The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Piotr Fedelinski - One of the best experts on this subject based on the ideXlab platform.
-
Boundary elements in shape design sensitivity analysis and optimal design of vibrating structures
Engineering Analysis With Boundary Elements, 1991Co-Authors: Tadeusz Burczyński, Piotr FedelinskiAbstract:Abstract A general approach to shape design sensitivity analysis and optimal design for dynamic transient and free vibrations problems using boundary elements is presented. The material derivatives and the Adjoint System method are applied to obtain first-order sensitivities for the effect of boundary shape variations. A numerical example of shape sensitivity analysis and optimal design for free vibrations of an elastic body is presented.
William W. Hager - One of the best experts on this subject based on the ideXlab platform.
-
Modified Legendre–Gauss–Radau Collocation Method for Optimal Control Problems with Nonsmooth Solutions
Journal of Optimization Theory and Applications, 2021Co-Authors: Joseph D. Eide, William W. Hager, Anil V. RaoAbstract:A new method is developed for solving optimal control problems whose solutions are nonsmooth. The method developed in this paper employs a modified form of the Legendre–Gauss–Radau orthogonal direct collocation method. This modified Legendre–Gauss–Radau method adds two variables and two constraints at the end of a mesh interval when compared with a previously developed standard Legendre–Gauss–Radau collocation method. The two additional variables are the time at the interface between two mesh intervals and the control at the end of each mesh interval. The two additional constraints are a collocation condition for those differential equations that depend upon the control and an inequality constraint on the control at the endpoint of each mesh interval. The additional constraints modify the search space of the nonlinear programming problem such that an accurate approximation to the location of the nonsmoothness is obtained. The transformed Adjoint System of the modified Legendre–Gauss–Radau method is then developed. Using this transformed Adjoint System, a method is developed to transform the Lagrange multipliers of the nonlinear programming problem to the costate of the optimal control problem. Furthermore, it is shown that the costate estimate satisfies one of the Weierstrass–Erdmann optimality conditions. Finally, the method developed in this paper is demonstrated on an example whose solution is nonsmooth.
-
Modified Radau Collocation Method for Solving Optimal Control Problems with Nonsmooth Solutions Part II: Costate Estimation and the Transformed Adjoint System
2018 IEEE Conference on Decision and Control (CDC), 2018Co-Authors: Joseph D. Eide, William W. HagerAbstract:A modified Legendre-Gauss-Radau collocation method is developed for solving optimal control problems whose solutions contain a nonsmooth optimal control. The method includes an additional variable that defines the location of nonsmoothness. In addition, collocation constraints are added at the end of a mesh interval that defines the location of nonsmoothness in the solution on each differential equation that is a function of control along with a control constraint at the endpoint of this same mesh interval. The transformed Adjoint System for the modified Legendre-Gauss-Radau collocation method along with a relationship between the Lagrange multipliers of the nonlinear programming problem and a discrete approximation of the costate of the optimal control problem is then derived. Finally, it is shown via example that the new method provides an accurate approximation of the costate.
-
CDC - Modified Radau Collocation Method for Solving Optimal Control Problems with Nonsmooth Solutions Part II: Costate Estimation and the Transformed Adjoint System
2018 IEEE Conference on Decision and Control (CDC), 2018Co-Authors: Joseph D. Eide, William W. Hager, Anil V. RaoAbstract:A modified Legendre-Gauss-Radau collocation method is developed for solving optimal control problems whose solutions contain a nonsmooth optimal control. The method includes an additional variable that defines the location of nonsmoothness. In addition, collocation constraints are added at the end of a mesh interval that defines the location of nonsmoothness in the solution on each differential equation that is a function of control along with a control constraint at the endpoint of this same mesh interval. The transformed Adjoint System for the modified Legendre-Gauss-Radau collocation method along with a relationship between the Lagrange multipliers of the nonlinear programming problem and a discrete approximation of the costate of the optimal control problem is then derived. Finally, it is shown via example that the new method provides an accurate approximation of the costate.
