設備余寿命予測に関する研究 -遺伝的アルゴリズムによる最適予測法-
公開日:
カテゴリ: 第8回
1. Introduction
Rolling bearing is the most part used in rotating machinery of industrial plant. The condition diagnosis technology of rolling bearing is very important and indispensable for the plant safety and operation stability. The purpose of this study is to improve the accuracy of the life prediction for a rolling bearing.The paper proposes a searching method for the optimum mathematic function for the high accurate prediction by using the genetic algorithms (GA). Firstly, for deciding the starting point of the prediction function, 10 initial genes expressed by UoXo Yo) are made, and the regression analysis of the inspection data for the life prediction is carried out from the starting point Mo. The exponential functions from one to five orders are used for the prediction function,The fitness is calculated by residual between measurements and predicted data. The exponential functions with high fitness are superior genes, and next generation's genes are generated based on them. The operation selection, crossover and mutation are done until the finishing condition is satisfied.The weights are added in the predicted data when regression analysis for dealing with the rapid change in state tendency of the machine. Optimum weights are also searched by GA. We will show the prediction results obtained by this method to verify the efficiencyT514-8507 ATBUT 1577, WENN #ARI RFR1ZTAIFA E-mail: chen@bio.mie-u,ac.jp2. Tendency Prediction of Rotating Machinerypropertyof rotation machine2.1 Vibration equipmentIn general, the machine condition can be divided into five stages, namely normal stage, early abnormal stage, middle abnormal stage, terminal abnormal stage and breakdown[1]. The purpose of tendency control of rotating machinery is judging these stages quantitatively. The values of some symptom parameters calculated from vibration signal for diagnosing state of a rotation machine has the tendency where the values rise with the abnormality level. An example of the relation between the abnormality level and the value of symptom parameter is shown in figure 1.Early stage fault Middle stage faultEnd stage faultNormal stateentBreakagesymptom parameter The level of faultValue of(a)Time0.04Time(b)Fig.1 Relation between fault level and symptom parameterThe value of a symptom parameter conforms to the normal----Confidenceintervalprobability distribution or weibull probability distribution when the vibration signal measured more than five times at same point continuously. Conceptive graph of the tendency control for rotating machinery is shown in figure 2.Lifetime limitationRegression curveConfidenceintervalForecastof regression curveFeature parameterConfidenceintervalx1x2x3xxxxTimeThe end of data measurementThe shortest longevityThe average longevityThe longest longevityFig.2Tendency control for rotating machineryFig. 22.2. Decision of optimum starting position of the regression curveThe life prediction is started from the point that the early abnormal stage. Or, the life prediction is started from the point at which the state is judged to be a slight fault by absolute judgment standard. However, the detection of an early abnormal stage by watching the graph of inspection data is difficult. Moreover, the value of symptom parameter changes with the operating conditions even if the same type of rolling bearing in a rotating machine.This study deals with the problem of the life prediction for a rolling bearing in a rotating machine by statistical test method. Time when significant difference in the value of a symptom parameter against normal state existed is judged as abnormal occurring time. The life prediction is started from the point of the abnormal occurring time. The equation used to judge the significant difference (m) of the value of the symptom parameter is shown as follows.N.NO significant difference(m)= (x2 ? x;), la* P/(N + N2 )(N,S? +N,5})significant difference(m)=(xz-1Here, N ... Number of samples fromT,to Tu- N2. Number of samples Tr; *; --- Average of specimen of N, X.Average of specimen of Nz; S... Average of standard deviationN, ; S ... Average of standard deviationN,2.3 Tendency prediction simulation methodProcedure of tendency prediction simulation is shown in Figure 3. Firstly, for deciding the starting point of the prediction function, 10 initial (XO, YO) expressed by genes[2] are made, and the regression analyses of the inspection data for the tendency prediction are carried out from the starting point uo. The exponential functions from one to five orders are used for the prediction function. The fitness[2] is calculated by residual between measured and predicted data. The calculation of the fitness (1) is shown by equation (2). The exponential functions with high fitness are excellent genes, and next generation's genes are generated based on them. The operation selection, crossover and mutation are done until the finishing condition is satisfied.0; -- y;)Fitness(I)=N-NHere, N-N, :Number of data for pridiction; y:Vibration value of inspection data; y':Vibration value of regression curve.startMaking of initial genesExecution of recurrenceCalculation of fitnessSelection and inheritance| Mutation and crossoverDecision of optimum solutionFig. 