Reliability Research of the Top-blowing Smelting System Based on Monte Carlo Algorithm FTA and FMECA

Transcription

1 doi: /jmmf Reliability Research of the Top-blowing Smelting System Based on Monte Carlo Algorithm FTA and FMECA Yu-tao XUE, Xiao-long ZHANG*, Le-jian SONG, Tong-xing CHEN, Rui-fang SUN The Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming , China Abstract To solve the problems of the system of top-submerged smelting which has many faults and it is difficult to control, a reliability analysis model was proposed by Monte Carlo Method FTA and FMECA. Failure data is provided by the smelting company, the data is collected top-submerged smelting system failure data of four years. First, the model of FTA is established, using Monte Carlo method to analyze the importance of bottom events of FTA, then using the method of FMECA to analyze the failure mode and the criticality of the system for the important degrees higher bottom. The main factors and the weakest link which affect the system of top-submerged smelting reliability are pointed out, the model analysis results show that the analysis is effective and accurate compared with engineering practice and expert experience. It is to provide a theoretical basis for the top blown smelting system of Reliability design construction and maintenance strategy. Keywords The System of Top-submerged Smelting; Monte Carlo Method; FTA; FMECA; Reliability Introduction Top-blown smelting system is widely used in smelting equipment of method smelting such as copper, lead, zinc, etc. In 2002, a smelting company in Yunnan province brought in the first top-blown smelting machine for our country to smelt copper. Aiming at solving the difficulties of predicting failures in the process of running and the problems of seriously affecting normal production efficiency and economic benefits, it s necessary to analyze the system reliability of this machine[1]-[4]. Wang Zhili [5], etc. used fault tree analysis (FTA) to assess the reliability of power systems. Their methods can design the reliability of power systems. Cai Zhiqiang [6], etc. came up with the FPBN network structure transformation and the probability parameter model based on the FMECA. Experiments showed that it can identify and predict the failure mode effectively. Marcantonio Catelan [7], etc. used FMECA method to analyze the failure mode and criticality of PV module, besides, they verified the effectiveness of FMECA. Zhang Yudong [8], etc. came up with model of the HRSG safety analysis based on FMECA and fuzzy FTA, and found the failure events which affect safety factor of HRSG most seriously, besides, provided security policy supports. Xia Jun, Lu Jing [9]-[10], etc. used FTA and FMECA respectively to analyze the reliability of metro doors and MAVs. They made sure the key mode of failures, and provided improving the system reliability with technical supports. Aiming at the difficulties of predicting the failures which top-blown smelting system has, this paper came up with the reliability model of top-blown smelting system, which is based on Monte Carlo Algorithm FTA and FMECA. In this paper, the data comes from the top-blown smelting system s actual production and running of a smelting company in almost the past 4 years. Monte Carlo Algorithm FTA can construct probability model and make 1

2 Journal of Modern Mathematics Frontier, Volume 6, 2017 randomized trials for it to solve mathematical problems of fault trees. This method can take full advantages of FTA and FMECA. They complete each other so that can quickly and effectively find the major factors and weakness which affect the reliability of top-blown smelting system. It provides the maintenance strategies of building top-blown smelting system with theoretical supports. Simulation Model Theory Analysis Model of Monte Carlo Algorithm for Fault Tree (FTA) Fault Tree Analysis is a kind of Causal Analysis. It uses the chart method to analyze the reasons and probabilities of system s malfunction from top to bottom. FTA can find the various reasons of malfunction from top events which means the start of a fault. We can analyze the simulation of FTA by Monte Carlo Algorithm, this method can be named as the way of random sampling or statistical tests. This method is a way to solve mathematical problems by constructing probabilistic models and making randomized trials [11]. The process of simulation is to make a system repeat a simulation which has a given number of times. Each simulation is actually to simulate the specific faults which the system might have in the actual working environment. Failure data will tell the possible time between failures and the time which take to restore toa usable state after the fault of the system. After series of simulation analysis and recording every situation of simulation, when the given simulation times reached, then construct a Summary Graph of the system running in the given life cycle. Building of the Simulation Model Assuming that there are n basic events constituting the system, which is replaced by S. Then: S={Z1,Z2,,Zi,, Zn}. The failure distribution function of every basic event is: F i (t) (i=1,2,,m) (1) Fault Tree Structure Function is replaced by [X(t)]. The system is replaced by X(t)=[x1 (t),x2(t),,xi(t),,xn(t)]. 1 the ith event happens at time t X i (t) = { 0 the ith event doesn t happen at time t (2) The statement of the top events at time t is replaced by (t), then: 1 the top event happens at time t ϕ(t) = { 0 the top event doesn t happen at time t (3) (2) The Process of the Simulation Running Monte Carlo Algorithm can solve practical problems that need to be solved by Random Variables. It can unite the problems to be solved and the Probability Model, then solve the probability that a random event happens by a method of test, use the probability of the event happening to estimate the probability of this random event, and deal with the estimated probability. Then we can get an approximate solution of the problem by it. The main contents of Monte Carlo Algorithm solving problems are: setting up the probability model of the actual problems; giving Sampling Distribution of different Random Variables in the Probability Distribution Model; establishing various estimator and counting test results[12]-[13]. The process of Monte Carlo Algorithm simulation running is as following: 1) If there are m basic events, we will sample randomly to every basic event. Then we can get samples of every basic event s failure time. Where, the sample of ith basic event s failure time is: 2

