Voting-based fault detection and diagnosis in systems with multiple - PowerPoint PPT Presentation

Voting-based Fault Diagnosis Recalculation of fault directions Rescale models: � X j V j + m j ( b j − b k )( b j − b k ) T � X T ¯ jk ¯ X jk = V − 1 V j ¯ X T j ¯ V − 1 k k x 2 State 2 State 3 State 1 x 1 26 / 39

Voting-based Fault Diagnosis Recalculation of fault directions Rescale models: � X j V j + m j ( b j − b k )( b j − b k ) T � X T ¯ jk ¯ X jk = V − 1 V j ¯ X T j ¯ V − 1 k k x ′ x 2 2 State 2 Extract fault direction for each State j : ◮ SVD on ¯ X T jk ¯ X jk ◮ Select initial   State 3 ◮ Calculate Q  ◮ Iterate until x ′ X T tr { Q  ¯ jk ¯ X jk } < qζ 2 1 State 1 x 1 26 / 39

Voting-based Fault Diagnosis Recalculation of fault directions Rescale models: � X j V j + m j ( b j − b k )( b j − b k ) T � X T ¯ jk ¯ X jk = V − 1 V j ¯ X T j ¯ V − 1 k k x ′ x 2 2 State 2 Extract fault direction for each State j : ◮ SVD on ¯ X T jk ¯ X jk  2 ◮ Select initial   State 3 ◮ Calculate Q  ◮ Iterate until x ′ X T  1 tr { Q  ¯ jk ¯ X jk } < qζ 2 1 State 1 x 1 26 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3  1 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3  1 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3  2 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3  2 3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3 3 2 State 1  3 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3 4 3 2 State 1  3 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2  4 State 3 4 3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2  4 State 3 4 5 3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3 4 5 3 2  5 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3 6 4 5 3 2  5 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3 6 4 5 3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 State 3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5  4 State 2  2 State 3  5  1  3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 3 5 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 6 3 5 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5  4 State 2 1  2 State 3 4  5  1  3 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 5 1 State 3 4 4 2 6 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 2 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4  4  2  3 2  5  1 State 1 State 4 State 6 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 6 1 2 5 State 1 State 4 State 6 2 3 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 2 State 1 State 4 State 6 2 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5  2 State 2  3 1 State 3 4  4  5  1 2 State 1 State 4 State 6 2 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis 1 3 4 State 5 State 2 2 1 State 3 4 6 2 State 1 State 4 State 6 2 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 2 State 1 State 4 State 6 2 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4  5  2  3 2  4  1 State 1 State 4 State 6 2 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 4 1 2 State 1 State 4 State 6 2 2 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis State 5 State 2 1 State 3 4 2 State 1 State 4 State 6 2 2 27 / 39

Voting-based Fault Diagnosis Voting-based Diagnosis ◮ Count how many times each state was identified. ◮ Select state with most votes � 1 , if d K = S j V K j = 0 , otherwise J � V T V K j = j K = 1 S d V T j =  rg mx j j ∈ [ 1 , J + 1 ] 28 / 39

Chiller simulation Outline Introduction 1 Fault detection and diagnosis with PCA 2 Voting-based Fault Diagnosis 3 4 Chiller simulation 5 Conclusions 29 / 39

Chiller simulation Centrifugal chiller 30 / 39

Chiller simulation Monitored variables Number ID Description Units 1 Condenser water flow rate F c kg/s 2 F r Refrigerant charge kg 3 F e Evaporator water flow rate kg/s 4 T cr Condenser inlet refrigerant temperature K m 2 5 A  Valve position 6 P e Evaporator pressure Pa 7 P c Condenser pressure Pa 8 W com Compressor power Watts 9 T eo Evaporator outlet water temperature K 10 T co Condenser outlet water temperature K 11 T e Evaporator inlet water temperature K 12 T c Condenser inlet water temperature K 13 T eor Evaporator outlet refrigerant temperature K 14 T cor Condenser outlet refrigerant temperature K 15 T er Evaporator inlet refrigerant temperature K 31 / 39