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Combining the advantages of discrete-and continuous-time scheduling models: Part 3. General algorithm

COMPUTERS & CHEMICAL ENGINEERING 2020年 139卷 106848-106848页

作者： Lee, Hojae Maravelias, Christos T. Univ Wisconsin Dept Chem & Biol Engn 1415 Engn Dr Madison WI 53706 USA

One of the main challenges in applying optimization-based scheduling techniques in process industries stems from the different process characteristics and constraints that need to be taken into account when generating a schedule. For instance, consideration of sequence-dependent changeovers may easily make the resulting optimization model computationally expensive. Accordingly, building upon the recently pro-posed Discrete-Continuous algorithm (Lee and Maravelias, 2018), we propose generalized algorithm that enables accurate and fast solution of difficult instances while efficiently handling a wide range of process characteristics. The algorithm combines modeling versatility with computational tractability while guar-anteeing the feasibility and accuracy of the final solution. Through a case study inspired by a real-world brewing process, we show that our algorithm provides accurate and high quality solutions to industrial-scale instances in reasonable time. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Chemical production scheduling solution algorithm Mixed-integer programming Process operations

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A customer selection and vehicle scheduling model for moving companies

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TRANSPORTATION LETTERS-THE INTERNATIONAL JOURNAL OF TRANSPORTATION RESEARCH 2020年第9期12卷 613-622页

作者： Yan, Shangyao Chu, James C. Hung, Wei-Che Natl Cent Univ Dept Civil Engn Taoyuan Taiwan Natl Taiwan Univ Dept Civil Engn 1 Roosevelt Rd Taipei 106 Taiwan

This study develops a model for customer selection and vehicle scheduling with time windows for moving companies. To reflect the actual operations of moving companies, the proposed model employs two major processes to extend the traditional vehicle routing models. First, loading and unloading activities of moving vehicles are explicitly modeled using the technique of time-space networks. Second, moving companies are flexible in selecting customers, thereby possibly maximizing the profit of companies. The model is formulated as an integer multi-commodity network with side constraints. A decomposition-based solution algorithm is developed to solve the problem efficiently. Results of a case study indicate that the proposed methodology efficiently generates reasonable plans of customer selection and vehicle scheduling. Sensitivity analysis shows that the proposed model properly responds to the change in critical parameters. Therefore, the proposed methodology has a strong potential to improve the operations and profitability of moving companies.

关键词： Moving company time-space network multi-commodity network flow model solution algorithm

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Complete-search Tensor Contractions for Optimizing High-order Methods

Complete-search Tensor Contractions for Optimizing High-orde...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： You, Hojun Kim, Chongam Seoul Natl Univ Dept Mech & Aerosp Engn Seoul 08826 South Korea Seoul Natl Univ Dept Mech & Aerosp Engn Inst Adv Aerosp Technol Seoul 08826 South Korea

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

A sophisticated solution algorithm with complex data structures is a crucial factor hindering both academia and industry from utilizing high-order methods. At the same time, compact data structures may also provide a wide variety of chances for improving the performance of the solution algorithm via optimization. In order to address this issue, we present an architecture-based and target-oriented optimization algorithm for high-order methods based on complete-search tensor contractions (CsTC). After briefly explaining the general framework of the proposed optimization procedure, CsTC is applied to the discontinuous Galerkin (DG) method. Among various ways to realize tensor contractions (TC), the GEMM (GEneral Matrix Multiplication)-based approach is adopted owing to its flexibility to handle moderate order of TC and the reusability of state-of-the-art GEMM primitives. One distinctive feature of the current optimization procedure is that both an optimized way to compute tensors and optimized index order of the associated tensors are simultaneously considered by not fixing the index order in a priori. The optimization procedure is then converted into an optimization problem to minimize the computational cost, and the optimized TC is inductively found by searching all candidates in search space. The whole process can be done automatically in a few minutes on a computer. The performance enhancement is determined by the mesh and solution parameters to be employed as well as a processor to be used, i.e. the CsTC optimization procedure is completely target-oriented and architecture-based. Various parameters and processors with different micro-architectures are investigated and compared with one another. All results verify that greater performance enhancement can be obtained as the order of the DG approximation increases and a more recent processor is employed. The CsTC optimization algorithm applied to a 3-D sinewave viscous flow governed by the compressible Navier-Stokes