3 t i = F i (η)(i=1,2,,m) (4) 2) If there are k minimal cut sets in the system, and there are n basic components in every cut set, then the structure function of minimal cut sets is: n φ j (t) = i=1 t i (j=1,2,,k) (5) If an event of the minimal cut sets happens, the top event of the system will happen, so its structure function is: k ϕ(t) = 1 j=1 (1 φ j (t)) (6) 3) Where, m failure time of basic units are t1k,t2k,,tmk. Where, k means the kth sampling. Order m sampling times as tf1,tf2,,tfk,,tfm., then tfk is the failure time Ym of the system. 4) Continue repeating these 3 steps above for M times, then these M simulation results Ym(m=1,2,,M) are got. Compare Ym and tm(m=1,2,,m)which means the M given times, if the top event of the system happens in the deadline, while Ym<tm, it means the system is under malfunction. Accumulate times of the fault Nm in the period tm. 5) Count the failure time of the system and the times of every basic event which the fault happens. Analyze every reliability index of the system, then calculate the result after simulation. Simulation flow chart is shown in Figure 3.2. The key point of Monte Carlo Algorithm is that it can make simulation for random variables. Random variables will have effect on behaviors of the system in the specific work. To achieve this goal, the computer must let the uniform distribution produce random numbers. In this paper, AVSIM+ is used as the simulation software. The following Figure 1 is the flow chart of Monte Carlo Algorithm FTA. j=j+1 Start Input simulation parameters Initialization simulation times j=1 Failure time random sampling of n basic componentst1j,t2j,,tnj System failure time schedulingtf1<tf2< <tfk< <tfn K=K+1 K=1 tfk<tmax Computational structure functionφ(t) N Φ(t)=1 Y Record failure time tfk statistical system failure number distribution Y N tfk=tmax N j M Y Reliability index of computing system End FIG. 1 FLOW CHART OF THE SIMULATION ALGORITHM 3

