1. School of Information Science and Engineering, Central South University, Changsha 410083, China 2. School of Metallurgy and Environment, Central South University, Changsha 410083, China
Root cause analysis (RCA) of abnormal aluminum electrolysis cell condition has long been a challenging industrial issue due to its inherent complexity in analyzing based on multi-source knowledge. In addition, accurate RCA of abnormal aluminum electrolysis cell condition is the precondition of improving current efficiency. RCA of abnormal condition is a complex work of multi-source knowledge fusion, which is difficult to ensure the RCA accuracy of abnormal cell condition because of dwindling and frequent flow of experienced technicians. In view of this, a method based on Fuzzy-Bayesian network to construct multi-source knowledge solidification reasoning model is proposed. The method can effectively fuse and solidify the knowledge, which is used to analyze the cause of abnormal condition by technicians providing a clear and intuitive framework to this complex task, and also achieve the result of root cause automatically. The proposed method was verified under 20 sets of abnormal cell conditions, and implements root cause analysis by finding the abnormal state of root node, which has a maximum posterior probability by Bayesian diagnosis reasoning. The accuracy of the test results is up to 95%, which shows that the knowledge reasoning feasibility for RCA of aluminum electrolysis cell.
◆ The height of aluminum molten. Suitable AL is able to maintain energy balance of the electrolytic cell and cell voltage stability.
Cell voltage ( CV)
◆ The suitable voltage to maintain the normal condition of cell is the source of heat of electrolysis, the most important means to regulate the energy balance of cell.
Molecular ratio ( MR)
◆ Affecting the solubility of alumina in the electrolyte and the primary crystal temperature is the main means to regulate the energy balance of cell.
Electrolyte level ( EL)
◆ Maintain the thermal stability and sensitivity of cell, the energy balance is robust with suitable EL when energy balance is disturbed, and EL affects effect coefficient and alumina solubility.
Feeding interval ( NB)
◆ The change of NB interval has influence on primary crystal temperature, superheat degree, furnace type and bottom sediment.
Voltage vibration ( VV)
◆ Vibration of voltage is the performance of the abnormal stability of cell.
Bath temperature ( BT)
◆ Affect the entire operation condition of cell.
Superheat degree ( SD)
◆ The difference value between the electrolyte temperature and the primary crystal temperature is a comprehensive reflection of the technical indicators for cell.
Flame color ( FC)
◆ Parameters can reflect the cell condition, and provide visual information for technologist.
Flame intensity ( FI)
Bath color ( BC)
Bath status ( BS)
Ledge length ( LL)
◆ LL has great influence on safe and stable operation of cell. What’s more, suitableLL is able to prevent leakage of cell and satisfied the need of superheat degree.
Side thickness ( HT)
◆ HT plays the role of insulation and insulation. It has a greater impact on energy balance because of reducing energy loss, and it’s the self-balancing bridge of cell.
Bottom sediment ( CS)
◆ CS caused by the lower superheat degree, and it has influence on bottom voltage and stability of cell.
Effect coefficient ( EC)
◆ Frequency of the anode effect occurs.
Bottom voltage ( BV)
◆ BV can reflect status of bottom crusting and bottom temperature.
Tab.1
Operating parameter
The influence of operating parameters each state
NB
◆ NB makes a difference to effect coefficient, the NB being large, likely to cause low alumina concentration, resulting in an anode effect. ◆ The alumina will not be complete fusion with small NB, and the alumina of no melt descend to the bottom of cell, which are easy to be sludge.
AL
◆ More energy will loss from cell bottom with high AL, and also the phenomena of temperature decreasing, bottom sludge being more, side ledge being thick will appear ◆ The phenomena of deep immersion in the bath of anode, bath temperature rising, the role of horizontal magnetic field increasing will cause the aluminum liquid in the tank by, prone to voltage swing phenomenon will occur, if aluminum molten level was low.