-
runge kutta methods in optimal control and the transformed Adjoint System
Numerische Mathematik, 2000Co-Authors: William W. HagerAbstract:The convergence rate is determined for Runge-Kutta discretizations of nonlinear control problems. The analysis utilizes a connection between the Kuhn-Tucker multipliers for the discrete problem and the Adjoint variables associated with the continuous minimum principle. This connection can also be exploited in numerical solution techniques that require the gradient of the discrete cost function.
Tadeusz Burczyński - One of the best experts on this subject based on the ideXlab platform.
-
Boundary elements in shape design sensitivity analysis and optimal design of vibrating structures
Engineering Analysis With Boundary Elements, 1991Co-Authors: Tadeusz Burczyński, Piotr FedelinskiAbstract:Abstract A general approach to shape design sensitivity analysis and optimal design for dynamic transient and free vibrations problems using boundary elements is presented. The material derivatives and the Adjoint System method are applied to obtain first-order sensitivities for the effect of boundary shape variations. A numerical example of shape sensitivity analysis and optimal design for free vibrations of an elastic body is presented.
Zhenping Feng - One of the best experts on this subject based on the ideXlab platform.
-
Study on continuous Adjoint optimization with turbulence models for aerodynamic performance and heat transfer in turbomachinery cascades
International Journal of Heat and Mass Transfer, 2017Co-Authors: Pengfei Zhang, Liming Song, Zhenping FengAbstract:Abstract A continuous Adjoint method for turbomachinery is presented based on the varied turbulence eddy viscosity (VEV), rather than the constant eddy viscosity (CEV) assumption. Firstly, the grid node coordinates variation and Jacobian Matrices is introduced to deduce the general Adjoint System. Then, an objective of entropy generation for aerodynamic and heat transfer is proposed to evaluate the loss of both flow and heat transfer. The VEV Adjoint Systems with Spalart-Allmaras and SST turbulence models are established for the compressible turbulent flow in turbine cascades with the adiabatic blade wall condition. The aerodynamic optimization cases for turbine cascades show that the VEV Adjoint System can achieve higher accuracy, quicker convergence and better optimal result than that of the CEV System in turbomachinery. Furthermore, the improvement of the VEV Adjoint method to the mass flow rate constraint is analyzed. Finally, the VEV Adjoint System with linearized turbulence model is presented for the isothermal blade wall condition. The optimization results demonstrate the ability of these Systems in optimizing the flow and heat transfer performance and reducing the turbine total loss.
-
Adjoint-Based Optimization Method With Linearized SST Turbulence Model and a Frozen Gamma-Theta Transition Model Approach for Turbomachinery Design
Volume 2B: Turbomachinery, 2015Co-Authors: Pengfei Zhang, Liming Song, Zhiduo Wang, Zhenping FengAbstract:In this paper, based on the grid node coordinates variation and Jacobian Matrices, the turbulent continuous Adjoint method with linearized turbulence model is studied and developed to fully account for the variation of turbulent eddy viscosity. The corresponding Adjoint equations, boundary conditions and the final sensitivities are formulated with a general expression. To implement the Adjoint optimization of the transition flow, a flow solver combining the transition model with the turbulence model is employed, and an Adjoint optimization framework with linearized SST turbulence model and a frozen Gamma-Theta transition model is established. In order to choose an appropriate objective for the transition flow optimization, four objectives are studied, including the entropy generation, the total pressure loss coefficient, the field integral of turbulent kinetic energy, the area ratio of transition and turbulent regions to the suciton side. And finally the entropy generation is adopted as the objective. Then, the derivation of the Adjoint System for the entropy generation optimization is presented. To demonstrate the validity of the Adjoint System for transition flow, four shape optimizations for the bypass transitions and the separation-induced transition are implemented. A 2D isentropic case for bypass transitions is conducted to compares the performances of the fully turbulent Adjoint System and the frozen Gamma-Theta transition Adjoint System, while the other isothermal case is performed to take the aerodynamic and heat transfer issues into account together. The case of separation-induced transition is performed and also consistent well with its flow mechanism. The four optimization results illustrate the effectiveness of the Adjoint System for the transition flow optimization, which can improves the performance of overall cascades and the transition region.Copyright © 2015 by ASME
-
Study and Verification of Continuous Adjoint System for Aerodynamic Optimization in Turbomachinery Cascades