3 Processing procedure of genetic algorithm283. Simulation and experiment resultsExamples of results of life prediction simulation are shown Figure 4 and Figure 5. These simulations were carried out by using 95 points from starting point, and the simulation results were verified by last 5 points. Figure 4 shows the rapid change pattern of the state tendency of a rolling bearing after abnormal stage, and figure 5 shows the gradual change pattern. The index recurrence curve is the optimum cuve for the lift prediction found out by the GA.3. Simulation and experiment resultsRotating machine for the experimentAccelerometerEqipment for loadingRotating shaftRolling bearing for the testExamples of results of life prediction simulation are shown Figure 4 and Figure 5. These simulations were carried out by using 95 points from starting point, and the simulation results were verified by last 5 points. Figure 4 shows the rapid change pattern of the state tendency of a rolling bearing after abnormal stage, and figure 5 shows the gradual change pattern. The index recurrence curve is the optimum curve for the lift prediction found out by the GA.15Vibration value- Vibration value--- Index recurrence curve --- linear regressionog . The second recurrence curve ---- The fourth recurrence curve -------- Index recurrence curve(GA none)Normal Break down Fig. 6 Rotating machine for the prediction tests In order to verify the efficiency of the method proposed here, we did accelerating fatigue test using a rolling bearing shown in fig. 6. The test conditions are follows: Rotating speed : 800rpm; Type of signal : vibration acceleration; Sampling frequency: 100kHz; Sampling time : 5sec.; Time interval of signal measurement: 2 min.; Type of bearing: NTN (6204LLUCM/5K); Load : 1800kg.Fig. 7 shows the change of values of symptom parameters (rms and Y) with time while the test, which are calculated by time signal of vibration acceleration.Fig. 8 shows the prediction result for the tested bearing. The data in the abnormal area are used for prediction, and the data in the prediction area are used for verification. The optimum prediction curve found out by using the method proposed in this paper is well fitting the data for verification.110o Joo?R Powe ve oR 50 60 70 80 90 100time Figure 4 The case of rapid change patter of the statetendencyVibration value- Vibration value e Index recurrence curve- linear regression . . The second recurrence curve ----- The fourth recurrence curve --------- Index recurrence curve(GA none)0.050.04577715 =N171151100.005O50 60 70 80 90 100time Fig. 5 The case of gradual change pattern of the statetendency010203040506070Time (h)W1=DON19 20 30 40 50 60 70Time (h) Fig.7 Values of symptom parameters while the life test-29TH0.18Normal state area0.16Abormal state area for pre diction0.140.12The optimum prediction starting position can be specified by statistical tests and GA.Optimum regression curve for the life prediction is indexrecurrence curve and the second recurrence curve. verification The method proposed in this paper has been verified by theexperiment of accelerating fatigue test for a rolling bearing.0.1Data for0.080.060.02Predicted area3053E050100150200250Fig. 8 Life prediction for the tested bearing4. ConclusionsThis paper has proposed a searching method of the optimum mathematic function for the high accurate life prediction of a rolling bearing in a rotating machine by using the genetic algorithms (GA).The following results were obtained in this study.Tendency prediction using genetic algorithm has been improved more than traditional methods.References [1] Riadh ZAIER, Peng CHEN, Norihiro ABE, ToshioTOYOTA: Optimal Periodic Inspection And Replacement Strategy for Plant Machinery by Reliability Theory And Genetic Algorithms, Journal of the Societyof Plant Engineers Japan, Vol.16, No.4, 2005, pp.12-20. [2] L. DAVIS, ““Handbook of Genetic Algorithms”, vanNo-strand Reinhold, A Division of Wadsworth, Inc, 1990.(23 F8 31 )30“ “設備余寿命予測に関する研究 -遺伝的アルゴリズムによる最適予測法-“ “陳山 鵬,Ho JINYAMA,小出 悠貴,Yuki KOIDE,李 可, Ka Li,薛 紅涛,Hongtao XUE,里永 憲昭,Noriaki SATONAGA