关键词： solution algorithm Navier Stokes Equations Optimization algorithm Unsteady Flows Discontinuous Galerkin Method Tetrahedral Element Aspect Ratio Finite Volume Method Artificial Neural Network Numerical Simulation

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Coupled Discrete Adjoints for Multiphysics in SU2

Coupled Discrete Adjoints for Multiphysics in SU2

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AIAA Aviation Forum

作者： Burghardt, Ole Gaugert, Nicolas R. Gomez, Pedro Palacios, Rafael Kattmann, Tobias Economon, Thomas D. TU Kaiserslautern Chair Sci Comp D-67663 Kaiserslautern Germany Imperial Coll London Dept Aeronaut London SW7 2AZ England Bosch Corp Res Fluid Dynam D-71272 Renningen Germany SU2 Fdn San Francisco CA 94158 USA

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

Many optimization problems in fluid dynamics are naturally constituted in a larger multiphysics setting, the most prominent ones nowadays being fluid-structure interaction and conjugate heat transfer or combinations of them. In the context of partitioned solution approaches, and from a software perspective, this means that two or more solvers are coupled by exchanging data at common physical boundaries during the simulation. Optimization methods relying on discrete adjoint solutions have to consider such couplings in order to give accurate gradients. This article presents a methodology for how coupled multiphysics adjoints can be computed efficiently in a way that is also independent of the choice or configuration of the underlying physical problem. Based on an implementation in SU2 (an open-source multiphysics simulation and design software(1)) we demonstrate how the same algorithm can be applied for shape sensitivity analysis on a conjugate heat transfer as well as a fluid-structure interaction test case.

关键词： Fluid Structure Interaction Conjugate Heat Transfer Pressure Coefficient Sensitivity Analysis Poisson's Ratio solution algorithm Aerodynamic Shape Optimization Incompressible Flow Material Properties Stiffness Matrices

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Solving inverse optimal control problems via value functions to global optimality

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JOURNAL OF GLOBAL OPTIMIZATION 2019年第2期74卷 297-325页

作者： Dempe, Stephan Harder, Felix Mehlitz, Patrick Wachsmuth, Gerd Tech Univ Bergakad Freiberg Fac Math & Comp Sci D-09596 Freiberg Germany Brandenburg Tech Univ Cottbus Senftenberg Chair Optimal Control Inst Math D-03046 Cottbus Germany

In this paper, we show how a special class of inverse optimal control problems of elliptic partial differential equations can be solved globally. Using the optimal value function of the underlying parametric optimal control problem, we transfer the overall hierarchical optimization problem into a nonconvex single-level one. Unfortunately, standard regularity conditions like Robinson's CQ are violated at all the feasible points of this surrogate problem. It is, however, shown that locally optimal solutions of the problem solve a Clarke-stationarity-type system. Moreover, we relax the feasible set of the surrogate problem iteratively by approximating the lower level optimal value function from above by piecewise affine functions. This allows us to compute globally optimal solutions of the original inverse optimal control problem. The global convergence of the resulting algorithm is shown theoretically and illustrated by means of a numerical example.

关键词： Bilevel optimal control Global optimization Inverse optimal control Optimality conditions solution algorithm

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Improved softened membrane model for prestressed composite box girders with corrugated steel webs under pure torsion

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JOURNAL OF CONSTRUCTIONAL STEEL RESEARCH 2019年 153卷 372-384页

作者： Zhou, Cong Li, Lifeng Wang, Lianhua Hunan Univ Coll Civil Engn Changsha 410082 Hunan Peoples R China Hunan Univ Key Lab Wind & Bridge Engn Hunan Prov Changsha 410082 Hunan Peoples R China

In this study, a theoretical model called the improved softened membrane model for torsion (ISMMT) is proposed for evaluating prestressed composite box girders with corrugated steel webs (PCBGCSWs) under pure torsion. First, considering the mechanical properties of PCBGCSWs, a series of equations are derived from equilibrium and compatibility conditions and constitutive relationships of the materials. In the equations, the criteria of shear flow equivalence and shear strain equivalence are adopted to determine the relationships between the concrete flanges and the corrugated steel webs (CSWs) before and after the yielding of the CSWs, respectively. Then, the solution algorithms, including a general algorithm for the entire torsional process and a simplified algorithm for the stage when both steel bars, the prestressing steel and the CSWs are in the elastic state, of the ISMMT are presented to solve all the equations. To validate the feasibility of the proposed theoretical model, the experimental results of a prismatic PCBGCSW under pure torsion available in the literature are selected for comparison. Additionally, a three-dimensional (3D) finite element (FE) model of the specimen is established using ABAQUS software. The results from the theoretical model, including the overall torque-twist curve, shear strain in the CSWs and strains in the prestressing steels and steel bars, are compared with those from the FE model and the experiment The theoretical, numerical and experimental results are in good agreement, demonstrating that the proposed analytical model accurately predicts the torsional behaviour of the PCBGCSWs under pure torsion, including the torsional behaviour during the pre- and post-cracking stages. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Prestressed composite box girders with corrugated steel webs Pure torsion Theoretical model Softened membrane model solution algorithm Finite element analysis

