189 research outputs found
Surrogate modeling in the design optimization of structures with discontinuous responses with respect to the design variables - A new approach for crashworthiness design
No full textAdvances to computational technology have resulted in the reduction of computational effort for crashworthiness analysis, hence enabling structural design optimization. Surrogate modeling has been shown to further reduce computational effort as well as to smooth noisy responses. Crashworthiness optimization problems are, though, ill posed as they include nonlinear, noncontinuous and noisy responses. This violates the Hadamard conditions for well-posed problems and therefore the applicability of gradient-based algorithms is limited. Here, discontinuities in the responses with respect to the design variables will be handled that result in large changes in the system functions with only small changes in the design variables using a novel surrogate modeling technique. The applicability of typical global surrogate models is limited when critical discontinuities are present. An efficient method has been developed here to identify the number of discontinuities and their position in the design domain. Previous works assume a said number of discontinuities; here though, the number of discontinuities is not given a priori. The discontinuities are identified by examining the relative difference in the response value of samples in immediate proximity of each other. Samples in the same continuous subdomain are clustered and a support vector machine for classification is exploited to locate discontinuities. Local approximations are then used for the continuous subspaces between the discontinuities. Lastly, a surrogate-based design optimization is carried out. Starting with a two-bar truss, demonstrating a snap-through discontinuity, this method is shown to account for such discontinuities. This is then integrated into an optimization framework. Further, a crash-absorbing tube is optimized that is impacted with an angle resulting in a noncontinuous design space: desired axial crushing and undesirable global buckling. After summarizing the results, advantages and possible limitations are discussed
Hybrid Kriging-assisted level set method for structural topology optimization
No full textThis work presents a hybrid optimization approach that couples Efficient Global Optimization (EGO) and Co-variance Matrix Adaptation Evolution Strategy (CMA-ES) in the Topology Optimization (TO) of mechanical structures. Both of these methods are regarded as good optimization strategies for continuous global optimization of expensive and multimodal problems, e.g. associated with vehicle crashworthiness. CMA-ES is flexible and robust to changing circumstances. Moreover, by taking advantage of a low-dimensional parametrization introduced by the Evolutionary Level Set Method (EA-LSM) for structural Topology Optimization, such Evolution Strategy allows for dealing with costly problems even more efficiently. However, it is characterized by high computational costs, which can be mitigated by using the EGO algorithm at the early stages of the optimization process. By means of surrogate models, EGO allows for the construction of cheap-to-evaluate approximations of the objective functions, leading to an initial fast convergence towards the optimum in opposition to a poor exploitive behavior. The approach presented here - the Hybrid Kriging-assisted Level Set Method (HKG-LSM) - first uses the Kriging-based method for Level Set Topology Optimization (KG-LSM) to converge fast at the beginning of the optimization process and explore the design space to find promising regions. Afterwards, the algorithm switches to the EA-LSM using CMA-ES, whose parameters are initialized based on the previous model. A static benchmark test case is used to assess the proposed methodology in terms of convergence speed. The obtained results show that the HKG-LSM represents a valuable option for speeding up the optimization process in real-world applications with limited computational resources. As such, the proposed methodology exhibits a much more general potential, e.g. when dealing with high-fidelity crash simulations
Pilots Relaxing and Reading Newspapers
No full textOne Sepia Photograph; 5" x 4"; Sergeant Seymour "Blackie" Furkman, Cohen, Herrington, Sergeant Ralph Duddeck during maneuvers at Keystone, F
Surrogate modeling in design optimization of structures with discontinuous responses: A new approach for ill-posed problems in crashworthiness design
No full textAdvances in computational technology have resulted in the dramatic reduction of computational time for crashworthiness analysis, hence enabling its structural design optimization. Surrogate modeling has been shown to further reduce computational effort as well as to smooth noisy responses. Crashworthiness optimization problems are, though, ill posed as they include nonlinear, noncontinuous and noisy responses. This violates the Hadamard conditions for well-posed problems and therefore the applicability of gradient-based algorithms is limited. Here, discontinuities in the responses with respect to the design variables will be handled that result in large changes in the system functions with only small changes in the design variables using a novel surrogate modeling technique. The applicability of typical global surrogate models is limited when critical discontinuities are present. An efficient method has been developed here to identify the number of discontinuities and their position in the design domain. Previous works assume a said number of discontinuities; here though, the number of discontinuities is not given a priori. The discontinuities are identified by examining the relative difference in the response value of samples in immediate proximity of each other. Samples in the same continuous subdomain are clustered and a support vector machine for classification is exploited to locate discontinuities. Local approximations are then used for the continuous subspaces between the discontinuities. Lastly, a surrogate-based design optimization is carried out. Starting with a two-bar truss, demonstrating a snap-through discontinuity, this method is shown to account for such discontinuities. This is then integrated into an optimization framework. Further academic example, namely a six-bar truss is modeled using the open-source framework Kratos Multiphysics and then optimized, showing the applicability of the method to problems with multiple discontinuities. Finally, a crash-absorbing tube is optimized that is impacted with an angle resulting in a noncontinuous design space: desired axial crushing and undesirable global buckling. After summarizing the results, advantages and possible limitations are discussed
Material parameter optimization of flax/epoxy composite laminates under low-velocity impact
