Wind Turbine Fault Prediction

Using Soft Label SVM

Rui Zhao Md Ridwan Al Iqbal Kristin P. Bennett Qiang Ji

Contact: zhaor@rpi.edu

Introduction: Motivation

Increasing growth of wind energy consumption

High cost of maintenance and repair

Significant lost of when turbine is forced out

[1]

Diavik Diamond

Mine, Canada [1]

Introduction: Background

Forced outage: turbine shutdown due to

unexpected internal fault of the system

Three main categories of prognostics strategies [3]

Physical modeling based approach

Signal analysis based approach

Machine learning based approach

Different components

of a wind turbine [2]

Introduction: Challenges

The developing process of fault is often

unknown – No exact label information

The signature of fault is often unknown –

No single indicative feature

Different turbines may have different

symptoms and causes of fault – Significant

heterogeneity

Problem Statement: Goal

Notation:

𝑥𝑡 ∈ 𝑅𝑑 is 𝑑-dimensional feature vector at time 𝑡

𝐱𝑛𝑙 = {𝑥𝑛, … , 𝑥𝑛+𝑙−1} is a subsequence of time series

𝑦𝑛𝑙 is binary hidden label of subsequence

-1: Normal

+1: Pre-fault

Goal: learn a mapping 𝑓: 𝑦𝑛𝑙 = sign(𝑓 𝐱𝑛

𝑙 )

Major challenge: Classification without exact labels

Problem Statement:

Assumptions

Exploit the uncertainty of label information

Empirical observations: The closer the time to the

forced outage, the more likely the turbine is at pre-

fault status.

Assumptions:

Non-decreasing probability of being in pre-fault

status as time approaches the forced outage

event.

𝑃 𝑦𝑛𝑙 = 1 𝐱𝑛

𝑙 ≥ 𝑃 𝑦𝑚𝑙 = 1 𝐱𝑚

𝑙 , ∀ 𝑛 > 𝑚

For testing purpose, assume

𝑦𝑛𝑙 =−1, 𝑛 < 𝑛−

1, 𝑛 > 𝑛+

Methods: SVM

Support Vector Machines (SVM) [4] as base framework

Parameterization: 𝑦𝑛 = sign 𝑓(𝐱𝑛) ≡ sign(𝐰𝑇𝜙 𝐱𝑛 + 𝑏)

Training data: 𝑦𝑛, 𝐱𝑛 𝑛=1𝑁

Model parameters: 𝐰, 𝑏

Primal problem:

min𝐰,𝑏

1

2𝐰2+ 𝛾

𝑛=1

𝑁

𝜉𝑛

subject to 𝑦𝑛 𝐰𝑇𝜙 𝐱𝑛 + 𝑏 ≥ 1 − 𝜉𝑛,

𝜉𝑛≥ 0, 𝑛 = 1,… ,𝑁

Requires fully supervision supplied with label 𝑦𝑛

(SVM-P)

Methods: Our Approach

Soft Label Support Vector Machines (SLSVM)

Same parameterization and model parameters as SVM

𝑦𝑛 = sign 𝑓(𝐱𝑛) ≡ sign(𝐰𝑇𝜙 𝐱𝑛 + 𝑏)

Training data: 𝑢𝑛+, 𝑢𝑛−, 𝐱𝑛 𝑛=1

𝑁

𝑃 𝑦𝑛 = 1 𝐱𝑛 = 𝑢𝑛+

𝑃 𝑦𝑛 = −1 𝐱𝑛 = 𝑢𝑛−

𝑢𝑛+ + 𝑢𝑛

− = 1, 𝑛 = 1,… ,𝑁

Primal problem:

min𝐰,𝑏

1

2𝐰2+ 𝛾

𝑛=1

𝑁

(𝑢𝑛+𝜉𝑛+ + 𝑢𝑛

−𝜉𝑛−)

subject to 𝐰𝑇𝜙 𝐱𝑛 + 𝑏 ≥ 1 − 𝜉𝑛+,

−𝐰𝑇𝜙 𝐱𝑛 − 𝑏 ≥ 1 − 𝜉𝑛−

𝜉𝑛+≥ 0, 𝜉𝑛

− ≥ 0, 𝑛 = 1,… , 𝑁

(SLSVM-P)

Methods: Comparison

Illustration of slack variables

SVM SLSVM

𝑦 = −1

𝑦 = 0

𝑦 = 1𝜉 = 0

𝜉 < 1 𝜉 < 1

𝜉 > 1

𝜉 = 0

𝑦 = −1

𝑦 = 0

𝑦 = 1

𝜉+ < 1𝜉− > 1

𝜉+ > 1𝜉− < 1

𝜉+ > 1𝜉− < 1

𝜉+ = 0𝜉− > 1

𝜉+ > 1𝜉− = 0

Methods: SLSVM

Lagrangian Dual problem

max𝜶𝒏+,𝜶𝒏−

𝑛=1

𝑁

(𝛼𝑛+ + 𝛼𝑛

−) −1

2

𝑚=1

𝑁

𝑛=1

𝑁

𝛼𝑚+ − 𝛼𝑚

− 𝛼𝑛+ − 𝛼𝑛

− 𝑘(𝐱𝑚, 𝐱𝑛)

subject to 0 ≤ 𝛼𝑛+ ≤ 𝛾𝑢𝑛

+, 0 ≤ 𝛼𝑛− ≤ 𝛾𝑢𝑛

−

𝑛=1𝑁 (𝛼𝑛

+ − 𝛼𝑛−) = 0, 𝑛 = 1, … , 𝑁

Where 𝑘 𝐱𝑚, 𝐱𝑛 = 𝜙 𝐱𝑚𝑇𝜙(𝐱𝑛) is the kernel function

(SLSVM-D)

