Abstract
Incipient fault detection and diagnosis for centrifugal chillers is significant for maintaining safe and effective system operation. Due to the advantages of simple learning algorithm and high generalization capability, the extreme learning machine (ELM) can identify faults quickly and precisely in comparison to conventional classification methods such as back propagation neural network (BPNN). This paper reports an effective diagnosis method for incipient chiller faults with the integration of kernel entropy component analysis (KECA) and voting based ELM (VELM). KECA was first performed to reduce the dimensionality of the original input data so as to minimize the model complexity and computational cost. Instead of using a single ELM, multiple independent ELMs were adopted in VELM, and then the class label could be predicted based on the majority voting method. Using the experimental data of seven typical faults together with a normal operation, the proposed KECA-VELM fault diagnostic model was trained and further validated. The results show that a better fault diagnosis performance can be achieved using the KECA-VELM classifier compared with the conventional BPNN, ELM and VELM based classifiers. The overall average fault diagnosis accuracy for the faults at the least severity level was reported over 95% based on the proposed method.
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Abbreviations
- H2 :
-
Rényi quadratic entropy [bit]
- sn :
-
geometrically weighted variance
- b:
-
threshold of hidden node
- Δt:
-
time interval between measurements [s]
- K(·):
-
kernel function
- p(·):
-
probability density function
- h(·):
-
activation function
- λ:
-
eigenvalue
- σ:
-
kernel width
- ψ:
-
element Rényi entropy
- τ ss :
-
time window length [s]
- x :
-
a sample vector
- w :
-
weight vector connecting the hidden nodes and the input nodes
- β :
-
weight vector connecting the hidden nodes and the output nodes
- e :
-
eigenvector
- K :
-
kernelmatrix
- I :
-
vector of ones
- D :
-
diagonal matrix storing the eigenvalues
- E :
-
eigenvector matrix
- H :
-
hidden layer output matrix
- H † :
-
Moore-Penrose generalized inverse of H
- O :
-
output matrix
- T :
-
target output matrix
- A/C:
-
air conditioning
- AHU:
-
air handling unit
- ANN:
-
artificial neural network
- BPNN:
-
back propagation neural network
- CPV:
-
cumulative percent variance [%]
- DX:
-
direct expansion
- ELM:
-
extreme learning machine
- FDD:
-
fault detection and diagnosis
- HVAC:
-
heating, ventilation and air conditioning
- KECA:
-
kernel entropy component analysis
- PC:
-
principal component
- PCA:
-
principal component analysis
- SL:
-
severity level
- SLFN:
-
single hidden layer feedforward neural network
- SVM:
-
support vector machine
- VELM:
-
voting based extreme learning machine
- VRF:
-
variable refrigerant flow
References
IEA, The Future of Cooling in China, International Energy Agency (2019).
IEA, The Future of Cooling, International Energy Agency (2018).
M. C. Comstock, Development of analysis tools for the evaluation of fault detection and diagnostics in chillers, Purdue University (1999).
S. Katipamula and M. R. Brambley, HVAC&R Research, 11(2), 169 (2005).
S. Katipamula and M. R. Brambley, HVAC&R Research, 11(1), 3 (2005).
Y. Shin, S. W. Karng and S. Y. Kim, Int. J. Refrig., 40, 152 (2014).
L. Sun, J. Wu, H. Jia and X. Liu, Chin. J. Chem. Eng., 25(12), 1812 (2017).
C. Fan, D. Yan, F. Xiao, A. Li, J. An and X. Kang, Build. Simul.-China, 14(1), 3 (2021).
H. Han, Z. K. Cao, B. Gu and N. Ren, HVAC&R Research, 16(3), 295 (2010).
Y. Guo, Z. Tan, H. Chen, G. Li, J. Wang, R. Huang, J. Liu and T. Ahmad, Appl. Energy, 225, 732 (2018).
Y. Guo, G. Li, H. Chen, J. Wang, M. Guo, S. Sun and W. Hu, Appl. Therm. Eng., 125, 1402 (2017).
S. Li and J. Wen, Energ. Buildings, 68, 63 (2014).
K.-P. Lee, B.-H. Wu and S.-L. Peng, Build. Environ., 157, 24 (2019).
