Papers by Keyword: Proper Orthogonal Decomposition

Abstract: Optimum design in civil structures like domes and vaults is a very old and ongoing research field. These structures are preferably designed to transport loads via membrane action. In this paper, we have considered a reinforced concrete dome and vault, where the bending moment and strain energy were used as objective function to be minimized using genetic algorithm, and model reduction method by proper orthogonal decomposition based on the results of finite element analysis of gradually changed design parameters. The proposed approach results are of a high accuracy compared to finite element based optimization.

Abstract: In this paper, a reduced order model is obtained for nonlinear dynamic analysis of a cantilever beam. Nonlinearity in the system is basically due to large deformation. A reduced order model is an efficient method to formulate low order dynamical model which can be obtained from data obtained from numerical technique such as finite element method (FEM). Nonlinear dynamical models are complex with large number of degrees of freedom and hence, are computationally intensive. With formulation of reduced order models (i.e. Macromodels) number of degrees of freedom are reduced to fewer degrees of freedom by using projection based method like Galerkin’s projection, so as to make system computationally faster and cost effective. These macromodels are obtained by extracting global basis functions from fully meshed model runs. Macromodels are generated using technique called proper orthogonal decomposition (POD) which gives good linear fit for the nonlinear systems. Using POD based macromodel, response of system can be computed using fewer modes instead of considering all modes of system. Macromodel is generated to obtain the response of cantilever beam with large deformation and hence, simulation time is reduced by factor of 90 approximately with error of order of 10^-4. Further, method of POD based reduced order model is aplied to beam with different loading conditions to check the robustness of the macromodel. POD based macromodel response gives good agreement with FEA model response for a cantilever beam.

Abstract: The stability of a metal forming production process is influenced by several sources of scatter such as variation of material and lubrication properties. Identification of the sources of variation is needed to optimize the process settings or to design a control strategy for the process. Many engineers point out sources of variation by experience, but in complex cases a computational identification algorithm may be used to investigate the process. When using parameter estimation in a control system, process forces can be used for the estimation. However, many parameters may influence the process forces. Therefore extensive models are needed to be able to identify the process parameters, including parameters such as tooling misalignment. In the current work, a thin steel flap bending process is studied. Measurements from an industrial press are used to identify the process parameters. A metamodel based inverse analysis procedure is used. The procedure is extended with proper orthogonal decomposition (POD) of the force curves to increase its convergence rate.

Abstract: Applying common surrogate models to problems have numerous output variables is computational expensive, since the number of surrogate models should be constructed equals to the number of output variables. This paper presents an efficient strategy to solve this problem. For that, snapshot Proper Orthogonal Decomposition (POD) is used to extract a few main basis modes from certain number of samples. The predicted result of a large-scale output problem comes from the linear superposition of these basis modes. Common surrogate models just need to predict the coefficients for these basis modes. Through this strategy, The Mach numbers at 36864 points around an airfoil are predicted by just constructing 12 kriging surrogate models. The predicted Mach number distributions fit with the CFD results very well, that proves the efficiency of this strategy.

Abstract: An algorithm, which combines the use of Domain Decomposition and Model Order Reduction methods based on Proper Orthogonal Decomposition, is proposed. The algorithm allows for the efficient handling of electro-mechanical coupled problems in MEMS, with a strong reduction of computing time with respect to standard monolithic or staggered solution strategies. Examples of coupled electro-mechanical problems, concerning a vibrating beam subject to variable electrostatic forces, are presented and discussed.

Abstract: The aim of this work is to present a POD (Proper Orthogonal Decomposition) based surrogate approach for sheet metal forming parametrized applications. The final displacement field for the stamped work-piece computed using a finite element approach is approximated using the method of snapshots for POD mode determination and kriging for POD coefficients interpolation. An error analysis, performed using a validation set, shows that the accuracy of the surrogate POD model is excellent for the representation of finite element displacement fields. A possible use of the surrogate to assess the quality of the stamped sheet is considered. The Green-Lagrange strain tensor is derived and forming limit diagrams are computed on the fly for any point of the design space. Furthermore, the minimization of a cost function based on the surrogate POD model is performed showing its potential for solving optimization problems.

Abstract: Dynamic wind pressures acting on structures are complicated functions of both time and space. The proper orthogonal decomposition technique (POD) is a method of detecting a new coordinate system which can most efficiently represent such random wind pressure fields to identify hidden deterministic structures. In this paper, the POD technique is applied to dynamic wind pressures on spatial structures in order to investigate the properties of these pressures and enable to understand the phenomena better. The results indicate that the POD technique can greatly reduce the amount of data that needs to be stored to re-examine the random wind pressure, which can be reconstructed by only a few dominant modes. It requires 5 modes with an accumulative proportion of 70~80% approximately. Moreover, the dominant modes can describe the spatial distributions of the fluctuating wind load effectively.

Abstract: Taking Harbin west railway station as the researching object, the wind load distribution as well as its effects, which are widely used in practice, is investigated. First, wind pressure distribution on a rigid model is measured simultaneously in a wind tunnel. Some special characteristics of the measured wind pressure, especially its fluctuating component, are discussed. Then the fluctuating wind pressure field is reconstructed based on the synchronous multi-pressure scanning technique of wind tunnel tests and the proper orthogonal decomposition (POD) technique. The influence of lower RC structure on wind-induced vibration is investigated using non-linear time-history analysis. At last, a new method is introduced to obtain equivalent static wind load (ESWL) that reproduce all largest load effects at the same time. With the synthetic application of above methods, the problems such as: complex time and spatial distribution of fluctuating wind; multi-mode vibration of wind-induced response; multiple equivalent objectives for ESWL, can be solved efficiently.

Abstract: The paper presents an experimental application of the Proper Orthogonal Decomposition (POD) to damage detection in steel beams. A damaged beam has been excited with a sinusoidal force, the acceleration response at points regularly spaced along the structure has been recorded and the relevant Proper Orthogonal Modes calculated. In this way it is possible to locate damage by comparing the measured dominant Proper Orthogonal Mode with a smoothed version of it which does not exhibit apparent peaks in correspondence with the damage. One of the principal advantages of the proposed damage detection technique is that it does not require vibration measurements to be performed on the undamaged structure. Moreover the ‘optimality’ of the proper orthogonal modes only requires the use of a few (one-two) of them which can be computed in real time during lab experiments or while the structure is functioning in the field.