Rolling bearing is the most part used in rotating machinery of industrial plant. The condition diagnosis technology of rolling bearing is very important and indispensable for the plant safety and operation stability. The purpose of this study is to improve the accuracy of the life prediction for a rolling bearing.The paper proposes a searching method for the optimum mathematic function for the high accurate prediction by using the genetic algorithms (GA). Firstly, for deciding the starting point of the prediction function, 10 initial genes expressed by UoXo Yo) are made, and the regression analysis of the inspection data for the life prediction is carried out from the starting point Mo. The exponential functions from one to five orders are used for the prediction function,The fitness is calculated by residual between measurements and predicted data. The exponential functions with high fitness are superior genes, and next generation's genes are generated based on them. The operation selection, crossover and mutation are done until the finishing condition is satisfied.The weights are added in the predicted data when regression analysis for dealing with the rapid change in state tendency of the machine. Optimum weights are also searched by GA. We will show the prediction results obtained by this method to verify the efficiencyT514-8507 ATBUT 1577, WENN #ARI RFR1ZTAIFA E-mail: chen@bio.mie-u,ac.jp2. Tendency Prediction of Rotating Machinerypropertyof rotation machine2.1 Vibration equipmentIn general, the machine condition can be divided into five stages, namely normal stage, early abnormal stage, middle abnormal stage, terminal abnormal stage and breakdown[1]. The purpose of tendency control of rotating machinery is judging these stages quantitatively. The values of some symptom parameters calculated from vibration signal for diagnosing state of a rotation machine has the tendency where the values rise with the abnormality level. An example of the relation between the abnormality level and the value of symptom parameter is shown in figure 1.Early stage fault Middle stage faultEnd stage faultNormal stateentBreakagesymptom parameter The level of faultValue of(a)Time0.04Time(b)Fig.1 Relation between fault level and symptom parameterThe value of a symptom parameter conforms to the normal----Confidenceintervalprobability distribution or weibull probability distribution when the vibration signal measured more than five times at same point continuously. Conceptive graph of the tendency control for rotating machinery is shown in figure 2.Lifetime limitationRegression curveConfidenceintervalForecastof regression curveFeature parameterConfidenceintervalx1x2x3xxxxTimeThe end of data measurementThe shortest longevityThe average longevityThe longest longevityFig.2Tendency control for rotating machineryFig. 22.2. Decision of optimum starting position of the regression curveThe life prediction is started from the point that the early abnormal stage. Or, the life prediction is started from the point at which the state is judged to be a slight fault by absolute judgment standard. However, the detection of an early abnormal stage by watching the graph of inspection data is difficult. Moreover, the value of symptom parameter changes with the operating conditions even if the same type of rolling bearing in a rotating machine.This study deals with the problem of the life prediction for a rolling bearing in a rotating machine by statistical test method. Time when significant difference in the value of a symptom parameter against normal state existed is judged as abnormal occurring time. The life prediction is started from the point of the abnormal occurring time. The equation used to judge the significant difference (m) of the value of the symptom parameter is shown as follows.N.NO significant difference(m)= (x2 ? x;), la* P/(N + N2 )(N,S? +N,5})significant difference(m)=(xz-1Here, N ... Number of samples fromT,to Tu- N2. Number of samples Tr; *; --- Average of specimen of N, X.Average of specimen of Nz; S... Average of standard deviationN, ; S ... Average of standard deviationN,2.3 Tendency prediction simulation methodProcedure of tendency prediction simulation is shown in Figure 3. Firstly, for deciding the starting point of the prediction function, 10 initial (XO, YO) expressed by genes[2] are made, and the regression analyses of the inspection data for the tendency prediction are carried out from the starting point uo. The exponential functions from one to five orders are used for the prediction function. The fitness[2] is calculated by residual between measured and predicted data. The calculation of the fitness (1) is shown by equation (2). The exponential functions with high fitness are excellent genes, and next generation's genes are generated based on them. The operation selection, crossover and mutation are done until the finishing condition is satisfied.0; -- y;)Fitness(I)=N-NHere, N-N, :Number of data for pridiction; y:Vibration value of inspection data; y':Vibration value of regression curve.startMaking of initial genesExecution of recurrenceCalculation of fitnessSelection and inheritance| Mutation and crossoverDecision of optimum solutionFig. 