Convection Coefficient Estimation by the Truncated Singular Value Decomposition Method Applied to the Associated Inverse Thermal Problem

Brandi, Analice Costacurta; Ansoni, Jonas Laerte; Seleghim, Paulo

doi:10.1080/01457632.2013.793116

Cited by 2 publications

(4 citation statements)

References 4 publications

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“…This can be shown by simulating the convergence trajectory on the error surfaces, whose two-dimensional versions were analysed in Brandi et al [2], where they contain structures, such as narrow valleys, multiple local minima, plateaus, etc. consequently, the corresponding convergence trajectories are expected to be erratic.…”

Section: Test Casementioning

confidence: 99%

“…The Singular Value Decomposition was applied in this paper to obtain a pseudo-inverse of the Hessian matrix with a better conditioning number: the eigenvectors corresponding to singular or near singular eigenvalues of H are truncated (TSVD). [2] In rough, this corresponds to throwing away sets of equations that are nearly linear-dependent solving Equation (9) in an average sense. These problematic equations attract the solution to the null space associated to H , resulting in increasingly larger corrections d k towards infinity.…”

Section: Optimization Algorithm and Regularizationmentioning

confidence: 99%

“…The inverse Hessian matrix used in the Newton's method is replaced by a pseudo-inverse built from the truncated singular value decomposition (TSVD) technique used to regularize the approximations of the convection coefficient. [2] However, the ITP modelling is highly expensive in computational terms and extremely sensitive to intrinsic errors, requiring considerable CPU processing time and accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Resolution of an inverse thermal problem using parallel processing on shared-memory multiprocessor architectures

Ansoni

Brandi

Seleghim

2014

Inverse Problems in Science and Engineering

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Advances in multi-cores CPUs and in Graphics Processors Units (GPUs) are attracting a lot of attention of the scientific community due to their parallel processing power in conjunction with their low cost. In recent years the resolution of inverse thermal problems (ITP) is gaining increasing importance and attention in simulation-based applied science and engineering. However, the resolutions of these problems are very sensitive to random errors and the computer cost is high. In an attempt to improve the computational performance to solve an ITP, the computational power of multi-core architectures was used and analysed; mainly those offered by the GPU via Compute Unified Device Architecture (CUDA) and multi-cores CPUs via Pthreads. Also, we developed the implementation of the Preconditioned Conjugate Gradient method as a kernel on GPU to solve several sparse linear systems. Our CUDA and Pthreads-based systems are, respectively, two and four times faster than the serial version, while maintaining comparable convergence behaviour.

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Section: Test Casementioning

confidence: 99%

Section: Optimization Algorithm and Regularizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Resolution of an inverse thermal problem using parallel processing on shared-memory multiprocessor architectures

Ansoni

Brandi

Seleghim

2014

Inverse Problems in Science and Engineering

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“…Liu and colleagues 10,29 found that the TSVD proved to be useful to decrease the distortion of the final results due to numerical instabilities introduced by the use of the classical, direct inversion algorithm. Brandi et al 30 used the TSVD to regularize the Hessian matrix in the convection heat transfer coefficient estimation. Shirangi and Alexandre 31 improved TSVD-based randomized maximum likelihood (RML) method for reservoir history matching and uncertainty assessment.…”

Section: Damjan and Mihamentioning

confidence: 99%

Numerical investigation of a two-stage serial vibration isolation system using frequency response function based substructuring method

Guo

Wang

Zhou

et al. 2017

Advances in Mechanical Engineering

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The mechanical system applied in industry and manufacturing fields is generally a complex multi-stage isolation system, which contains a lot of connection parts. In order to better analyze the effect of the connection parts, the transfer path model of a two-stage serial system is developed in this article using frequency response function based substructuring method. To verify the proposed transfer path model, a finite element model that simulates a two-stage serial vibration isolation system is built. By comparing the predicted results and exact values, the model proves to be correct. Furthermore, the random noise is introduced into the system-level frequency response functions for error sensitivity analysis and the influence on the substructure frequency response functions is quantified through comparison. Since the possible errors are unknown in the experimental measurement, 5%, 25%, and 50% random errors are introduced into all the input frequency response functions individually to analyze the influence of different noise levels on the prediction accuracy. In order to solve the ill-conditioned inverse problem involved in the model, the truncated singular value decomposition is also applied. The simulation results show that compared with the direct-inverse method, truncated singular value decomposition can decrease the prediction error caused by the introduced noise more effectively.

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Convection Coefficient Estimation by the Truncated Singular Value Decomposition Method Applied to the Associated Inverse Thermal Problem

Cited by 2 publications

References 4 publications

Resolution of an inverse thermal problem using parallel processing on shared-memory multiprocessor architectures

Resolution of an inverse thermal problem using parallel processing on shared-memory multiprocessor architectures

Numerical investigation of a two-stage serial vibration isolation system using frequency response function based substructuring method

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