An Improved Stochastic Upscaling Method for Multiscale Engineering Systems

2014 ◽  
Author(s):  
Recep M. Gorguluarslan ◽  
Seung-Kyum Choi
Keyword(s):  
Structural Engineering ◽  
Optimization Procedure ◽  
Scale Model ◽  
Fine Scale ◽  
Engineering Systems ◽  
Coarse Scale ◽  
Design Problems ◽  
Scale Parameters ◽  
Engineering Design Problems ◽  
Generalized Polynomial

A stochastic multiscale modeling technique is proposed to construct coarse scale representation of a fine scale model for use in engineering design problems. The complexity of the fine scale heterogeneity under uncertainty is replaced with the homogenized coarse scale parameters by seeking agreement between the responses at both scales. Generalized polynomial chaos expansion is implemented to reduce the dimensionality of propagating uncertainty through scales and the computational costs of the upscaling method. It is integrated into a hybrid optimization procedure with the genetic algorithm and sequential quadratic programming. Two structural engineering problems that involve uncertainties in elastic material properties and geometric properties at fine scales are presented to demonstrate the applicability and merit of the proposed technique.

A Set-Based System for Eliminating Infeasible Designs in Engineering Problems Dominated by Uncertainty

1997 ◽  
Author(s):  
William W. Finch ◽  
Allen C. Ward
Keyword(s):  
Electronic Circuit ◽  
Predicate Logic ◽  
Software Tool ◽  
Design Parameters ◽  
Engineering Systems ◽  
Multiple Sources ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Engineering Problems ◽  
Prototype Software

Abstract This paper gives an overview of a system which eliminates infeasible designs from engineering design problems dominated by multiple sources of uncertainty. It outlines methods for representing constraints on sets of values for design parameters using quantified relations, a special class of predicate logic expressions which express some of the causal information inherent in engineering systems. The paper extends constraint satisfaction techniques and describes elimination algorithms that operate on quantified relations and catalogs of toleranced or adjustable parts. It demonstrates the utility of these tools on a simple electronic circuit, and describes their implementation and test in a prototype software tool.

scholarly journals Optimal Solution of Structural Engineering Design Problems using Crow Search Algorithm

2019 ◽  
Vol 4 (4) ◽  
pp. 968-981
Author(s):  
Madhur Agarwal
Keyword(s):  
Engineering Design ◽  
Design Problem ◽  
Structural Engineering ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Worst Case ◽  
Design Problems ◽  
Beam Design ◽  
Engineering Design Problems ◽  
Better Than

In real world, the structural engineering design problems are large scale non-linear constrained problems. In the present study, crow search algorithm (CSA) is applied to find the optimal solution of structural engineering design problems such as pressure vessel design problem, welded beam design problem and tension/ compression string design problem. The numerical results are compared with the existing results reported in the literature including metaheuristic algorithms and it is found that the results obtained by the crow search algorithm are better than other existing algorithms. Further, the effectiveness of the algorithm is verified to be better than the existing algorithms by statistical analysis using mean, median, best case, and worst case scenarios. The present study confirms that the crow search algorithm may be easily and effectively applied to various structural design problems.

Quantified Relations: A Class of Predicate Logic Design Constraints Among Sets of Manufacturing, Operating, and Other Variations

1996 ◽  
Author(s):  
William W. Finch ◽  
Allen C. Ward
Keyword(s):  
Engineering Design ◽  
Predicate Logic ◽  
Operating Conditions ◽  
Causal Relationships ◽  
Engineering Systems ◽  
Multiple Sources ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Computing Effort ◽  
And Performance

Abstract This paper addresses a class of engineering design problems in which multiple sources of variations affect a product’s design, manufacture, and performance. Examples of these sources include uncertainty in nominal dimensions, variations in manufacture, changing environmental or operating conditions, and operator adjustments. Quantified relations (QR’s) are defined as a class of predicate logic expressions representing constraints between sets of design variations. Within QR’s, each variable’s quantifier and the order of quantification express a physical system’s causal relationships. This paper also presents an algorithm which propagates intervals through QR’s involving continuous, monotonic equations. Causal relationships between variables in engineering systems are discussed, and a tabular representation for them is presented. This work aims to broaden the application of automated constraint satisfaction algorithms, shortening design cycles for this class of problem by reducing modeling, and possibly computing effort. It seems to subsume Ward’s prior work on the Label Interval Calculus, extending the approach to a wider range of engineering design problems.