4 Journal of Modern Mathematics Frontier, Volume 6, 2017 The working principle of simulation is as following: Predict the unreliability of a system after running for one year. The established system model can make simulation for random failure of every basic event which constitutes the system. If the established model needs to make simulation running for 500 times, and every time of working must be more than one year. If one of the basic events happens, the system model will judge if the top event of the system happens. In the simulation process, if the life of the system is not more than one year for about 65 times, then the estimated value of the system s unavailability is: F=65/500. When the reliability is under analysis, the solving formula which is used for simulation method is: λ Q(t) = (1 λ+μ e(λ+μ)t ) (7) The formula above can be used to calculate the unavailability of the system event at time t. According to the formula, it is assumed that the fault of the studied basic event is unrelated with any other events statement. If the studied event is the backup for other events, then the probability of failure which shows the event is under statement of backup is less than the probability of failure while running. FMECA Analysis Theory FMECA is one of the most important technical means of fault analysis. It s a method which can analyze the failure modes and the potential impacts of the system, and can count and analyze the degree of harm of each failure mode and the probability of occurrence. FMECA analysis mainly consists of two parts: failure mode (FMEA) and hazard analysis (CA). FMECA is mainly to explain the potential security issues and reliability issues of the system. It also can explain the maintenance issues and the supportability issues of the system. Hazard analysis (CA) is based on FMEA method. It can comprehensively analyze the incidence and the severity of every failure mode, then get the results of the quantitative analysis and the effects that each factor gives to the system, finally evaluate the influences that it gives the reliability of the system [14]. Based on the degree of risk of the top-blowing smelting system, each failure mode is analyzed. Combining with the overview of the top-blowing smelting system and the degree of the harm to the whole system, the cause of failure of the top-blowing smelting system is discovered, failure critical subsystem is distinguished. According to the cause of failure and the main failure system, the reliability of the top-blowing smelting system can be improved effectively. The formula to calculate the criticality of the top-blowing smelting system is: CR i = n j=1 CR ij (8) Where- Because of the occurrence of the failure mode j, the formula to calculate the criticality when the subsystem of the top-blowing smelting system goes wrong is: CR ij = α ij β ij λ i (9) Where- The probability which subsystem i goes wrong because of the failure mode j; - The damage extent which subsystem i goes wrong because of the failure mode j; - The failure rate of the subsystem i, here it means the average failure rate of the equipment. The formula to calculate each variable is: α ij = n j n i (10) 4

5 Where- Times that the jth failure mode of the top-blowing smelting system happens in the subsystem i; - Failure times that the subsystem happens in all failure modes of the top-blowing smelting system. According to the international drafts, the values are shown in table 1: TABLE1 VALUE TABLE Extent of Damage that Parts Occur 1 This Part Must Have Damage 0.5 This Part Has the Possibility of Damage 0.1 This Part Seldom Has Damage 0 There Are No Influences on This Part λ i = N i t (11) Where- The total times of failure that subsystem occurs in the set time; - The grand total running time of the top-blowing smelting system. The basic work flow of the FMECA method is shown in Figure 2. The function of the subsystem is analyzed Analysis of potential failure modes Analysis of potential failure effects Analysis of potential failure cause / mechanism Analysis of detection difficulty Determine the probability of occurrence of failure Determine the extent of fault damage Determine the average failure rate The harm of each model is calculated Draw the potential failure mode and effect analysis table Come to the need to deal with the fault FIG. 2 THE BASIC WORK FLOW OF FMECA The Model Overall Flowchart of the Monte Carlo Algorithm s FTA and FMECA (Reverse FTF) By comprehensively analyzing the Monte Carlo Algorithm, FTA and FMECA, combining with the features of top-blowing smelting system of the metallurgical industry, this paper comes up with the FTA and FMECA (reverse FTF) algorithm model based on the Monte Carlo Algorithm. The overall flowchart is as following: 5

6 Journal of Modern Mathematics Frontier, Volume 6, 2017 Using AVSI M+ to estab lish fault tree Identify events at all levels Solving the minimal cut set Monte Carlo analysi s and calcula tion of the establi shmen t of the FTA System life cycle Simulation times setting Random seed number Important point setting Results of compre hensiv e data statisti cs Ranking of event importance FMEC A analy sis of impo rtant event s Hazard grade determination of each event Relia bility anal ysis concl usio n FIG. 3 GENERAL FLOW CHART OF REVERSE FTF MODEL Case Analysis The Analysis Process of the Monte Carlo Fault Tree Firstly, the fault tree model of the top-blowing smelting system is established by Monte Carlo Algorithm as shown in Figure 4: FIG. 4 THE FTA OF TOP-SUBMERGED SMELTING SYSTEM In Figure 4, the logic among all the events of the top-blowing smelting system is distinguished by the method of fault tree analysis. The fault tree showed how the different events of the top-blowing smelting system influence each other that the system went wrong. The main fault location of the top-blowing smelting system consists of three parts, the gun system fault, the lining failure and the flue fault are included. Finally, there are 12 bottom 6

