PMU Time Series Data Mining

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1 PMU Time Series Data Mining Natasha Balac, Ph.D Chuck Wells, Ph.D Nicole Wolter Albert Nguyen Jake Schurmeier Predictive Analytics Center of Excellence (PACE) San Diego Supercomputer Center University of California, San Diego

2 Brief History of SDSC : NSF national supercomputer center; managed by General Atomics : NSF PACI program leadership center; managed by UCSD PACI: Partnerships for Advanced Computational Infrastructure : Internal transition to support more diversified research computing Still NSF national resource provider 2009-future: Multi-constituency cyberinfrastructure (CI) center Provide data-intensive CI resources, services, and expertise for campus, state, and nation Approaching $1B in lifetime contract and grant activity

3 Gordon Speeds and Feeds INTEL SANDY BRIDGE COMPUTE NODE Sockets & Cores 2 & 16 Clock speed 2.6 GHz DRAM capacity and speed 64 GB, 1,333 MHz INTEL710 emlc FLASH I/O NODE NAND flash SSD drives 16 SSD capacity per drive & per node 16 * 300 GB = 4.8 TB SMP SUPER-NODE (VIA VSMP) Compute nodes / I/O Nodes 32 / 2 Addressable DRAM 2 TB Addressable memory including flash 11.6 TB GORDON (AGGREGATE) Compute Nodes 1,024 Compute cores 16,384 Peak performance 341 TF DRAM/SSD memory Architecture Link Bandwidth Vendor INFINIBAND INTERCONNECT 64 TB DRAM; 300 TB SSD Dual-Rail, 3D torus QDR Mellanox LUSTRE-BASED DISK I/O SUBSYSTEM (SHARED) Total storage: current/planned 4 PB/6 PB (raw) Total bandwidth 100 GB/s

4 PMU Frequency Data

5 Sampling PMU Frequency Data and Fast Fourier Transformation (FFT) Transforming Frequency Data to FFT Data 23 samples of Frequency Data was taken from the PMU at different times The FFT was computed for each sample Each FFT was standardized by setting the max value to 1 The following slides are the standardized FFT for the various time samples

6 FFT at Various Time (1 of 4) X-Axis = Frequency Y-Axis: Magnitude

7 FFT at Various Time (2 of 4) X-Axis = Frequency Y-Axis: Magnitude

8 FFT at Various Time (3 of 4) X-Axis = Frequency Y-Axis: Magnitude

9 FFT at Various Time (4 of 4) X-Axis = Frequency Y-Axis: Magnitude

10 Time Series Representation and Similarity Measure Transforming FFT Data into FFT Bins For each preceding sample, FFT Frequencies are discretized into 25 bins For each bin the mean and the sum are calculated Correlation matrix comparing the corresponding event and control frequency bins

11 FFT Correlation Matrix Control Group Event Group

12 Simple Anomaly Detection Benford s Law Also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In this distribution, the number 1 occurs as the leading digit about 30% of the time, while larger numbers occur in that position less frequently: 9 as the first digit less than 5% of the time Benford's Law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution

13 40% Benford Distribution Between Compressed and Uncompressed Data 35% 30% 25% Benford Compressed Uncompress 20% 15% 10% 5% 0% First Digit

14 40% Benford Distribution Between Control and Event 35% 30% 25% Control Event 20% 15% 10% 5% 0% First Digit

15 Next Steps Alternate time series representation and dimensionality reduction Discrete wavelet transform Discrete Haar Wavelet Transform (DTWT) Adaptive Piecewise Constant Approximation Symbolic Aggregate Approximation (SAX) representation

16 Time Series Data Mining Pattern Discovery and Clustering for Motif discovery K-motif detection Anomaly detection or finding discords Distance-based Clustering Self Organizing Map (SOM) Multi-resolution Clustering (MPAA) ARIMA EM-Clustering Hidden Markov Model (HMM) Motif-based clustering

17 Classification Descriptive techniques Supervised learning - maps data into predefined categories/classes Nearest Neighbor classifier Applies the similarity measures to the object to be classified to determine its best classification based on the existing data that has already been classified Decision trees A set of rules are inferred from the training data, and this set of rules is then applied to any new data to be classified

18 Clustering K-means X X X X Hierarchical Clustering

19 Scalability From one to multiple PMUs multivariate time series mining Sub-second data collection and processing

20 Analytics Architecture OSIsoft PI server direct export to Hadoop Hadoop & myhadoop with Mahout KNIME batch job Revolution Analytics R libraries for Big Data Once the models are trained (near)real-time scoring can be implemented on the sensor streams enabling large prediction window horizon

21 Thank you! For further information, contact: Chuck Wells Natasha Balac

PACE Predictive Analytics Center of Excellence @ San Diego Supercomputer Center, UCSD. Natasha Balac, Ph.D.

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