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Voting-based fault detection and diagnosis in systems with multiple operating conditions Carlos F . Alcala Controls Research Group May 18, 2016 1 / 39 Outline Introduction 1 Fault detection and diagnosis with PCA 2 Voting-based Fault

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SLIDE 1

Voting-based fault detection and diagnosis in systems with multiple operating conditions

Carlos F . Alcala

Controls Research Group

May 18, 2016

1 / 39

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SLIDE 2

Outline

1

Introduction

2

Fault detection and diagnosis with PCA

3

Voting-based Fault Diagnosis

4

Chiller simulation

5

Conclusions

2 / 39

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SLIDE 3

Introduction

Outline

1

Introduction

2

Fault detection and diagnosis with PCA

3

Voting-based Fault Diagnosis

4

Chiller simulation

5

Conclusions

3 / 39

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SLIDE 4

Introduction

JCI Chillers

4 / 39

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SLIDE 5

Introduction

Chiller Operation Cost

5 / 39

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SLIDE 6

Introduction

HVAC Service Market

6 / 39

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SLIDE 7

Introduction

Connected Chillers

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SLIDE 8

Introduction

Data-Driven FDD

2 4 6 x1 0 20 40 60 80100 2 4 6 Sample x2

Measured variables

8 / 39

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SLIDE 9

Introduction

Data-Driven FDD

2 4 6 x1 0 20 40 60 80100 2 4 6 Sample x2

x1 x2

Measured variables

8 / 39

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SLIDE 10

Introduction

Data-Driven FDD

2 4 6 x1 0 20 40 60 80100 2 4 6 Sample x2

x1 x2

Measured variables PCA model

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SLIDE 11

Introduction

Chiller Data - Time Series

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SLIDE 12

Introduction

Chiller Data - Three Loads

10 / 39

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SLIDE 13

Introduction

Chiller Data - Principal Component Space

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SLIDE 14

Introduction

Chiller Data - Principal Component Space

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SLIDE 15

Introduction

FDD - Single normal model

Normal 1

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SLIDE 16

Introduction

FDD - Single normal model

Normal 1 Fault1 N1

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SLIDE 17

Introduction

FDD - Single normal model

Normal 1 Fault1 N1 Fault2 N1

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SLIDE 18

Introduction

FDD - Single normal model

Normal 1 Fault1 N1 Fault2 N1 Normal 2

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SLIDE 19

Introduction

FDD - Single normal model

Normal 1 Fault1 N1 Fault2 N1 Normal 2 Fault1 N2

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SLIDE 20

Introduction

FDD - Single normal model

Normal 1 Fault1 N1 Fault2 N1 Normal 2 Fault1 N2 Fault2 N2

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SLIDE 21

Introduction

FDD - T wo normal models

Normal 1 Fault1 N1 Fault2 N1 Normal 2

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SLIDE 22

Introduction

FDD - T wo normal models

Normal 1 Fault1 N1 Fault2 N1 Normal 2 Fault1 N2 Fault2 N2

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SLIDE 23

Introduction

FDD - Multiple normal models

Normal 1 Fault1 N1 Fault2 N1 Normal 2

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SLIDE 24

Introduction

FDD - Multiple normal models

Normal 2 Normal 1 Fault1 N1 Fault2 N1

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SLIDE 25

Introduction

FDD - Multiple normal models

Normal 2 Normal 1 Fault1 N1 Fault2 N1 Fault1 N2 Fault2 N2

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SLIDE 26

Introduction

FDD - Multiple normal models

Normal 1 Normal 2 Fault1 N1 Fault2 N1 Fault1 N2 Fault2 N2

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SLIDE 27

Introduction

FDD - Multiple normal models

Normal 1 Fault1 N1 Fault2 N1 Normal 2 Fault1 N2 Fault2 N2

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SLIDE 28

Introduction

FDD - Multiple states

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 29

Introduction

FDD - Multiple states

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 30

Introduction

FDD - Multiple states

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 31

Introduction

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 32

Introduction

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 33

Introduction

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 34

Introduction

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 35

Introduction

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 36

Introduction

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 37

Fault detection and diagnosis with PCA

Outline

1

Introduction

2

Fault detection and diagnosis with PCA

3

Voting-based Fault Diagnosis

4

Chiller simulation

5

Conclusions

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SLIDE 38

Fault detection and diagnosis with PCA

Data sampling

x =

  • x1

x2

  • Time 

x1 x2 x

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SLIDE 39

Fault detection and diagnosis with PCA

Data sampling

x =

  • x1

x2

  • Time 

      t1 x1,1 x2,1 t2 x1,2 x2,2 . . . . . . . . . tm x1,m x2,m       = X X = [x1 x2 · · · xm]T

x1 x2

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SLIDE 40

Fault detection and diagnosis with PCA

Data scaling

b = 1 m

m

  • =1

x = 1 m XT1m S = 1 m − 1

  • XTX − mbbT

V = (diag (S))

