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Frontiers of Chemical Science and Engineering

ISSN 2095-0179

ISSN 2095-0187(Online)

CN 11-5981/TQ

Postal Subscription Code 80-969

2018 Impact Factor: 2.809

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Front. Chem. Sci. Eng.    2017, Vol. 11 Issue (3) : 414-428    https://doi.org/10.1007/s11705-017-1663-x
RESEARCH ARTICLE
A knowledge reasoning Fuzzy-Bayesian network for root cause analysis of abnormal aluminum electrolysis cell condition
Weichao Yue1, Xiaofang Chen1(), Weihua Gui1, Yongfang Xie1, Hongliang Zhang2
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
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Abstract

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.
Keywords abnormal aluminum electrolysis cell condition      Fuzzy-Bayesian network      multi-source knowledge solidification and reasoning      root cause analysis     
Corresponding Author(s): Xiaofang Chen   
Just Accepted Date: 10 May 2017   Online First Date: 11 August 2017    Issue Date: 23 August 2017
 Cite this article:   
Weichao Yue,Xiaofang Chen,Weihua Gui, et al. A knowledge reasoning Fuzzy-Bayesian network for root cause analysis of abnormal aluminum electrolysis cell condition[J]. Front. Chem. Sci. Eng., 2017, 11(3): 414-428.
 URL:  
https://academic.hep.com.cn/fcse/EN/10.1007/s11705-017-1663-x
https://academic.hep.com.cn/fcse/EN/Y2017/V11/I3/414
Fig.1  Schematic diagram of aluminum electrolysis cell
Parameter Effect analysis
Aluminum molten level ( AL) ◆ 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  The choice of characteristic parameters and characteristics state
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  Analysis of cause and effect among parameters
Fig.2  RCA of ASARC based on FBN
Fig.3  Knowledge solidification modeling steps based on Fuzzy-Bayesian network
Fig.4  Causal relationship among characteristic parameters
Fig.5  The fuzzy state division of AL
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  State of observable nodes
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  Prior probabilities of fuzzy states for root nodes
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  Condition probability of variable ‘voltage vibration (VV)’
// 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  Algorithm 1 The RCA of abnormal cell condition based on fuzzy-Bayesian network reasoning
Fig.6  MSKR model based on Fuzzy-Bayesian network
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  The abnormal aluminum electrolysis cell condition used to validate
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  Validation results
Fig.7  The statistical results of verification
VV v BT L SD N BS H LL N HT N BV N FC B FI W BC R CS N
Tab.9  
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