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Newton-Krylov Solver for Robust Turbomachinery Aerodynamic Analysis

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AIAA JOURNAL 2020年第3期58卷 1320-1336页

作者： Xu, Shenren Mohanamuraly, Pavanakumar Wang, Dingxi Mueller, Jens-Dominik Northwestern Polytech Univ Yangtze River Delta Res Inst Taicang 215400 Peoples R China Queen Mary Univ London Sch Engn & Mat Sci London E1 4NS England Shaanxi Key Lab Internal Aerodynam Aeroengines Sch Power & Energy 1 Dongxiang Rd Xian 710072 Peoples R China Shaanxi Key Lab Internal Aerodynam Aeroengines 1 Dongxiang Rd Xian 710072 Peoples R China

Steady computational fluid dynamics solvers based on the Reynolds-averaged Navier-Stokes equations are the primary workhorses for turbomachinery aerodynamic analysis due to their good engineering accuracy at a low computational cost. However, even state-of-the-art steady solvers suffer from convergence slowdown or failure when applied to challenging off-design conditions. This severely limits the reliable nonlinear and linearized turbomachinery aerodynamic analysis over a wide operating range. To alleviate the convergence difficulties, a nonlinear flow solver using the Newton-Krylov method is developed. This is the first time the Newton-Krylov algorithm is used for achieving robust analysis of turbomachinery aerodynamics in the open literature. The proposed solution algorithm features 1) the exact Jacobian matrix forming, 2) straightforward parallelization, and 3) a reliable globalization strategy;and it aims to achieve fast machine-zero convergence. The solver accuracy is validated using four test cases: an airfoil, a linear turbine cascade, a centrifugal compressor, and an axial compressor. Machine-zero convergence is achieved for all cases over a wide range of operating conditions without manual intervention. The method shows great potential for enabling an automated and reliable whole-map turbomachinery aerodynamic analysis, and it paves the way for a robust and efficient linearized aerodynamic analysis, such as adjoint, time-linearized, and eigenvalue analyses.

关键词： Turbomachinery Reynolds Averaged Navier Stokes Courant Friedrichs Lewy Airfoil Centrifugal Compressor Aerodynamics solution algorithm Message Passing Interface Flow Conditions Conductivity Coefficients

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Interpretation of Experimental Tensile Test Results and Its Implication on Damage Modeling

Interpretation of Experimental Tensile Test Results and Its ...

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AIAA Science and Technology (SciTech) Forum and Exposition

作者： Arnold, Steven M. Lerch, Bradley A. Ricks, Trenton M. NASA Glenn Res Ctr Multiscale Modeling Mat & Struct Div Cleveland OH 44135 USA NASA Glenn Res Ctr Mat & Struct Div Cleveland OH 44135 USA

ISBN: (数字)9781624105784

ISBN: (纸本)9781624105784

To improve prognostics for predicting component life, coupon tests were conducted on Ti-6Al-4V to investigate the development of damage. Various test types were employed (tension, creep, stress relaxation and fatigue) under a wide range of temperatures and loading rates to engage various amounts of time-dependent and damage behavior. Both stiffness degradation and Poisson's ratio were monitored to see if they were useful in indicating the initiation and accumulation of damage and subsequently the onset of failure. Stiffness exhibited large decreases with increasing strain when calculated using engineering stress and strain. However, minimal stiffness change was observed when using the true stress and strain values. Poisson's ratio was monitored on every test and showed promise as a damage indicator. However, calculation of Poisson's ratio was found to be more involved than expected;due to anisotropy and the presence of strain gradients along the specimen at large applied strains. First, the material had a moderate texture and resulted in anisotropy of the strains. Second, the evolution of instantaneous Poisson's ratio as a function of axial strain showed strange and unexpected behaviors, which necessitated a more extensive analysis of its development. This led to a discussion on the use of small versus large strain approaches and the importance of making consistent measurements, i.e. axial and transverse strain measurements over the same volume of material. Additionally, finite element analysis of a tensile sample indicated that non-uniform strain occurred in the sample prior to attaining the maximum strength. This coupled with the location at which transverse strain was measured had a significant influence on the resulting values of instantaneous Poisson's ratio.