3 Processing procedure of genetic algorithm283. Simulation and experiment resultsExamples of results of life prediction simulation are shown Figure 4 and Figure 5. These simulations were carried out by using 95 points from starting point, and the simulation results were verified by last 5 points. Figure 4 shows the rapid change pattern of the state tendency of a rolling bearing after abnormal stage, and figure 5 shows the gradual change pattern. The index recurrence curve is the optimum cuve for the lift prediction found out by the GA.3. Simulation and experiment resultsRotating machine for the experimentAccelerometerEqipment for loadingRotating shaftRolling bearing for the testExamples of results of life prediction simulation are shown Figure 4 and Figure 5. These simulations were carried out by using 95 points from starting point, and the simulation results were verified by last 5 points. Figure 4 shows the rapid change pattern of the state tendency of a rolling bearing after abnormal stage, and figure 5 shows the gradual change pattern. The index recurrence curve is the optimum curve for the lift prediction found out by the GA.15Vibration value- Vibration value--- Index recurrence curve --- linear regressionog . The second recurrence curve ---- The fourth recurrence curve -------- Index recurrence curve(GA none)Normal Break down Fig. 6 Rotating machine for the prediction tests In order to verify the efficiency of the method proposed here, we did accelerating fatigue test using a rolling bearing shown in fig. 6. The test conditions are follows: Rotating speed : 800rpm; Type of signal : vibration acceleration; Sampling frequency: 100kHz; Sampling time : 5sec.; Time interval of signal measurement: 2 min.; Type of bearing: NTN (6204LLUCM/5K); Load : 1800kg.Fig. 7 shows the change of values of symptom parameters (rms and Y) with time while the test, which are calculated by time signal of vibration acceleration.Fig. 8 shows the prediction result for the tested bearing. The data in the abnormal area are used for prediction, and the data in the prediction area are used for verification. The optimum prediction curve found out by using the method proposed in this paper is well fitting the data for verification.110o Joo?R Powe ve oR 50 60 70 80 90 100time Figure 4 The case of rapid change patter of the statetendencyVibration value- Vibration value e Index recurrence curve- linear regression . . The second recurrence curve ----- The fourth recurrence curve --------- Index recurrence curve(GA none)0.050.04577715 =N171151100.005O50 60 70 80 90 100time Fig. 5 The case of gradual change pattern of the statetendency010203040506070Time (h)W1=DON19 20 30 40 50 60 70Time (h) Fig.7 Values of symptom parameters while the life test-29TH0.18Normal state area0.16Abormal state area for pre diction0.140.12The optimum prediction starting position can be specified by statistical tests and GA.Optimum regression curve for the life prediction is indexrecurrence curve and the second recurrence curve. verification The method proposed in this paper has been verified by theexperiment of accelerating fatigue test for a rolling bearing.0.1Data for0.080.060.02Predicted area3053E050100150200250Fig. 8 Life prediction for the tested bearing4. ConclusionsThis paper has proposed a searching method of the optimum mathematic function for the high accurate life prediction of a rolling bearing in a rotating machine by using the genetic algorithms (GA).The following results were obtained in this study.Tendency prediction using genetic algorithm has been improved more than traditional methods.References [1] Riadh ZAIER, Peng CHEN, Norihiro ABE, ToshioTOYOTA: Optimal Periodic Inspection And Replacement Strategy for Plant Machinery by Reliability Theory And Genetic Algorithms, Journal of the Societyof Plant Engineers Japan, Vol.16, No.4, 2005, pp.12-20. [2] L. DAVIS, ““Handbook of Genetic Algorithms”, vanNo-strand Reinhold, A Division of Wadsworth, Inc, 1990.(23 F8 31 )30“ “設備余寿命予測に関する研究 -遺伝的アルゴリズムによる最適予測法-“ “陳山 鵬,Ho JINYAMA,小出 悠貴,Yuki KOIDE,李 可, Ka Li,薛 紅涛,Hongtao XUE,里永 憲昭,Noriaki SATONAGA