China
Africa
Explore chapters and articles related to this topic
An adjoint optimization method for partially cavitating hydrofoils with free-surface effects
Published in C. Guedes Soares, T.A. Santos, Trends in Maritime Technology and Engineering Volume 1, 2022
D. Anevlavi, K.A. Belibassakis
This paper addresses the performance prediction problem of partially cavitating hydrofoils moving steadily under a free surface as an inverse problem, as an extension to (Anevlavi, et al, 2021). The sensitivities required for the gradient-based optimization algorithm are derived using the continuous adjoint method (Papadimitriou, et al, 2007). Among optimization methods, adjoint methods are of interest due to their ability to efficiently handle large numbers of design variables. The objective function follows the assumption of constant pressure on the cavity boundary. The primary and adjoint boundary value problems are solved numerically at each optimization cycle using a source-vorticity BEM solver (Katz, 2001). The hydrofoil/cavity boundary is re-modeled using B-spline parametrization (De Boor, 1978) with the coordinates of the control points included in the design variable vector.
Sonar Performance Models
Published in Paul C. Etter, Underwater Acoustic Modeling and Simulation, 2017
The principal application of adjoint models is sensitivity analysis. When quantitative estimates of sensitivity are desired, a mathematical model of the phenomenon or relationship is required. While models have been used to assess the impacts of perturbations and thus to estimate sensitivity, a more efficient approach is to use the model’s adjoint to determine optimal solutions. The adjoint operates backward in the sense that it determines a gradient with respect to input from a gradient with respect to output. In a temporally continuous model, this would appear as integration backwards in time. If there are no numerical instabilities associated with irreversible processes in the tangent linear model acting forward in time, there will be none in the adjoint acting backward in time (a tangent linear model provides a first-order approximation to the evolution of perturbations in a nonlinear forecast trajectory). The greatest limitation to the application of adjoints is that the results are useful only when a linearized approximation is valid. The adjoint operator (matrix transpose) back-projects information from data to the underlying model. Geophysical modeling calculations generally use linear operators that predict data from models. The usual task is to find the inverse of these calculations, that is, to find models (or make maps) from the data. The adjoint operator tolerates imperfections in the data and does not demand that the data provide full information.
3
Published in Qingyan Chen, Zhiqiang Zhai, Xueyi You, Tengfei Zhang, Inverse Design Methods for the Built Environment, 2017
Qingyan Chen, Zhiqiang Zhai, Xueyi You, Tengfei Zhang
The adjoint method computes the derivative of the objective function with respect to the design variables, so that the method can search for the direction that gradually minimizes the objective function. The curve in Fig. 3.1 can be used to represent the relationship between a design variable and the design objective. The adjoint method first initializes a starting point (ξ, O(ξ)). The method then computes the gradient and adjusts the design variable in the direction that minimizes the objective function. This procedure is repeated until the minimum has been found. It is possible, of course, that this method will identify only the local optima. However, a reasonable estimate of the ξ can speed up convergence, and thus local optima can be avoided.
Shape optimisation of trimaran ship hull using CFD-based simulation and adjoint solver
Published in Ships and Offshore Structures, 2022
Geometry deformation and mesh morphing are executed together in mesh deformation step. Mesh morphing is applied iteratively on the geometry. Adjoint solvers take a CFD flow solution and calculate the sensitivity of cost function (drag force) for all variables. The advantage of the adjoint method is that computational effort for obtaining the sensitivities of an objective does not grow with an increasing number of design variables. The computational cost is essentially independent of the number of design variables since the adjoint method requires only one CFD and adjoint solution for any number of design variables. The fundamental task in solving the adjoint of the modelled physical phenomena is to compute the cost function sensitivity with respect to the mesh. Here, is the objective function, and is the vector of design variables. For minimisation of the gradients, should be computed (He et al. 2018). where D represents the shape sensitivity of the observed value concerning (wall boundary) the grid node locations that are linked to design variables as a control point and n is the number of these design variables.
Inverse boundary problem in estimating heat transfer coefficient of a round pulsating bubbly jet: design of experiment
Published in Applied Mathematics in Science and Engineering, 2022
Honeyeh Razzaghi, Farshad Kowsary, Mohammad Layeghi
Among many numerical inverse methods, the conjugate gradient method (CGM) together with adjoint equations lead to an efficient inverse algorithm for solving nonlinear IHCP. It is a powerful technique for function estimation and minimizing the objective functional. The adjoint method is a whole-domain, efficient algorithm with high accuracy which works by solving three sub-problems; the direct, the sensitivity, and the adjoint problems. This method has been studied by many researchers in heat transfer problems. Some notable surveys in this field can be found in Refs. [24–32].
Reliability-based topology optimization using the response surface method for stress-constrained problems considering load uncertainty
Published in Engineering Optimization, 2022
Changzheng Cheng, Bo Yang, Xuan Wang, Kai Long
As can be seen from Equation (25), the term still needs to be derived. With the aid of the global displacement , the term can expressed as where is a selection matrix that used to separate the node displacement vector of element e from the global displacement vector. Assuming the external load F is irrelevant to the filtered density, taking the derivative of both sides of the equation concerning the filtered density, reads as Then, the term can be expressed as By substituting Equation (29) and Equation (25) into Equation (21), can be rewritten as Owing to the huge amounts of design variables in this problem, the adjoint method needs to be introduced to improve computational efficiency. The adjoint vector is determined by the solution of the following adjoint formulation: With the adjoint vector solved from Equation (31), the derivative of the performance function w.r.t. can be simplified as Now, substituting Equations (22), (23), (24) and (26) into Equation (32), the complete formula of the derivative of w.r.t. can be obtained.