Analytical Upgridding Method To Preserve Dynamic Flow Behavior

2010 ◽  
Vol 13 (03) ◽  
pp. 473-484 ◽  
Author(s):  
Seyyed Abolfazl Hosseini ◽  
Mohan Kelkar
Keyword(s):  
Single Phase ◽  
Flow Behavior ◽  
Pressure Profile ◽  
Scale Model ◽  
Optimum Number ◽  
Fine Scale ◽  
Coarse Scale ◽  
Flow Process ◽  
Number Of Layers ◽  
Pressure Profiles

Summary A geocellular model contains millions of gridblocks and needs to be upscaled before the model can be used as an input for flow simulation. Available techniques for upgridding vary from simple methods such as proportional fractioning to more complicated methods such as maintaining heterogeneities through variance calculations. All these methods are independent of the flow process for which simulation is going to be used, and are independent of well configuration. We propose a new upgridding method that preserves the pressure profile at the upscaled level. It is well established that the more complex the flow process, the more detailed the level of heterogeneity needed in the simulation model. In general, ideal upscaling is the process that preserves the "pressure profile" from the fine-scale model under the applicable flow process. In our method, we upgrid the geological model using simple flow equations in porous media. However, it should be remembered that to obtain a better match between fine scale and coarse scale, we also need to use appropriate upscaling of the reservoir properties. The new method is currently developed for single-phase flow; however, we used it for both single-phase and two-phase flows for 2D and 3D cases. The method differs fundamentally from the other methods that try to preserve heterogeneities. In those methods, gridblocks are combined that have similar velocities (or other properties) by assuming constant pressure drop across the blocks. Instead, we combine the gridblocks that have similar pressure profiles, although to release some of our assumptions such as having constant velocities in gridblocks, we balance our equation with the K2 term. The procedure is analytical and, hence, very efficient, but preserves the pressure profile in the reservoir. The gridblocks (or layers) are combined in a way so that the difference between fine- and coarse-scale pressure profiles is minimized. In addition, we also propose two new criteria that allow us to choose the optimum number of layers more accurately so that a critical level of heterogeneity is preserved. These criteria provide insight into the overall level of heterogeneity in the reservoir and the effectiveness of the layering design. We compare the results of our method with proportional layering and the King et al. method (King et al. 2006) and show that, for the same number of layers, the proposed method captures the results of the fine-scale model better. We show that the layer merging not only depends on the variation in the permeability between the gridblocks (K2 term), but also on the relative magnitude of the permeability values by combining 1/K2 and K2 terms.

Two-Stage Upscaling of Two-Phase Flow: From Core to Simulation Scale

SPE Journal ◽  
2006 ◽  
Vol 11 (03) ◽  
pp. 304-316 ◽  
Author(s):  
Arild Lohne ◽  
George A. Virnovsky ◽  
Louis J. Durlofsky
Keyword(s):  
Capillary Pressure ◽  
Effective Properties ◽  
Absolute Permeability ◽  
Scale Model ◽  
Phase Flow ◽  
Fine Scale ◽  
Coarse Scale ◽  
Two Stage ◽  
Two Phase ◽  
Rate Dependent

Summary In the coarse-scale simulation of heterogeneous reservoirs, effective or upscaled flow functions (e.g., oil and water relative permeability and capillary pressure) can be used to represent heterogeneities at subgrid scales. The effective relative permeability is typically upscaled along with absolute permeability from a geocellular model. However, if no subgeocellular-scale information is included, the potentially important effects of smaller-scale heterogeneities (on the centimeter to meter scale) in both capillarity and absolute permeability will not be captured by this approach. In this paper, we present a two-stage upscaling procedure for two-phase flow. In the first stage, we upscale from the core (fine) scale to the geocellular (intermediate) scale, while in the second stage we upscale from the geocellular scale to the simulation (coarse) scale. The computational procedure includes numerical solution of the finite-difference equations describing steady-state flow over the local region to be upscaled, using either constant pressure or periodic boundary conditions. In contrast to most of the earlier investigations in this area, we first apply an iterative rate-dependent upscaling (iteration ensures that the properties are computed at the appropriate pressure gradient) rather than assume viscous or capillary dominance and, second, assess the accuracy of the two-stage upscaling procedure through comparison of flow results for the coarsened models against those of the finest-scale model. The two-stage method is applied to synthetic 2D reservoir models with strong variation in capillarity on the fine scale. Accurate reproduction of the fine-grid solutions (simulated on 500'500 grids) is achieved on coarse grids of 10'10 for different flow scenarios. It is shown that, although capillary forces are important on the fine scale, the assumption of capillary dominance in the first stage of upscaling is not always appropriate, and that the computation of rate-dependent effective properties in the upscaling can significantly improve the accuracy of the coarse-scale model. The assumption of viscous dominance in the second upscaling stage is found to be appropriate in all of the cases considered. Introduction Because of computational costs, field-simulation models may have very coarse cells with sizes up to 100 to 200 m in horizontal directions. The cells are typically populated with effective properties (porosity, absolute permeability, relative permeabilities, and capillary pressure) upscaled from a geocellular (or geostatistical) model. In this way, the effects of heterogeneity on the geocellular scale will be included in the large-scale flow calculations. The cell sizes in geocellular models may be on the order of 20 to 50 m in horizontal directions. However, heterogeneities on much smaller scales (cm- to m- scale) may have a significant influence on the reservoir flow (Coll et al. 2001; Honarpour et al. 1994), and this potential effect cannot be captured if the upscaling starts at the geocellular scale.