Methods: Solution

(SLSVM-D) can be solved by quadratic

programming [5]

From KKT condition, we can recover 𝐰, 𝑏

Given new data 𝐱, we can evaluate its score

𝑓 𝐱 = 𝐰𝑇𝜙 𝐱 + 𝑏 =

𝑛=1

𝑁

𝛼𝑛+ − 𝛼𝑛

− 𝑘 𝐱, 𝐱𝑛 + 𝑏

Methods: Generalized

Formulation

Generalized primal problem

min𝐰,𝑏

1

2𝐰𝑝+ 𝛾

𝑐=1

2

𝑛=1

𝑁

𝑢𝑛𝑐𝐸[𝑓 𝐱𝑛 , 𝑦𝑐]

𝑝 > 0 : order of regularization

𝑢𝑛𝑐 = 𝑃 𝑦𝑛 = 𝑦𝑐 𝐱𝑛 , 𝑦𝑐 = −1𝑐 : soft label

𝐸(𝑓 𝐱𝑛 , 𝑦𝑐) : loss function, e.g.

Hinge loss: 𝐸 = max (0,1 − 𝑦𝑐𝑓(𝐱𝑛))

Squared hinge loss: 𝐸 = max 0,1 − 𝑦𝑐𝑓 𝐱𝑛2

Squared loss: 𝐸 = 1 − 𝑦𝑐𝑓 𝐱𝑛2

Optimization: ADMM [6] for primal problem and quadratic

programming for dual problem

(SLSVM-PG)

Experiment – Data

Source: 55 channels of sensor data collected

from 125 wind turbines (GE 1.6 MW)

Granularity: data are sampled at sub-second level and averaged over 10 minutes period.

Other facts:

Time span: June 2013 to May 2014

Number of forced outages: 38

Total down time: 2350 hours

Fault related component: electrical subsystem

Experiment – Process

sensor

series

SLSVM

trainingClassification

Data pre-

processing

Feature

extraction

AUC,

feature

rank

Empirical

probability

assignment

Output: Input:

Locate

forced

outages

1. Data cleaning

2. Channel pruning

Experiment – Process

1. Customized normalization

2. Spatial feature: covariance

3. Temporal feature: autoregressive model coefficients

sensor

series

SLSVM

trainingClassification

Data pre-

processingFeature

extraction

AUC,

feature

rank

Empirical

probability

assignment

Output: Input:

Locate

forced

outages

Experiment – Process

1. Logged 38 forced outages events

2. Truncate up to 12 days prior to event

sensor

series

SLSVM

trainingClassification

Data pre-

processing

Feature

extraction

AUC,

feature

rank

Empirical

probability

assignment

Output: Input:

Locate

forced

outages

Experiment – Process

1. Linear

2. Sigmoid

3. Exponential

sensor

series

SLSVM

trainingClassification

Data pre-

processing

Feature

extraction

AUC,

feature

rank

Empirical

probability

assignment

Output: Input:

Locate

forced

outages

Experiment – Process

3 different loss functions 𝐸2 different values of regularization order 𝑝Linear kernel is used

sensor

series

SLSVM

trainingClassification

Data pre-

processing

Feature

extraction

AUC,

feature

rank

Empirical

probability

assignment

Output: Input:

Locate

forced

outages

Experiment – Process

Based on assumed

groundtruth labels

sensor

series

SLSVM

trainingClassification

Data pre-

processing

Feature

extraction

AUC,

feature

rank

Empirical

probability

assignment

Output: Input:

Locate

forced

outages

Experiment – Soft Labels

Experiment – Process

sensor

series

SLSVM

trainingClassification

Data pre-

processing

Feature

extraction

AUC,

feature

rank

Empirical

probability

assignment

Output: Input:

Locate

forced

outages

Results – Classification

Prediction quality

All soft label approach outperforms hard label approach

(standard SVM) with exponential soft label performs the best

Results – Classification

Prediction quality

All soft label approach outperforms hard label approach

(standard SVM) with exponential soft label performs the best

Extension for feature selection is considered

Results – Classification

Prediction quality

All soft label approach outperforms hard label approach

(standard SVM) with exponential soft label performs the best

Extension for feature selection is considered

Simple clustering method performs the worst

Results – Classification

Prediction horizon

Varies the prediction horizon and subsequence length

18 hours ahead achieves the highest average AUC value 0.91

Results – Feature selection

L1-norm regularized formulation for feature selection

Summary

Formalize a time-series classification problem for wind

turbine prognostics

Proposed a classification framework SLSVM that can

handle uncertainty of label information

Extend SLSVM with feature selection capability to

provide insight for prognostics

Demonstrate the effectives of SLSVM for fault

prediction on real turbine operation data

Thank you

References

[1] Global Energy Council, Global Wind Energy Report, 2016

[2] M. Schlechtingena, I. F. Santosb and S. Achichec, Wind turbine condition monitoring based on SCADA data using normal behavior models, Applied Soft Computing, 2013

[3] Z. Hameed, Y. Hong, Y. Cho, S. Ahn, and C. Song, Condition monitoring and fault detection of wind turbines and related algorithms: A review, Renewable and Sustainable Energy Reviews, 2009

[4] B. E. Boser, I. M. Guyon, and V. N. Vapnik, A training algorithm for optimal margin classifier, ACM annual workshop on Computational Learning theory, 1992

[5]S. Boyd and L. Vandenberghe, Convex Programming, Cambridge University Press, 2004

[6] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Foundations and Trends in Machine Learning, 2011

Contact: zhaor@rpi.edu

Q&A