1 2

x1 x2 b

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SLIDE 41

Fault detection and diagnosis with PCA

Data scaling

b = 1 m

m

  • =1

x = 1 m XT1m S = 1 m − 1

  • XTX − mbbT

V = (diag (S))

1 2

¯ X =

  • X − 1mbT

V−1

x1 x2 b x′

1

x′

2 19 / 39

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SLIDE 42

Fault detection and diagnosis with PCA

Data scaling

b = 1 m

m

  • =1

x = 1 m XT1m S = 1 m − 1

  • XTX − mbbT

V = (diag (S))

1 2

¯ X =

  • X − 1mbT

V−1

x1 x2 b x ¯ x = V−1 (x − b) x′

1

x′

2 19 / 39

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SLIDE 43

Fault detection and diagnosis with PCA

PCA modeling

¯ S = 1 m − 1 ¯ XT ¯ X

x′

1

x′

2 20 / 39

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SLIDE 44

Fault detection and diagnosis with PCA

PCA modeling

¯ S = 1 m − 1 ¯ XT ¯ X ¯ S = PΛPT + ˜ P ˜ Λ ˜ PT

x′

1

x′

2

P ˜ P

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SLIDE 45

Fault detection and diagnosis with PCA

PCA modeling

¯ S = 1 m − 1 ¯ XT ¯ X ¯ S = PΛPT + ˜ P ˜ Λ ˜ PT M = PΛ−1PT τ2 + ˜ P ˜ PT δ2 ζ2 = gzχ2

α(hz)

x′

1

x′

2

P ˜ P ζ2

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SLIDE 46

Fault detection and diagnosis with PCA

Fault detection

nde(x) = xTMx

x′

1

x′

2

ζ2 x

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SLIDE 47

Fault detection and diagnosis with PCA

Fault detection

nde(x) = xTMx Fault nde(x) > ζ2 Not fault nde(x) ≤ ζ2

x′

1

x′

2

ζ2 Not fault Fault

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SLIDE 48

Fault detection and diagnosis with PCA

Fault diagnosis

Faulty measurement x = x∗ + f

x′

1

x′

2

x x∗ f

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SLIDE 49

Fault detection and diagnosis with PCA

Fault diagnosis

Faulty measurement x = x∗ + f Reconstruction nde(zj) = xTQjx Q = M − Mj

  • T

j Mj

−1 T

j M

x′

1

x′

2

x 1 z1 2 z2

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SLIDE 50

Fault detection and diagnosis with PCA

Fault diagnosis

Faulty measurement x = x∗ + f Reconstruction nde(zj) = xTQjx Q = M − Mj

  • T

j Mj

−1 T

j M

Fault is in x1 since nde(z1) ≤ ζ2

x′

1

x′

2

x 1 z1 2 z2

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SLIDE 51

Fault detection and diagnosis with PCA

Extraction of fault direction

Scaling: ¯ Xƒ =

  • Xƒ − 1qbT

V−1 SVD: ¯ XT

ƒ ¯

Xƒ = LƒD2

ƒ LT ƒ

Lƒ = [l1 l2 · · · ln] Select: j = l1, j = 1; Calculate Qj

While tr

  • Qj ¯

XT

ƒ ¯

Xƒ

  • > qζ2

j+1 = [j lj+1] Calculate Qj+1 j = j + 1 Normal x′

1

x′

2

Fault ƒ ƒ ¯ Xƒ

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SLIDE 52

Voting-based Fault Diagnosis

Outline

1

Introduction

2

Fault detection and diagnosis with PCA

3

Voting-based Fault Diagnosis

4

Chiller simulation

5

Conclusions

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SLIDE 53

Voting-based Fault Diagnosis

Building the state library

Data sampling: X

x1 x2

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SLIDE 54

Voting-based Fault Diagnosis

Building the state library

Data sampling: X PCA modeling: b, V, ¯ XT

ƒ ¯

Xƒ, M, ζ2, m

x1 x2

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SLIDE 55

Voting-based Fault Diagnosis

Building the state library

Data sampling: X PCA modeling: b, V, ¯ XT

ƒ ¯

Xƒ, M, ζ2, m PCA monitoring:

x1 x2 Normal 1

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SLIDE 56

Voting-based Fault Diagnosis

Building the state library

Data sampling: X PCA modeling: b, V, ¯ XT

ƒ ¯

Xƒ, M, ζ2, m PCA monitoring:

◮ Detection ◮ Diagnosis

◮ Reconstruction,

  • r

◮ Engineer is

needed to determine nature of fault x1 x2 Normal 1

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SLIDE 57

Voting-based Fault Diagnosis

Building the state library

Data sampling: X PCA modeling: b, V, ¯ XT

ƒ ¯

Xƒ, M, ζ2, m PCA monitoring:

◮ Detection ◮ Diagnosis

◮ Reconstruction,

  • r

◮ Engineer is

needed to determine nature of fault x1 x2 Normal 1

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SLIDE 58

Voting-based Fault Diagnosis

Building the state library

Data sampling: X PCA modeling: b, V, ¯ XT

ƒ ¯

Xƒ, M, ζ2, m PCA monitoring:

◮ Detection ◮ Diagnosis

◮ Reconstruction,

  • r

◮ Engineer is

needed to determine nature of fault x1 x2 Normal 1 Fault N1

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SLIDE 59

Voting-based Fault Diagnosis

Building the state library

Data sampling: X PCA modeling: b, V, ¯ XT

ƒ ¯

Xƒ, M, ζ2, m PCA monitoring:

◮ Detection ◮ Diagnosis

◮ Reconstruction,

  • r

◮ Engineer is

needed to determine nature of fault x1 x2 Normal 1 Fault N1

25 / 39

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SLIDE 60

Voting-based Fault Diagnosis

Building the state library

Data sampling: X PCA modeling: b, V, ¯ XT

ƒ ¯

Xƒ, M, ζ2, m PCA monitoring:

◮ Detection ◮ Diagnosis

◮ Reconstruction,

  • r

◮ Engineer is

needed to determine nature of fault x1 x2 Normal 1 Fault N1

25 / 39

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SLIDE 61

Voting-based Fault Diagnosis

Building the state library

Data sampling: X PCA modeling: b, V, ¯ XT

ƒ ¯

Xƒ, M, ζ2, m PCA monitoring:

◮ Detection ◮ Diagnosis

◮ Reconstruction,

  • r

◮ Engineer is

needed to determine nature of fault x1 x2 Normal 1 Fault N1 Normal 2

25 / 39

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SLIDE 62

Voting-based Fault Diagnosis

Recalculation of fault directions

Rescale models: ¯ XT

jk ¯

Xjk = V−1

k

  • Vj ¯

XT

j ¯

XjVj + mj(bj − bk)(bj − bk)T V−1

k x1 x2 State 1 State 2 State 3

26 / 39

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SLIDE 63

Voting-based Fault Diagnosis

Recalculation of fault directions

Rescale models: ¯ XT

jk ¯

Xjk = V−1

k

  • Vj ¯

XT

j ¯

XjVj + mj(bj − bk)(bj − bk)T V−1

k

Extract fault direction for each State j:

◮ SVD on ¯

XT

jk ¯

Xjk

◮ Select initial  ◮ Calculate Q ◮ Iterate until

tr{Q ¯ XT

jk ¯

Xjk} < qζ2

x1 x2 State 1 State 2 State 3 x′

1

x′

2 26 / 39

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SLIDE 64

Voting-based Fault Diagnosis

Recalculation of fault directions

Rescale models: ¯ XT

jk ¯

Xjk = V−1

k

  • Vj ¯

XT

j ¯

XjVj + mj(bj − bk)(bj − bk)T V−1

k

Extract fault direction for each State j:

◮ SVD on ¯

XT

jk ¯

Xjk

◮ Select initial  ◮ Calculate Q ◮ Iterate until

tr{Q ¯ XT

jk ¯

Xjk} < qζ2

x1 x2 State 1 State 2 State 3 x′

1

x′

2

1 2

26 / 39

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SLIDE 65

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6

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SLIDE 66

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 1

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SLIDE 67

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 1 2

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SLIDE 68

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 2

27 / 39

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SLIDE 69

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 2 3

27 / 39

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SLIDE 70

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 3 3

27 / 39

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SLIDE 71

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 3 3 4

27 / 39

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SLIDE 72

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 3 4 4

27 / 39

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SLIDE 73

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 3 4 4 5

27 / 39

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SLIDE 74

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 3 4 5 5

27 / 39

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SLIDE 75

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 3 4 5 5 6

27 / 39

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SLIDE 76

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 3 4 5 6

27 / 39

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SLIDE 77

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2

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SLIDE 78

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 2 3 4 5

27 / 39

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SLIDE 79

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1

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SLIDE 80

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 3

27 / 39

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SLIDE 81

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 3 4

27 / 39

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SLIDE 82

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 3 4 5

27 / 39

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SLIDE 83

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 3 4 5 6

27 / 39

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SLIDE 84

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4

27 / 39

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SLIDE 85

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 1 2 3 4 5

27 / 39

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SLIDE 86

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 1 2 4 5 6

27 / 39

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SLIDE 87

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4

27 / 39

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SLIDE 88

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 1 2 3 4 5

27 / 39

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SLIDE 89

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 1 2 3 5 6

27 / 39

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SLIDE 90

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 2

27 / 39

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SLIDE 91

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 2 1 2 3 4 5

27 / 39

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SLIDE 92

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 2 1 2 3 4 6

27 / 39

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SLIDE 93

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 2

27 / 39

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SLIDE 94

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 2 1 2 3 4 5

27 / 39

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SLIDE 95

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 2 1 2 4

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SLIDE 96

Voting-based Fault Diagnosis

Voting-based Diagnosis

State 1 State 2 State 3 State 4 State 5 State 6 2 1 4 2 2

27 / 39

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SLIDE 97

Voting-based Fault Diagnosis

Voting-based Diagnosis

◮ Count how many times each state was identified. ◮ Select state with most votes

VK

j =

  • 1,

if dK = Sj 0,

  • therwise

VT

j = J

  • K=1

VK

j

Sd

j = rg mx j∈[1, J+1]

VT

j

28 / 39

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SLIDE 98

Chiller simulation

Outline

1

Introduction

2

Fault detection and diagnosis with PCA

3

Voting-based Fault Diagnosis

4

Chiller simulation

5

Conclusions

29 / 39

slide-99
SLIDE 99

Chiller simulation

Centrifugal chiller

30 / 39

slide-100
SLIDE 100

Chiller simulation

Monitored variables

Number ID Description Units 1 Fc Condenser water flow rate kg/s 2 Fr Refrigerant charge kg 3 Fe Evaporator water flow rate kg/s 4 Tcr Condenser inlet refrigerant temperature K 5 A Valve position m2 6 Pe Evaporator pressure Pa 7 Pc Condenser pressure Pa 8 Wcom Compressor power Watts 9 Teo Evaporator outlet water temperature K 10 Tco Condenser outlet water temperature K 11 Te Evaporator inlet water temperature K 12 Tc Condenser inlet water temperature K 13 Teor Evaporator outlet refrigerant temperature K 14 Tcor Condenser outlet refrigerant temperature K 15 Ter Evaporator inlet refrigerant temperature K

31 / 39

slide-101
SLIDE 101

Chiller simulation

Simulated faults and loads

Fault type Affected variable Value change (%) Leak in condenser water flow Fc 0, 10, 20, 30, 40 Leak in refrigerant flow Fr 0, 10, 20, 30, 40 Leak in evaporator water flow Fe 0, 10, 20, 30, 40

Load type Te (K) Te (F) Low 280 44 Medium 282 48 High 284 52

32 / 39

slide-102
SLIDE 102

Chiller simulation

Simulated states

T ype Reduction percent State ID Fc Fr Fe Load Low Medium High Normal 13 26 Faulty 10 1 14 27 20 2 15 28 30 3 16 29 40 4 17 30 10 5 18 31 20 6 19 32 30 7 20 33 40 8 21 34 10 9 22 35 20 10 23 36 30 11 24 37 40 12 25 38

33 / 39

slide-103
SLIDE 103

Chiller simulation

Chiller data

Leak in condenser water. Low load.

10 20 30 40 50 −6 −4 −2 2 4 PC1 PC2

State 0 State 1 State 2 State 3 State 4 34 / 39

slide-104
SLIDE 104

Chiller simulation

Chiller data

Leak in condenser water. All loads.

20 40 60 80 100 120 140 −10 −5 5 PC1 PC2

State 0 State 1 State 2 State 3 State 4 State 13 State 14 State 15 State 16 State 17 State 26 State 27 State 28 State 29 State 30 35 / 39

slide-105
SLIDE 105

Chiller simulation

Diagnosis Results

1 3 6 9 12 15 18 21 24 27 30 33 36 39 40 1 3 6 9 12 15 18 21 24 27 30 33 36 39

Actual State ID Identified State ID

Rate (%) 25 50 75 Method multiVoting singleFixed Fault Type Normal Fc Fr Fe Load high medium low

36 / 39

slide-106
SLIDE 106

Chiller simulation

Rate of correct diagnosis

condenserWater evaporatorWater refrigerant 25 50 75 100 25 50 75 100 25 50 75 100 high medium low 10 20 30 40 10 20 30 40 10 20 30 40

Leak level (%) Diagnosis rate (%)

method: multiVoting singleFixed

37 / 39

slide-107
SLIDE 107

Conclusions

Outline

1

Introduction

2

Fault detection and diagnosis with PCA

3

Voting-based Fault Diagnosis

4

Chiller simulation

5

Conclusions

38 / 39

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SLIDE 108

Conclusions

Conclusions

◮ Any state can be used to perform FDD ◮ Fault directions can be recalculated from any

state

◮ All states vote to perform diagnosis ◮ Proposed method has a larger rate of correct

diagnosis than the traditional PCA method

39 / 39