关键词： Tensile Tests Ultimate Tensile Strength Temperature Stresses Finite Element Analysis Ti 6Al 4V Extensometer Viscoplasticity Compressibility Effect Catastrophic Failure solution algorithm

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Toward a Pseudo-Time Accurate Formulation of the Adjoint and Tangent Systems

Toward a Pseudo-Time Accurate Formulation of the Adjoint and...

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AIAA Science and Technology (SciTech) Forum and Exposition

作者： Padway, Emmett Mavriplis, Dimitri Univ Wyoming Dept Mech Engn Laramie WY 82071 USA

ISBN: (数字)9781624105784

ISBN: (纸本)9781624105784

This paper presents efforts to better compute sensitivities using adjoint and tangent systems for primal problems with partial or incomplete convergence. First we apply the unsteady adjoint to the steady equations to obtain a pseudo-time accurate formulation of the tangent and adjoint systems. This approach is demonstrated for the tangent and adjoint systems for three different solution algorithms: forward Euler and 5-stage Runge-Kutta pseudo-time evolution, and a quasi-Newton method. Proofs for the forward Euler and quasi-Newton method systems are shown. Those for the 5-stage Runge-Kutta scheme are found in the Appendix. Verification results for the derived schemes are shown followed by three test cases. The first test case compares results of the steady-state adjoint to the pseudo-time accurate formulation, showing magnitude differences and evaluating the angle between the two computed sensitivity vectors. The second case compares the steady-state method to the pseudo-time accurate formulation in a subsonic case for a non-converging primal problem. This case shows that while averaging the state decreases the angle between the two vectors, there are still significant magnitude differences between the vectors. The final test case is a transonic case with a non-converging primal and shows that the sensitivity vector computed from an averaged state still has a significant angle difference with the vector computed from the pseudo-time accurate result. Finally, an investigation into the effect of averaging the pseudo-time accurate adjoint computes sensitivities is presented.

关键词： Adaptive Mesh Refinement solution algorithm Computational Fluid Dynamics Multidisciplinary Design Optimization Finite Difference Method Triangular Element Drag Coefficient Stiffness Matrices Lift Coefficient Euler Equations

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Investigation of a Local Correlation-based Transition Model in a Newton-Krylov algorithm

Investigation of a Local Correlation-based Transition Model ...

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AIAA Science and Technology (SciTech) Forum and Exposition

作者： Piotrowski, Michael G. H. Zingg, David W. Univ Toronto Inst Aerosp Studies Toronto ON M3H 5T6 Canada NASA Ames Res Ctr Moffett Field CA 94035 USA

ISBN: (数字)9781624105784

ISBN: (纸本)9781624105784

A fully-coupled, implicit Newton-Krylov algorithm with laminar-turbulent boundary-layer transition prediction capabilities for three-dimensional external aerodynamic flows has been developed. The gamma-(R) over tildee(theta t) Local Correlation-Based Transition Model with helicity-based crossflow correlations is modified and fully coupled to the Spalart-Allmaras turbulence model in a parallel Newton-Krylov-Schur flow solver. Deep convergence is obtained using an efficient pseudo-transient continuation time marching strategy, consisting of an approximate-Newton phase followed by an inexact-Newton phase, with source-term time stepping and exponential penalty functions used to address the strong sources and non-smooth functions introduced by the transition model. A modification to the Flength function is introduced to improve the numerical convergence behaviour of the model. The current implementation is validated using two- and three-dimensional transition test cases, with the results obtained using the modified transition model comparing well with experiment. The elimination of discontinuities in the transition model makes it a suitable candidate for gradient-based shape optimization algorithms.

关键词： solution algorithm Natural Laminar Flow Spalart Allmaras Turbulence Model Laminar Turbulent Transition Optimization algorithm Angle of Attack Reynolds Averaged Navier Stokes Aerodynamic Shape Optimization Swept Wing Free Stream Turbulence

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