scholarly journals Low-speed airfoil optimization using constrained differential evolution

2020 ◽  
Vol 12 (4) ◽  
pp. 83-94
Author(s):  
Mihai-Vladut HOTHAZIE ◽  
Matei MIRICA
Keyword(s):  
Evolutionary Algorithm ◽  
Lift Coefficient ◽  
Optimization Procedure ◽  
Aerodynamic Performance ◽  
Optimum Shape ◽  
Design Problems ◽  
Airfoil Optimization ◽  
Engineering Design Problems ◽  
Wide Range ◽  
Differential Evolutionary Algorithm

Nowadays, algorithms designed to optimize the shape of an airfoil are being developed by many researchers. In this paper, to achieve an optimum shape configuration, a methodology based on an evolutionary algorithm is proposed. The main objective is to find the optimum shape of a known airfoil that gives the best aerodynamic performance for a fixed lift coefficient. For the airfoil parametrization, the class-shape method is used to develop a well-behaved geometry. The paper underlines the implementation of a constrained differential evolutionary algorithm using the free penalty scheme by varying the coefficients of the shape parametrization function. The aim is to obtain a better aerodynamic performance for a predetermined lift coefficient by imposing a fixed maximum airfoil thickness interval. The method is a general optimization procedure and can be implemented in a wide range of engineering design problems.

scholarly journals Integrating coarse-scale uncertain soil moisture data into a fine-scale hydrological modelling scenario

2011 ◽  
Vol 8 (3) ◽  
pp. 6031-6067
Author(s):  
H. Vernieuwe ◽  
B. De Baets ◽  
J. Minet ◽  
V. R. N. Pauwels ◽  
S. Lambot ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Moisture Content ◽  
Soil Moisture Content ◽  
Epistemic Uncertainty ◽  
Hydrological Modelling ◽  
Scale Model ◽  
Fine Scale ◽  
Coarse Scale ◽  
Soil Moisture Data ◽  
External Data

Abstract. In a hydrological modelling scenario, often the modeller is confronted with external data, such as remotely-sensed soil moisture observations, that become available to update the model output. However, the scale triplet (spacing, extent and support) of these data is often inconsistent with that of the model. Furthermore, the external data can be cursed with epistemic uncertainty. Hence, a method is needed that not only integrates the external data into the model, but that also takes into account the difference in scale and the uncertainty of the observations. In this paper, a synthetic hydrological modelling scenario is set up in which a high-resolution distributed hydrological model is run over an agricultural field. At regular time steps, coarse-scale field-averaged soil moisture data, described by means of possibility distributions (epistemic uncertainty), are retrieved by synthetic aperture radar and assimilated into the model. A method is presented that allows to integrate the coarse-scale possibility distribution of soil moisture content data with the fine-scale model-based soil moisture data. To this end, a scaling relationship between field-averaged soil moisture content data and its corresponding standard deviation is employed.

