phenomena such as photon emission, absorption, and scattering. The solution of the governing integrodifferential equation of radiative transfer is a complex process, more when the effect of participating medium and wavelength properties are taken into consideration. Although a generic formulation of such radiative transport problem can be modeled for a wide variety of problems with non-gray, non-diffusive surfaces, there is always a trade-off between simplicity and accuracy of the problem. Recently, solutions of complicated mathematical problems with statistical methods based on randomization of naturally occurring phenomena have gained significant importance. Photon bundles with discrete energy can be replicated with random numbers describing the emission, absorption, and scattering processes. Photon Monte Carlo (PMC) is a simple, yet powerful technique, to solve radiative transfer problems in complicated geometries with arbitrary participating medium. The method, on the one hand, increases the accuracy of estimation, and on the other hand, increases the computational cost. The participating media -generally a gas, such as CO₂, CO, and H₂O- present complex emission and absorption spectra. To model the emission/absorption accurately with random numbers requires a weighted sampling as different sections of the spectrum carries different importance. Importance sampling (IS) was implemented to sample random photon of arbitrary wavelength, and the sampled data provided unbiased training of MC estimators for better results. A better replacement to uniform random numbers is using deterministic, quasi-random sequences. Halton, Sobol, and Faure Low-Discrepancy Sequences are used in this study. They possess better space-filling performance than the uniform random number generator and gives rise to a low variance, stable Quasi-Monte Carlo (QMC) estimators with faster convergence. An optimal supervised learning scheme was further considered to reduce the computation costs of the PMC simulation. A one-dimensional plane-parallel slab problem with participating media was formulated. The history of some randomly sampled photon bundles is recorded to train an Artificial Neural Network (ANN), back-propagation model. The flux was calculated using the standard quasi PMC and was considered to be the training target. Results obtained with the proposed model for the one-dimensional problem are compared with the exact analytical and PMC model with the Line by Line (LBL) spectral model. The approximate variance obtained was around 3.14%. Results were analyzed with respect to time and the total flux in both cases. A significant reduction in variance as well a faster rate of convergence was observed in the case of the QMC method over the standard PMC method. However, the results obtained with the ANN method resulted in greater variance (around 25-28%) as compared to the other cases. There is a great scope of machine learning models to help in further reduction of computation cost once trained successfully. Multiple ways of selecting the input data as well as various architectures will be tried such that the concerned environment can be fully addressed to the ANN model. Better results can be achieved in this unexplored domain.

Keywords: radiative heat transfer, Monte Carlo Method, pseudo-random numbers, low discrepancy sequences, artificial neural networks

Procedia PDF Downloads 181