7 events in this fault tree model. The simulation of the fault tree is running in the software AVSIM+. The times of simulation have great effects on the simulation results of the Monte Carlo Algorithm. Because the times of simulation can t be calculated by formulas in the settings of simulation parameters, the best simulation times need test to determine. It s known in the experimental procedure, if the simulation times are too few, the estimation errors produced will be relatively big. However, too many simulation times will lead to the calculation of time-consuming. By simulating for 200, 800, 1400 and 2000, etc., the estimation errors are shown in Figure 5. Then the four simulation results are drawn as curves which the Figure 6 shows. It s seen in the figure that the estimation errors changed inconspicuously when the simulation times reach The error rate is % when the simulation times are It s relatively reasonable. a. The simulation for 200 b. The simulation for 800 c. The simulation for 1400 d. The simulation for 2000 FIG. 5 THE ESTIMATED ERROR OF THE DIFFERENT SIMULATION NUMBER FIG. 6 THE ESTIMATED ERROR CURVE GRAPH 7

8 Journal of Modern Mathematics Frontier, Volume 6, 2017 Value the simulation times as 2000, the importance of every bottom event, which is shown in Table 2, is obtained by fault tree simulation analysis with Monte Carlo Algorithm: TABLE 2 THE SYSTEM OF TOP-SUBMERGED SMELTING FTA SIMULATION RESULTS OF IMPORTANCE Fault Location Number Bottom Event Importance Fault Location Number Bottom Event Importance EVENT0 Matte Erosion EVENT6 Slags Splashing EVENT1 Too High Furnace EVENT7 Too High Slags Temperature Temperature EVENT2 Not Smooth Hole EVENT8 The Reaction Between Slags and Periclase EVENT3 Abnormal Furnace EVENT9 Severe Temperature Temperature Fluctuations EVENT4 Gun Uneven Inner Wall EVENT10 Disturbance Scour of the Combustion Erosion EVENT5 Too Quick Speed of EVENT11 Flue Gas Condensation Gun Down The number of the importance represents that the importance of influences that bottom events give to the system, while if it s the weakness of the system. By analyzing the data in Table 2, the bottom events of first six importance of the top-blowing smelting system are chosen to be analyzed by FMECA. The order of the importance is: EVENT2 >EVENT4>EVENT5>EVENT9>EVENT7>EVENT11. The Analysis Process of FMECA By collecting the original production data of top-blowing smelting system for about hours, there will be 316 pieces of failure data selected after comprehensive analysis. They mainly consist of information of failure time, symptom description and failure analysis, etc. The 316 pieces of failure data of top-blowing smelting system after comprehensive analysis is counted and analyzed, the numbers of failure which each fault location of top-blowing smelting system occurs are calculated by statics formulas and counted in frequency distribution. The results are shows in Table 3: TABLE 3 FAULT FREQUENCY TABLE The Number of Fault Location The Fault Location Times Frequency GATE0 Gun System GATE1 Lining Member GATE2 Flue Member It s known by the table above that the failure times of the gun system are the most in the subsystem, and the fault frequency is 68.67%. It s mainly shown as burning lance tips, wall burning and cyclone damage, etc. According to the importance analysis of FTA in last section and the grand total time that the collecting of the failure data costs, the failure data of the bottom events of the first six importance is selected as 272. The failure modes and the harmfulness are comprehensively analyzed by the Table 1 and the formulas listed in section 1.2. The results are shown in the Table 4 and Table 5: 8

9 TABLE 4 FAILURE MODE FREQUENCY TABLE Numbers of Failure Modes Failure Modes Times Frequency EVENT2 Holes is not smooth EVENT4 Guns uneven inner wall of the combustion EVENT5 Gun decentralization too fast EVENT9 Severe temperature fluctuations EVENT7 Slag temperature is too high EVENT11 Flues gas condensation TABLE 5 THE SYSTEM OF TOP-SUBMERGED SMELTING HARMFULNESS ANALYSIS TABLE Subsystem Numbers of Failure Modes Failure Modes CR EVENT2 Holes is not smooth E E-04 Gun System EVENT4 Guns uneven inner wall of the combustion E E E-03 EVENT5 Gun decentralization too fast E E-04 EVENT9 Severe temperature fluctuations E E-04 Lining Member 6.37E-04 EVENT7 Slag temperature is too high E E-04 Flue Member EVENT11 Flues gas condensation E E E-04 To evaluate the criticality of the system more intuitively, the criticality of each subsystem and the first six failure modes are respectively shown by a histogram and a line chart as following Figures 7 and 8: FIG. 7 HISTOGRAM OF THE HAZARD DEGREE DISTRIBUTION OF EACH SUBSYSTEM FIG. 8 THE DISTRIBUTION OF FAULT MODE DAMAGE DEGREE Figure 7 shows that the highest criticality is which of the spray gun. What s more, in the actual production running, the main function of the spray gun is to provide the top-blowing smelting system with air, oxygen and reaction 9

