Compression of an Array of Similar Crash Test Simulation Results

Description

Big data thrives on extracting knowledge from a large number of data sets. But how is an application possible when a single data set is several gigabytes in size? The innovative data compression techniques from the field of machine learning and modeling using Bayesian networks, which have been theoretically developed and practically implemented here, can reduce these huge amounts of data to a manageable size. By eliminating redundancies in location, time, and between simulation results, data reductions to less than 1 % of the original size are possible. The developed method represents a promising approach whose use goes far beyond the application example of crash test simulations chosen here. 1 Introduction 1.1 Overview of proposed lossy compression method 1.2 Outline 1.3 Contributions 1.4 Danksagung 2 Crash test simulation results 2.1 Calculation of crash test simulation results 2.1.1 Governing Equations 2.1.2 Contact Algorithm 2.1.3 Best practice 2.2 Contents and properties 2.3 Simulation data management systems 3 State-of-the-art compression methods 3.1 Information theory and its limits on data compression 3.1.1 Single random variables 3.1.2 General stochastic processes 3.1.3 Markov chains 3.2 Types of data compression 3.3 Components of data compression 3.3.1 Quantization 3.3.2 Prediction and transformation 3.3.3 Encoding 4 Dimensionality reduction methods 4.1 Previous work 4.2 Principal component analysis 4.2.1 Data model 4.2.2 Singular value decomposition 4.2.3 Properties 4.2.4 Calculation of truncated singular value decompositions 4.3 Predictive principal component analysis 4.3.1 Gathering information 4.3.2 Offline method 4.3.3 Online method 4.3.4 Crucial parameters 4.3.5 Segmentation into parts 5 Induced Markov chains for data compression 5.1 The induced Markov chain encoder 5.2 Time complexity of iMc encoding 5.3 Adaptive Arithmetic coding using iMc 5.4 Theory of induced Markov chains 5.5 Divergence of empirical and stationary distribution 5.6 Choice of a spanning tree 5.7 Combination with prediction methods 5.7.1 Tree differences 5.7.2 Lorenzo predictor 5.7.3 Graph differences 5.8 Differentiation of induced Markov chains 5.8.1 Prediction by Partial Matching and Dynamic Markov Coding 5.8.2 Bayesian Networks 5.8.3 Markov Random Fields 6 Evaluation 6.1 Methodology 6.2 Benchmark data sets 6.2.1 Chrysler Silverado 6.2.2 OEM 1 6.2.3 OEM 2 6.3 PPCA’s crucial parameters 6.3.1 Number of principal components 6.3.2 Internal Precision and amendment steps 6.3.3 Small parts threshold 6.4 Compression factors 6.4.1 Silverado 6.4.2 OEM 1 6.4.3 OEM 2 6.5 Run times 6.6 Application fields 7 Conclusion 7.1 Summary 7.2 Outlook and future work 7.2.1 Runtime 7.2.2 Compression factor