Volume 6B: Turbomachinery, 2013Co-Authors: Pengfei Zhang, Zhenping FengAbstract:This paper is a further study of the authors’ previous work on the continuous Adjoint method based on the variation in grid node coordinates and Jacobi Matrices of the flow fluxes. This method simplifies the derivation and expression of the Adjoint System, and reduces the computation cost. In this paper, the differences between the presented and the traditional methods are analyzed in details by comparing the derivation processes and the Adjoint Systems. In order to demonstrate the reliability and accuracy of the Adjoint System deduced by the authors, the presented method is applied to different optimal problems, which include two inverse designs and two shape optimizations in both 2D and 3D cascades. The inverse designs are implemented by giving the isentropic Mach number distributions along the blade wall for 2D inviscid flow and 3D laminar flow. The shape optimizations are implemented with the objective function of the entropy generation in flow passage for 2D and 3D laminar flows. In the 3D optimal case, this method is validated by supersonic turbine design case with and without mass flow rate constraint. The numerical results testify the accuracy of this Adjoint method, which includes only the boundary integrals, and furthermore, the universality and portability of this Adjoint System for inverse designs and shape optimizations are demonstrated.Copyright © 2013 by ASME
-
Aerodynamic inverse design optimization for turbine cascades based on control theory
Science China Technological Sciences, 2012Co-Authors: Zhenping Feng, Liming SongAbstract:Based on control theory, Adjoint System for the general problem of turbomachinery aerodynamic optimization was studied and developed in the present paper by using the variation technique in the grid node coordinates combined with Jacobian Matrics of flow fluxes. Then the Adjoint System for aerodynamic design optimization of turbine cascade governed by compressible Navier-Stokes equations was derived in detail. With the purpose of saving computation resources, the mathematic method presented in this paper avoids the coordinate System transforming in the traditional derivation process of the Adjoint System and makes the Adjoint System much more sententious. Given the general expression of objective functions consisting of both boundary integral and field integral, the Adjoint equations and their boundary conditions were derived, and the final expression of the objective function gradient including only boundary integrals was formulated to reduce the CPU cost, especially for the complex 3D configurations. The Adjoint System was solved numerically by using the finite volume method with an explicit 5-step Runge-Kutta scheme and Riemann approximate solution of Roe’s scheme combined with multi-grid technique and local time step to accelerate the convergence procedure. Finally, based on the aerodynamic optimization theory in the present work, 2D and 3D inviscid and viscous inverse design programs of axial turbomachinery cascade for both pressure distribution and isentropic Mach number distribution on the blade wall were developed, and several design optimization cases were performed successfully to demonstrate the ability and economy of the present optimization System.
-
Inverse Problem for Isentropic Mach-Number on Blade Wall in Aerodynamic Shape Design of Turbomachinery Cascades by Using Adjoint Method
Volume 7: Turbomachinery Parts A B and C, 2011Co-Authors: Liming Song, Pengfei Zhang, Zhenping FengAbstract:This paper presents an approach of the continuous Adjoint System deduction based on the variation in grid node coordinates, in which the variation in the gradient of flow quantity is converted into the gradient of the variation in flow quantity and the gradient of the variation in grid node coordinates, which avoids the coordinate System transforming in the traditional derivation process of Adjoint System and make the Adjoint System much more sententious. By introducing the Jacobian matrix of viscous flux to the gradient of flow variables, the Adjoint System for turbomachinery aerodynamic design optimization governed by compressible Navier-Stokes equations is derived in details. Given the general expression of objective functions consisted of both boundary integral and field integral, the Adjoint equations and their boundary conditions are derived, and the final expression of the objective function gradient including only boundary integrals is formulated to reduce the CPU cost. Then the Adjoint System is numerically solved by using the finite volume method with an explicit 5-step Runge-Kutta scheme and Riemann approximate solution of Roe’s scheme combined with multi-grid technique and local time step to accelerate the convergence procedure. Finally, the application of the method is illustrated through a turbine cascade inverse problem with an objective function of isentropic Mach number distribution on the blade wall.Copyright © 2011 by ASME
Joseph D. Eide - One of the best experts on this subject based on the ideXlab platform.