CV
◆ The phenomena of bath temperature and superheat degree reducing, flame color being blue and white, flame intensity being weak, bath color being red, boiling hard and longer ledge will appear, if CV was low. ◆ The phenomena of bath temperature increment, superheat degree and alumina concentration increasing, flame color being yellow, flame intensity being weak, bath color being highlight, fluidity of bath being quick, ledge being smaller, bottom sediment being more and side ledge being thinner will appear, ifCV was high.
MR
◆ If MR was low, alumina solubility will decrease which will be conducive to the precipitation of aluminum from bath with higher surface tension, and the electrolysis temperature will be lower with the chance of secondary oxidation of aluminum reduce, moreover, the amount of sodium precipitation decreased. ◆ If MR was high, the phenomena will appear which contain primary crystal temperature increasing, superheat degree being smaller, side ledge being thicker, superheat being higher.
EL
◆ The high EL will result in gas discharge difficult, and the chance of anode spikes appearance will increase, what’s more, bath boiling will be difficult, resistance increase, the effect coefficient increase. ◆ The low EL will result in energy stability being poor and it’s sensitive to heat changes, and easy to generate precipitation and produce anode effects.
Tab.2
Fig.2
Fig.3
Fig.4
Fig.5
Child node name
State of child node name
FC
Blue white ( FCB)
Lavender ( FCL)
Yellow ( FCY)
FI
Weak ( FIW)
Normal ( FIN)
BC
Red ( BCR)
Red yellow ( BCRY)
Highlight ( BCH)
BS
Hard ( BSH)
Equably ( BSE)
Fiercely ( BSF)
CS
Normal ( CSN)
Seriously ( CSS)
Very serious ( CSV)
Tab.3
Root node name
Prior probability of each state of root node
AL
ALL
ALN
ALH
(0.04,0.05,0.06)
(0.87,0.88,0.89)
(0.06,0.07,0.08)
0.05
0.88
0.07
CV
CVL
CVN
CVH
(0.08,0.09,0.1)
(0.84,0.85,0.86)
(0.05,0.06,0.07)
0.09
0.85
0.06
MR
MRL
MRN
MRH
(0.09,0.1,0.11)
(0.81,0.82,0.83)
(0.07,0.07,0.09)
0.1
0.82
0.08
EL
ELL
ELN
ELH
(0.02,0.03,0.04)
(0.91,0.92,0.93)
(0.04,0.05,0.06)
0.03
0.92
0.05
NB
NBS
NBN
NBL
(0.05,0.06,0.07)
(0.89,0.9,0.91)
(0.03,0.04,0.05)
0.06
0.9
0.04
Tab.4
Variable states
The prior probability of each state of child nodes??
ALL
ALN
ALH
CVL
CVN
CVH
CVL
CVN
CVH
CVL
CVN
CVH
VVN
0
0
0.05
0.15
0.96
0.85
0.11
0.16
0.7
VVS
0.05
0.25
0.4
0.66
0.04
0.15
0.18
0.3
0.24
VVV
0.95
0.75
0.55
0.19
0
0
0.71
0.54
0.06
Tab.5
// Initialization // Input: ?BN: a fuzzy-Bayesian network
? Ei: the evidence of ith node of abnormal cell condition
? sij: the jth state of ith node
? N: the number of nodes
? M: the number of root nodes
? n: the group of abnormal cell conditions
?node_sizes: the set of state sizes of each node
?for groupth = 1: n // groupth is the number of conditions
???for i= 1: N
????? si = TFN (Ei); // the states si of Ei divided by experienced experts ?????with Triangular fuzzy number
????? P(sij) = Defuzzification(sij); // according to experienced knowledge ?????and data knowledge
???end
???for i= 1: N
?????dag( Ei, Ei+k) = true; // the directed line of the the ith node to (i+k)?????th node is added based on the process knowledge
???end
???node_sizes= [ ]; the set of numbers of states of each node
???Bnet= mk_bnet (dag, node_sizes);
???bnet.CPD{ Ei} = tabular_CPD (bnet, Ei, P(si )); // P(si) the set of prior ????probability of ith node’s states
???Engine= jtree_inf_engine (bnet); // joint tree inference engine
???[engine,[]] = enter_evidence (engine, E); // adding evidence to model
???for Mth= 1: M
?????Marg= marginal_nodes (engine, sMth); // Marginal probability ?????calculation of Mthth root nodes
?????Marg. T;
?????P( Mth) = max(Marg. T(1), Marg. T(3)); // the maximum posterior ?????probability of root node’s
?????p(sMthj| E) = max(P(Mth), P(Mth-1)); // the jth state of Mthth root ?????node is the root cause for groupthth cell condition
???end
?end
// Output: Root cause
???The estimation of maximum posterior probability of each group ???condition .
