Approximation Methods for High Dimensional Simulation Results
Daniela Steffes-lai
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Daniela Steffes-lai, Approximation Methods for High Dimensional Simulation Results (2014), Logos Verlag, Berlin, ISBN: 9783832591632
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Beschreibung / Abstract
This work addresses the analysis of a sequential chain of processing steps, which is particularly important for the manufacture of robust product components. In each processing step, the material properties may have changed and distributions of related characteristics, for example, strains, may become inhomogeneous. For this reason, the history of the process including design-parameter uncertainties becomes relevant for subsequent processing steps. Therefore, we have developed a methodology, called PRO-CHAIN, which enables an efficient analysis, quantification, and propagation of uncertainties for complex process chains locally on the entire mesh. This innovative methodology has the objective to improve the overall forecast quality, specifically, in local regions of interest, while minimizing the computational effort of subsequent analysis steps. We have demonstrated the benefits and efficiency of the methodology proposed by means of real applications from the automotive industry.
Inhaltsverzeichnis
- BEGINN
- 1 Introduction
- 1.1 Context
- 1.2 Main Focus and Structure
- 2 Notation and Fundamentals
- 2.1 Terminology
- 2.2 Fundamentals and General Approaches
- 2.3 Sheet Metal Forming Processes with Example
- 3 Mathematical Concepts
- 3.1 Design of Experiments
- 3.2 Sensitivity Analysis
- 3.3 Dimension Reduction Methods
- 3.4 Metamodels
- 3.5 Stochastic Finite Element Methods
- 4 Parameter Classification Using Sensitivity Analysis
- 4.1 Importance and Nonlinearity Classes
- 4.2 Clustering Using the Nonlinearity Measure
- 4.3 Efficiency
- 4.4 Conclusions
- 5 Processing of the Database
- 5.1 Parameter Space Dimension Reduction
- 5.2 Iterative Extension of the Database
- 5.3 Ensemble Compression of the Database
- 6 Forecast Model and Propagation of Variations
- 6.1 Approximation of New Designs
- 6.2 Computation of Statistics
- 6.3 Propagation of All Relevant Scatter Information to the Next Processing Step
- 6.4 Quality Control
- 6.5 Efficiency
- 6.6 Conclusions
- 7 Benchmarks and Industrial Applications
- 7.1 Numerical Comparison Between the New Methodology and a Stochastic Collocation Method
- 7.2 Forming of a Pan with Secondary Design Elements
- 7.3 Process Chain Forming-to-Crash
- 8 Conclusions and Future Directions
- Bibliography
- List of Figures
- List of Tables
- Acronyms
- List of Symbols