Substituting of a Thermodynamic Simulation with a Metamodel in the Scope of Multiscale Modelling

2016 ◽  
Vol 879 ◽  
pp. 1207-1212 ◽  
Author(s):  
Piotr Macioł ◽  
Danuta Szeliga ◽  
Łukasz Sztangret
Keyword(s):  
Thermodynamic Simulation ◽  
Multiscale Simulation ◽  
Scale Model ◽  
Precipitation Kinetic ◽  
Fine Scale ◽  
Coarse Scale ◽  
Computational Point ◽  
Computing Power ◽  
Thermodynamic Computations ◽  
Scale Models

A typical multiscale simulation consists of numerous fine scale models, usually one for each computational point of a coarse scale model. One of possible ways of limiting computing power requirements is replacing fine scale models with some simplified and speeded up ersatz ones. In this paper, the authors attempt to develop a metamodel, replacing direct thermodynamic computations of precipitation kinetic with an advanced approximating model. MatCalc simulator has been used for thermodynamic modelling of precipitation kinetic. Typical heat treatment of P91 steel grade was examined. Selected variables were chosen to be modelled with approximating models. Several attempts with various approximation variants (interpolation algorithms and Artificial Neural Networks) have been investigated and its comparison is included in the paper.

Adaptive Local-Global Multiscale Simulation of the In-situ Conversion Process

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 2112-2127 ◽  
Author(s):  
Faruk O. Alpak ◽  
Jeroen C. Vink
Keyword(s):  
Injection Rate ◽  
Multiscale Method ◽  
Scale Model ◽  
Fine Scale ◽  
Coarse Scale ◽  
Scale Models ◽  
Pattern Scale ◽  
Heat Injection ◽  
Coarse Grids

Summary Numerical modeling of the in-situ conversion process (ICP) is a challenging endeavor involving thermal multiphase flow, compositional pressure/volume/temperature (PVT) behavior, and chemical reactions that convert solid kerogen into light hydrocarbons and are tightly coupled to temperature propagation. Our investigations of grid-resolution effects on the accuracy and performance of ICP simulations demonstrated that ICP-simulation outcomes (e.g., oil/gas production rates and cumulative volumes) may exhibit relatively large errors on coarse grids, where “coarse” means a gridblock size of more than 3 to 5 m. On the other hand, coarse-scale models are attractive because they deliver favorable computational performance, especially for optimization and uncertainty quantification workflows that demand a large number of simulations. Furthermore, field-scale models become unmanageably large if gridblock sizes of 3 to 5 m or less have to be used. Therefore, there is a clear business need to accelerate the ICP simulations with minimal compromise of accuracy. We developed a novel multiscale-modeling method for ICP that reduces numerical-modeling errors and approximates the fine-scale simulation results on relatively coarse grids. The method uses a two-scale adaptive local-global solution technique. One global coarse-scale and multiple local fine-scale near-heater models are timestepped in a sequentially coupled fashion. At a given global timestep, the global-model solution provides accurate boundary conditions to the local near-heater models. These boundary conditions account for the global characteristics of the thermal-reactive flow and transport phenomena. In turn, fine-scale information about heater responses is upscaled from the local models, and used in the global coarse-scale model. These flow-based effective properties correct the thermal-reactive flow and transport in the global model either explicitly, by updating relevant coarse-grid properties for the next timestep, or implicitly, by repeatedly updating the properties through a convergent iterative scheme. Upon convergence, global coarse-scale and local fine-scale solutions are compatible with each other. We demonstrate the much-improved accuracy and efficiency delivered by the multiscale method by use of a 2D cross-section pattern-scale ICP simulation problem. The following conclusions are reached through numerical testing: (1) The multiscale method significantly improves the accuracy of the simulation results over conventionally upscaled models. The method is particularly effective in correcting the global coarse-scale model through the use of the fine-scale information about heater temperatures to regulate the heat-injection rate into the formation more accurately. The effective coarse-grid properties computed by the multiscale method at every timestep also enhance the accuracy of the ICP simulations, as demonstrated in a dedicated test case, in which a constant heat-injection rate is enforced across models of all investigated resolutions. (2) Multiscale ICP models result in accelerated simulations with a speed-up of four to 16 times with respect to fine-scale models “out of the box” without any special optimization effort. (3) Our multiscale method delivers high-resolution solutions in the vicinity of the heaters at a reduced computational cost. These fine-scale solutions can be used to better understand the evolution of the fluids and solids (e.g., kerogen conversion and coke deposition) in the vicinity of the heaters (several-feet-long spatial scale). Simultaneously, with the fine-scale near-heater solutions, the local-global coupled multiscale model provides key commercial ICP performance indicators at the pattern scale (several-hundred-feet-long spatial scale) such as production functions.

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