Sliding window based fault detectionfrom high-dimensional data streams

Liangwei ZhangDivision of Operation and Maintenance Engineering

Authors: Liangwei Zhang, Janet Lin, Ramin Karim

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OUTLINE

1. Background

2. Problem statement

3. Existing work

4. Sliding Window-based ABSAD

5. Summary

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Problem: Detect ”something has gone wrong”, fault detection

Structured Semi-structured Unstructured

Terabytes Records Transactions Tables, files Dimensions

3Vs of Big Data

Batch Real-time Near-real-time Streams

Volume Velocity

Variety

1. Background

• Big Data

128+64 sensors (High dimensionality)

1Hz, 86400 samplesper day (Data stream)

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Veracity, Value, Visualization, Volatility, Validity, Venue, Vocabulary, Vagueness…

1. Background• ISO 13374-2, OSA-CBM (Open System Architecture for

Condition-Based Maintenance)

1. Data Acquisition

2. Data Manipulation

3. State Detection

4. Health Assessment

5. Prognostics

6. Decision Support

7. Presentation

Sensor / Transducer / Manual Entry

External systems, data archiving and

block configuration

CO

MM

ON

NET

WO

RK

Fault detection

Fault detectionand diagnosis (FDD)

FDD and prognosis

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(anomaly detection,outlier detection)

1. Background

• Fault detection

– Fault detection aims to identify defective states and

conditions within complex industrial systems, subsystems

and components

– Detect “something has gone wrong”

– From a machine learning viewpoint, it answers “yes or no”,

skewed binary classification problem

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1 Background

• Machine Learning, models are fixed once learned.

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2. Problem statement

• Curse of dimensionality– Number of training samples (exponentially increased)

– Notions like proximity, distance, neighborhood becomeless meaningful (the concentration of norms)

– Probability theory is counter-intuitive

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2. Problem statement

• Requirements from data stream– Real-time or near real-time response

– One-scan algorithms

– Concept drift

• System has time-varying characteristics due to seasonalflunctuation, equipment aging, process drifting, etc.

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3. Existing work

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• Typically, extension of existing algorithms– Exponential weighted PCA

– Sliding window PCA

– Recursive PCA

• The key is the learned model should be refined, enhanced, and personalized while stream evolves so as to accomodate the natural drift in data stream.

• Research in fault detection from high-dimensional data stream is under-explored.

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4.1 ABSAD: fault detection from high-dimensionaldata

Zhang, Liangwei, Jing Lin, and Ramin Karim. "An angle-based subspace anomaly detection approach to high-dimensional data: With an application to industrial fault detection." Reliability Engineering & System Safety 142 (2015): 482-497.

4.2 Sliding window-based ABSAD

• sliding window strategy

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1 100

101

2 3 …

Initial Model (parameters)

Window size L: 100

EvaluationEvaluation

Data stream

102 103 104 …New Model (new parameters)

• Parameters: window profile

• ”Primitive model”: initial model is built once for all

Stage 1: Offline model trainingStage 2: Online fault detection

• Model structure

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4.2 Sliding window-based ABSAD

Stage 1:Offline Model Training

Stage 2:Online Fault Detection

Data preparation

Feature normalization

Derivation of reference sets

Selection of relevant subspaces

Computation to local outlier scores

Determination of the control limit

start

Data preprocessing

Feature normalization

Derivation of the reference set

Selection of the relevant subspace

Computation to the local outlier score

Current window profile:(memory-resident data)

LOS exceeds the control limit

Samples (a matrix)

Several consecutive

faults detected

Yes

Trigger an alarm

Yes

No

Mean vector

Standard deviation

vector

k-Distance

vector

Control limit

No

Update the window profile

Sampling/Resampling

KNN list (a set of

sets)

Initialize the first window

• Computational complexity – The first stage takes the same complexity as the ABSAD

approach, O ∙max , . If some structure is employed, O log ∙max ,

– The time complexity of the second stage for processing a single sample is O ∙max , and the space complexity is O ∙max ,

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4.2 Sliding window-based ABSAD

• Numerical illustration: data– System modeled on the input-output form

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4.2 Sliding window-based ABSAD

• Numerical illustration: data– 95 fault-irrelevant dimensions were added to create a high-

dimensional setting

– 4 datasets (4 faults), 2000 by 100 matrix

– All faults were induced starting from the 1501st sample

– slow drifts were added starting from the 1001st sample

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4.2 Sliding window-based ABSAD

• Numerical illustration: results and discussion– Fault detection results on scenario 2

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4.2 Sliding window-based ABSAD

4.2 Sliding window-based ABSAD

• Numerical illustration: results and discussion

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5. Conclusion

• The sliding window-based ABSAD approach can be adaptive to the time-varying behavior of the concerned system

• The sliding window ABSAD can perform isochronously online fault detection by trading space for time.

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Acknowledgement

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Thank you!