Tab.6
Fig.6
Group
Corresponding state of the variables
VV
BT
BT
EC
BS
LL
HT
BV
FC
FI
BC
CS
1
VVV
BTN
SDN
ECN
BSE
LLN
HTN
BVN
FCL
FIN
BCRY
CSN
2
VVN
BTN
SDN
ECH
BSE
LLN
HTNa
BVN
FCL
FIN
BCRY
CSN
3
VVN
BTN
SDN
ECH
BSE
LLN
HTN
BVH
FCL
FIN
BCRY
CSV
4
VVN
BTL
SDL
ECN
BSH
LLN
HTN
BVH
FCB
FIW
BCR
CSS
5
VVN
BTN
SDL
ECN
BSH
LLN
HTN
BVH
FCB
FIW
BCR
CSS
6
VVV
BTL
SDN
ECN
BSE
LLN
HTN
BVN
FCL
FIN
BCRY
CSN
7
VVN
BTH
SDH
ECN
BSF
LLS
HTNa
BVN
FCY
FIW
BCH
CSN
8
VVN
BTN
SDH
ECN
BSF
LLS
HTNa
BVS
FCY
FIW
BCH
CSN
9
VVV
BTN
SDL
ECH
BSE
LLL
HTT
BVN
FCL
FIN
BCRY
CSN
10
VVN
BTN
SDN
ECH
BSE
LLL
HTT
BVH
FCL
FIN
BCRY
CSN
11
VVN
BTL
SDH
ECN
BSF
LLS
HTNa
BVN
FCB
FIW
BCH
CSN
12
VVN
BTN
SDL
ECH
BSH
LLL
HTT
BVH
FCB
FIW
BCR
CSS
13
VVV
BTL
SDN
ECH
BSH
LLN
HTN
BVN
FCB
FIW
BCR
CSN
14
VVN
BTN
SDH
ECN
BSE
LLN
HTN
BVN
FCY
FIW
BCRY
CSS
15
VVN
BTN
SDL
ECN
BSH
LLN
HTN
BVH
FCL
FIN
BCR
CSV
16
VVS
BTL
SDL
ECN
BSE
LLN
HTN
BVH
FCB
FIW
BCRY
CSV
17
VVN
BTL
SDN
ECN
BSE
LLL
HTT
BVH
FCL
FIN
BCRY
CSV
18
VVN
BTH
SDH
ECN
BSF
LLN
HTN
BVN
FCY
FIW
BCH
CSN
19
VVS
BTN
SDL
ECN
BSE
LLL
HTT
BVN
FCB
FIN
BCR
CSN
20
VVV
BTN
SDH
ECN
BSF
LLS
HTNa
BVN
FCY
FIW
BCH
CSN
Tab.7
Variables
state
Group number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
AL
Low
0.5075
0
0
0
0
0.252
0.0038
0.0001
0.0273
0
0
0
0.254
0.0002
0
0.0028
0
0.0038
0.0059
0.986
High
0.48
0.003
0.004
0.112
0.14
0.407
0.0072
0.0021
0.887
0.003
0.003
0.053
0.395
0.0018
0.139
0.0662
0.054
0.0072
0.591
0.0136
CV
Low
0.0319
0.0003
0.0002
0.685
0.0334
0.797
0.0001
0.0005
0.1138
0.0007
0.0112
0
0.819
0.0001
0.0295
0.949
0.163
0
0.329
0.0018
High
0.0031
0.0012
0.0018
0.001
0.0016
0.001
0.998
0.0785
0.0002
0.0013
0.0008
0.13
0.0002
0.0789
0.0015
0.0003
0.004
1
0.001
0.0062
MR
Low
0.198
0.0117
0.0124
0.0103
0.002
0.454
0.108
0.935
0.0116
0.0112
1
0.0066
0.4503
0.935
0.0019
0.013
0.258
0.1075
0.0086
0.1133
High
0.129
0.0163
0.0176
0.3017
0.847
0.004
0.01
0.0008
0.1194
0.0168
0
0.948
0.0047
0.0001
0.851
0.087
0.093
0.0105
0.1914
0.0207
NB
Short
0.0003
0.0005
1
0
0.0222
0
0.0205
0.0022
0.006
0.017
0
0.624
0.0006
0.0255
1
0.0655
0.632
0.0453
0.0051
0.002
Long
0.0007
0.977
0
0.006
0.0018
0.035
0.0055
0.0318
0.605
0.283
0.085
0
0.901
0.0015
0
0.0035
0.001
0.0007
0.0069
0.032
EL
Low
0.0226
0.0301
0.036
0.0272
0.0274
0.0218
0.0238
0.0231
0.0646
1
0.0219
0.0696
0.0358
0.0236
0.0294
0.0266
0.0283
0.024
0.0255
0.0231
High
0.0464
0.0549
0.0441
0.0448
0.0456
0.0462
0.0462
0.0459
0.0914
0
0.0451
0.0814
0.0622
0.0414
0.0506
0.0464
0.0477
0.047
0.0475
0.0459
Reasoning result
AL