No full textSince natural fibers have great potential as an alternative to synthetic fibers when the components are impacted at low energies, their mechanical properties under different types of loads need to be investigated. This can be accomplished by using finite element analysis, which is based on the definition of numerical models that reproduce the objects of the physical phenomenon under study. In defining these models, many parameters of the material cards are determined by experimental tests. However, experiments are time-consuming and costly, and it is not always possible to perform all the necessary tests to determine the values for all unknown parameters. For this purpose, the trial-and-error method is usually used. In this work, we present an optimization procedure for predicting the behavior of flax/epoxy composite laminates under low-velocity impact, using the LS-DYNA solver for numerical simulation. The study aims at identifying the values of relevant parameters that allow for predicting the experimental force–displacement trend as accurately as possible and reproducing the damage mechanisms numerically. Each step of the optimization flow is performed with the external tool LS-OPT, using dynamic time warping as a similarity measure to efficiently handle noise. For this purpose, we use the Efficient Global Optimization algorithm, a strategy based on surrogate modeling techniques. We address a multi-target scenario, i.e., we consider several energy levels simultaneously, aiming to find an optimal parameter configuration that is less sensitive to variations in impact energy. The results obtained not only demonstrate the potential of surrogate-based optimization to identify material parameters, but also provide a characterization of the studied composite configuration in view of future applications
Bayesian Optimization for Solution Space: code and results
No full text<p>This is the code and the results of the work on combining the solution space method with bayesian optimization contained in <em>P. Ascia, E. Raponi and F. Duddeck; Bayesian Optimization of Structural Systems subjected to Crash Constraints represented by the Solution Space Approach</em>.</p>
<p>The files contain:</p>
<ul>
<li><em>Ascia-SolSpaceOptimizationResults.zip</em> contains the code to run the optimization, all data produced, and the code to generate the plots. </li>
<li><em>Ascia-SolSpaceOptimization.zip </em>contains only the code to run the optimization.</li>
</ul>
<p>The code is sensitive to the folder naming and positioning. To properly run the code we recommend creating a virtual environment using the information contained in <em>setup.yml </em>and using LS-Dyna with a full license.</p>
Computing solution-compensation spaces using an enhanced Fourier-Motzkin algorithm
No full textIn complex system design, design variables can be divided into two groups, early‐ and late‐decision variables. Early‐decision variables are equipped with tolerance regions which are specified during the early stages of the development process. Tolerance is necessary to account for changes of design variable values due to later and therefore unknown, design restrictions. In this sense, early‐decision variables are subject to lack‐of‐knowledge uncertainty. Tolerance regions for early‐decision variables can be significantly increased by the use of late‐decision variables. The latter are not equipped with tolerance regions and, by contrast, have to be arbitrarily well adjustable within their design intervals. The values of late‐decision variables are chosen in a later development phase when further design restrictions are known. Late‐decision variables then may compensate for the choice of early‐decision variables. Solution‐compensation spaces are regions of early‐ and late‐decision variables where for all values of early‐decision variables values for late‐decision variables from their associated intervals exist such that all design requirements are satisfied. A new approach to compute solution‐compensation spaces for linear systems is introduced. It is based on an enhanced Fourier‐Motzkin‐Elimination algorithm which uses H‐redundancy removal. The new algorithm is applied to a design problem from vehicle dynamics and we show that it outperforms the so‐called basic projection algorithm presented in [ Vogt M. E., Duddeck F., Wahle M., Zimmermann M. "Optimizing tolerance to uncertainty in systems design with early-and late-decision variables." IMA Journal of Management Mathematics]
Hyper and strong singularities of the Fourier BEM
No full textThe range of applications of Boundary Element Methods(BEM)is restricted to cases where the fundamental solution is known. An approach recently developed by the author via the Fourier transform generalizes the BEM to the so-called Fourier BEM
(Fourier BEM—generalization of boundary element methods by Fourier Transform. Springer, Berlin HeidelbergNewYork, 2002). There, new boundary integral equations (BIE) are formulated, which consist only of Fourier transformed terms and lead to equivalent matrices as in the standard approach. They make use of only the Fourier transform of the fundamental solution,
which is much easier to obtain (available for all cases as long as the differential operator is linear and has constant coefficients). No inverse transform and no fundamental solution in the original space are required. Here, the theory is summarized and an example of anisotropic elasticity is given to motivate the discussion of singularities, which is the topic of this paper. It is shown, that all types of singularities (weak, strong, and hyper)
occur as in the standard approach and that they require a
new treatment because they are originating from newly
developed integral equations. The main result is that the non-regular parts of the strong and hyper singular integrals cancel if ordered correctly
Hyper and Strong Singularities of the Fourier Boundary Element Method
No full textThe range of applications of Boundary Element Methods (BEM) is restricted to cases where the fundamental solution is known. An approach recently developed by the author via the Fourier transform generalizes the BEM to the so-called Fourier BEM (Fourier BEM—generalization of boundary element methods by Fourier Transform. Springer, Berlin Heidelberg New York, 2002). There, new boundary integral equations (BIE) are formulated, which consist only of Fourier transformed terms and lead to equivalent matrices as in the standard approach. They make use of only the Fourier transform of the fundamental solution, which is much easier to obtain (available for all cases as long as the differential operator is linear and has constant coefficients). No inverse transform and no fundamental solution in the original space are required. Here, the theory is summarized and an example of anisotropic elasticity is given to motivate the discussion of singularities, which is the topic of this paper. It is shown, that all types of singularities (weak, strong, and hyper) occur as in the standard approach and that they require a new treatment because they are originating from newly developed integral equations. The main result is that the non-regular parts of the strong and hyper singular integrals cancel if ordered correctly
Draping simulation with a new finite element formulation involving an internal unit cell
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