Y. Zhao, S. W. Wang and F. Xiao, Appl. Energy, 112, 1041 (2013).
G. N. Li, Y. P. Hu, H. X. Chen, L. M. Shen, H. R. Li, M. Hu, J. Liu and K. Sun, Energ. Buildings, 116, 104 (2016).
Z. W. Wang, L. Wang, K. F. Liang and Y. Y. Tan, Appl. Therm. Eng., 141, 898 (2018).
Z. Du, X. Jin and Y. Yang, Appl. Energy, 86(9), 1624 (2009).
Z. Du, B. Fan, X. Jin and J. Chi, Build. Environ., 73, 1 (2014).
C. C. Chang and C. J. Lin, ACM Trans. Intell. Syst. Technol., 2(3), 1 (2011).
J. Liang and R. Du, Int. J. Refrig., 30(6), 1104 (2007).
H. Han, B. Gu, J. Kang and Z. R. Li, Appl. Therm. Eng., 31(4), 582 (2011).
K. Yan, W. Shen, T. Mulumba and A. Afshari, Energ. Buildings, 81, 287 (2014).
R. Huang, J. Liu, H. Chen, Z. Li, J. Liu, G. Li, Y. Guo and J. Wang, Appl. Therm. Eng., 136, 633 (2018).
G.-B. Huang, Q.-Y. Zhu and C.-K. Siew, Neurocomputing, 70(1), 489 (2006).
G. Huang, H. Zhou, X. Ding and R. Zhang, IEEE T. Syst. Man Cy. B, 42(2), 513 (2012).
W. Zong and G.-B. Huang, Neurocomputing, 74(16), 2541 (2011).
A. A. Mohammed, R. Minhas, Q. J. Hu and M. A. Sid-Ahmed, Pattern Recogn., 44(10), 2588 (2011).
Y. Xu, Y. Dai, Z. Y. Dong, R. Zhang and K. Meng, Neural Comput. Appl., 22(3), 501 (2013).
M. Zhang, X. Liu and Z. Zhang, Chin. J. Chem. Eng., 24(8), 1013 (2016).
S. Haidong, J. Hongkai, L. Xingqiu and W. Shuaipeng, Knowl. Based Syst., 140, 1 (2018).
Z. Chen, L. Wu, S. Cheng, P. Lin, Y. Wu and W. Lin, Appl. Energy, 204, 912 (2017).
J. Cao, Z. Lin, G.-B. Huang and N. Liu, Inf. Sci., 185(1), 66 (2012).
Y. Chen and L. Lan, Energ. Buildings, 41(8), 881 (2009).
Z. M. Du, X. Q. Jin and L. Z. Wu, Build. Environ., 42(9), 3221 (2007).
X. Yu, J. Wu and Y. Gao, CIESC J., 71(7), 3151 (2020).
R. Jenssen, IEEE Trans. Pattern Anal. Mach. Intell., 32(5), 847 (2010).
Y. Xia, Q. Ding, Z. Li and A. Jiang, Build. Simul.- China, 14(1), 53 (2021).
L. Bai, Z. Han, J. Ren and X. Qin, Appl. Soft Comput., 92, 106245 (2020).
A. Rényi, On measures of entropy and information, In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics. The Regents of the University of California (1961).
E. Parzen, Ann. Math. Statis, 33(3), 1065 (1962).
R. Jenssen, T. Eltoft, M. Girolami and D. Erdogmus, Kernel maximum entropy data transformation and an enhanced spectral clustering algorithm, in Conference on Advances in Neural Information Processing Systems (2006).
D. Serre, Matrices: Theory and applications, Second edition, New York, Springer (2010).
Acknowledgements
The financial supports for the Natural Science Foundation of Zhejiang Province (Project No. LQ19E060007 and No. LY20F030010) and The Science and Technology Project of Zhejiang Province (Project No. LGG21F030009) are gratefully acknowledged.
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Xia, Y., Ding, Q., Jiang, A. et al. Incipient fault diagnosis for centrifugal chillers using kernel entropy component analysis and voting based extreme learning machine. Korean J. Chem. Eng. 39, 504–514 (2022). https://doi.org/10.1007/s11814-021-0864-7
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DOI: https://doi.org/10.1007/s11814-021-0864-7