NB
NB
CV
MR
CV
CV
MR
AL
EL
MR
MR
NB
MR
NB
CV
MR
CV
AL
AL
Low
Long
Short
Low
High
Low
High
Low
High
Low
Low
High
Long
Low
Short
Low
Low
High
High
Low
Result given by experts
AL
NB
NB
CV
MR
CV
CV
MR
AL
EL
MR
MR
CV
MR
NB
CV
MR
CV
AL
AL
Low
Long
Short
Low
High
Low
High
Low
High
Low
Low
High
Low
Low
Short
Low
Low
High
High
Low
Δ
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
Tab.8
Fig.7
Tab.9
1
Qiu Z X. Principles and Applications of Aluminum Electrolysis. Xuzhou: China University of Mining Press, 1998, 508–510
2
Gui W H, Wang C, Xie Y F , Song S, Meng Q F. Knowledge automation is a necessary method for universities to realize spanning development for process industry. China science founding, 2015(5): 337–342
3
Guo J, Gui W H, Wen X F. Multi-objective optimization for aluminum electrolysis production process. Journal of Central South University, 2012, 43(2): 548–553
4
Stam M A, Taylor M P, Chen J J J, Mulder A, Rodrigo R . Common behaviour and abnormalities in aluminum reduction cells. TMS Light Metals,2008, 309–314
5
Majid N A A , Taylor M P , Chen J J J , Stam M A , Mulder A , Young B R . Aluminum process fault detection by multiway principal component analysis. Control Engineering Practice, 2011, 19(4): 367–379 https://doi.org/10.1016/j.conengprac.2010.12.005
6
Rooney J J, Heuvel L N V. Root cause analysis for beginners. Quality progress, 2004, 37(7): 45–56
7
Doggett A M. Root cause analysis: A framework for tool selection. Quality Management Journal, 2005, 12(4): 34
8
Demirli K, Vijayakumar S. Fuzzy assignable cause diagnosis of control chart patterns. Fuzzy Information Processing Society, 2008, 1–6
9
Ruiz-Sarmiento J R , Galindo C , Gonzalez-Jimenez J . Scene object recognition for mobile robots through semantic knowledge and probabilistic graphical models. Expert Systems with Applications, 2015, 42(22): 8805–8816 https://doi.org/10.1016/j.eswa.2015.07.033
10
Kordy B, Pouly M, Schweitzer P . Probabilistic reasoning with graphical security models. Information Sciences, 2016, 342: 111–131 https://doi.org/10.1016/j.ins.2016.01.010
11
Wee Y Y, Cheah W P, Tan S C, Wee K K. A method for root cause analysis with a Bayesian belief network and fuzzy cognitive map. Expert Systems with Applications, 2015, 42(1): 468–487 https://doi.org/10.1016/j.eswa.2014.06.037
12
Alaeddini A, Dogan I. Using Bayesian networks for root cause analysis in statistical process control. Expert Systems with Applications, 2011, 38(9): 11230–11243 https://doi.org/10.1016/j.eswa.2011.02.171