-
Modified Legendre–Gauss–Radau Collocation Method for Optimal Control Problems with Nonsmooth Solutions
Journal of Optimization Theory and Applications, 2021Co-Authors: Joseph D. Eide, William W. Hager, Anil V. RaoAbstract:A new method is developed for solving optimal control problems whose solutions are nonsmooth. The method developed in this paper employs a modified form of the Legendre–Gauss–Radau orthogonal direct collocation method. This modified Legendre–Gauss–Radau method adds two variables and two constraints at the end of a mesh interval when compared with a previously developed standard Legendre–Gauss–Radau collocation method. The two additional variables are the time at the interface between two mesh intervals and the control at the end of each mesh interval. The two additional constraints are a collocation condition for those differential equations that depend upon the control and an inequality constraint on the control at the endpoint of each mesh interval. The additional constraints modify the search space of the nonlinear programming problem such that an accurate approximation to the location of the nonsmoothness is obtained. The transformed Adjoint System of the modified Legendre–Gauss–Radau method is then developed. Using this transformed Adjoint System, a method is developed to transform the Lagrange multipliers of the nonlinear programming problem to the costate of the optimal control problem. Furthermore, it is shown that the costate estimate satisfies one of the Weierstrass–Erdmann optimality conditions. Finally, the method developed in this paper is demonstrated on an example whose solution is nonsmooth.
-
Modified Radau Collocation Method for Solving Optimal Control Problems with Nonsmooth Solutions Part II: Costate Estimation and the Transformed Adjoint System
2018 IEEE Conference on Decision and Control (CDC), 2018Co-Authors: Joseph D. Eide, William W. HagerAbstract:A modified Legendre-Gauss-Radau collocation method is developed for solving optimal control problems whose solutions contain a nonsmooth optimal control. The method includes an additional variable that defines the location of nonsmoothness. In addition, collocation constraints are added at the end of a mesh interval that defines the location of nonsmoothness in the solution on each differential equation that is a function of control along with a control constraint at the endpoint of this same mesh interval. The transformed Adjoint System for the modified Legendre-Gauss-Radau collocation method along with a relationship between the Lagrange multipliers of the nonlinear programming problem and a discrete approximation of the costate of the optimal control problem is then derived. Finally, it is shown via example that the new method provides an accurate approximation of the costate.
-
CDC - Modified Radau Collocation Method for Solving Optimal Control Problems with Nonsmooth Solutions Part II: Costate Estimation and the Transformed Adjoint System
2018 IEEE Conference on Decision and Control (CDC), 2018Co-Authors: Joseph D. Eide, William W. Hager, Anil V. RaoAbstract:A modified Legendre-Gauss-Radau collocation method is developed for solving optimal control problems whose solutions contain a nonsmooth optimal control. The method includes an additional variable that defines the location of nonsmoothness. In addition, collocation constraints are added at the end of a mesh interval that defines the location of nonsmoothness in the solution on each differential equation that is a function of control along with a control constraint at the endpoint of this same mesh interval. The transformed Adjoint System for the modified Legendre-Gauss-Radau collocation method along with a relationship between the Lagrange multipliers of the nonlinear programming problem and a discrete approximation of the costate of the optimal control problem is then derived. Finally, it is shown via example that the new method provides an accurate approximation of the costate.