10 Journal of Modern Mathematics Frontier, Volume 6, 2017 raw materials. It s the most important part of the top-blowing smelting system. The life of the spray gun which is the core component of the top-blowing smelting system is the key factor to affect the production working rate, besides it s also the one of representatives which can affect advanced degree of the top-blowing lance smelting technology[15-16]. Figure 8 intuitively shows the criticality of the first six importance of the fault events. The order is: EVEN4>EVEN2>EVEN11>EVEN7>EVEN9>EVEN5. That means guns uneven inner wall of the combustion, not smooth of the gun hole, coagulation of the gas and relatively high of slag temperature are major factors which influence the reliability of the top-blowing smelting system. Severe fluctuation of the temperature and too quick speed to lowering gun are also weakness of the top-blowing smelting system. By some means, the occurrence of above failure modes is controlled to effectively reduce the failure rates of the top-blowing smelting system. Conclusion In this paper, by extracting effective fault information in the data of the actual production run, using proposed Monte Carlo Algorithm FTA and the reliability model of the top-blowing smelting system of FMECA to analyze the failure data, then the key factors and the weakest link which affect the reliability of the top-blowing smelting system are fast and effectively found. Comparing the conclusion and the production practice, the result meets the actual production. The effectiveness of the method is proved. The theories to establish the equipment failure case base and fast and effectively predict faults are provided. ACKNOWLEDGMENT The authors would like to acknowledge the many helpful suggestions of anonymous reviewers. This work was supported byyunnan Applied basic research projects (2013FZ009); Kunming University of Science and Technology Natural Science Research Fund Project (KKSY ). REFERENCES [1] Zhang Xiao-long, Yao Shi wen, Hu Jian-hang, et al. Adaptive soft measurement of process parameters of ISA furnace during copper melting based on generalized maximum entropy regression[j]. Journal of Kunming University of Science and Technology: Natural Science Edition, 2012(4): [2] Huda N, Naser J, Brooks G, et al. Computational Fluid Dynamic Modeling of Zinc Slag Fuming Process in Top-Submerged Lance Smelting Furnace[J]. Metallurgical & Materials Transactions B, 2012, 43(1): [3] Zhang Bang-qi, Zhu Zu-ze. Practice and discuss on prolonging lifetime for YCC isasmelt Furnace[J]. Nonferrous Metals, 2005,57(4): [4] Wei Tao, Shen Qiang-hua, Zhan Huan-wu, et al. The development thinking of lance life of top-blown melting furnace[j]. Science Technology and Engineering, 2009, 9(19): [5] Wang Li-zhi, Wang Xue-qi, Fu Bo, et al. A method of reliability evaluation for electrical power system based on FTA[J]. Automatic Control Systems & Equipments, 2015(5): [6] Cai Zhi-qiang, Sun Shu-dong, Si Shu-bin, et al. Modeling of failure prediction Bayesian network based on FMECA[J]. Systems Engineering Theory & Practice, 2013, 33(1): [7] Catelani M, Ciani L, Cristaldi L, et al. Electrical performances optimization of Photovoltaic Modules with FMECA approach[j]. Measurement, 2013, 46(10): [8] Zhang Yu-dong, Qin Li, Pu Wei, et al. Safety analysis of waste heat boiler based on FMECA and fuzzy FTA[J]. Journal of Safety Science and Technology, 2015(8): [9] Xia Jun, Liu Ping, Ren Jin-bao. Application of Reverse FTF in Metro Door Failure Analysis[J]. Machinery Design & Manufacture, 2014(3):

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