13
Weidl G, Madsen A L, Israelson S. Applications of object-oriented Bayesian networks for condition monitoring, root cause analysis and decision support on operation of complex continuous processes. Computers & Chemical Engineering, 2005, 29(9): 1996–2009 https://doi.org/10.1016/j.compchemeng.2005.05.005
14
Ferreira L, Borenstein D. A fuzzy-Bayesian model for supplier selection. Expert Systems with Applications, 2012, 39(9): 7834–7844 https://doi.org/10.1016/j.eswa.2012.01.068
15
Cai B, Liu Y, Fan Q , Zhang Y , Liu S Y , Ji R. Multi-source information fusion based fault diagnosis of ground-source heat pump using Bayesian network. Applied Energy, 2014, 114: 1–9 https://doi.org/10.1016/j.apenergy.2013.09.043
16
Zeng S P, Li J, Ding L . Fault diagnosis system for 350 KA pre-baked aluminum reduction cell based on BP neural network. TMS–Light Metals, 2007
17
Taylor M P, Zhang W D, Wills V, Schmid S . A dynamic model for the energy balance of an electrolysis cell. Chemical Engineering Research & Design, 1996, 74(8): 913–933 https://doi.org/10.1205/026387696523094
18
Zhou T.Study of alumina concentration control based on intelligent characteristic model. Advanced Materials Research. Trans Tech Publications, 2011, 317: 1314–1317
19
Tessier J, Tarcy G P, Batista E, Wang X . Towards on-line monitoring of alumina properties at a pot level. Light Metals, 2012: 633–638
20
Zeng S P, Wang S, Qu Y . Control of temperature and aluminum fluoride concentration based on model prediction in aluminum electrolysis. Advances in Materials Science and Engineering, 2014, 3:1–5
Bishop C M. Pattern Recognition and Machine Learning. New York: Springer-Verlag,2006, 373–375
26
Kabak M, Burmaoğlu S, Kazançoğlu Y. A fuzzy hybrid MCDM approach for professional selection. Expert Systems with Applications, 2012, 39(3): 3516–3525 https://doi.org/10.1016/j.eswa.2011.09.042
27
Wan S. Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making. Applied Mathematical Modelling, 2013, 37(6): 4112–4126 https://doi.org/10.1016/j.apm.2012.09.017
28
Li P, Chen G, Dai L , Zhang L . A fuzzy Bayesian network approach to improve the quantification of organizational influences in HRA frameworks. Safety Science, 2012, 50(7): 1569–1583 https://doi.org/10.1016/j.ssci.2012.03.017
Hsu Y L, Lee C H, Kreng V B. The application of fuzzy Delphi method and fuzzy AHP in lubricant regenerative technology selection. Expert Systems with Applications, 2010, 37(1): 419–425 https://doi.org/10.1016/j.eswa.2009.05.068