TIME-FREQUENCY BASED SENSOR FUSION IN THE ASSESSMENT AND MONITORING OF MACHINE PERFORMANCE DEGRADATION

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1 Proceedings of IMECE 0 00 ASME International Mechanical Engineering Congress & Exosition New Orleans, Louisiana, November 17-, 00 IMECE00-MED-303 TIME-FREQUENCY BASED SENSOR FUSION IN THE ASSESSMENT AND MONITORING OF MACHINE PERFORMANCE DEGRADATION Dragan Djurdjanovic Jun Ni, Professor 1 The University of Michigan, Ann Arbor, The University of Michigan, Ann Arbor, Det. of Mechanical Engineering, Det. of Mechanical Engineering, 50 G. G. Brown, 350 Hayward St., Director of the S. M. Wu Manufacturing Research Ann Arbor, MI ; USA Center Phone: H. H. Dow, 300 Hayward St, Fax: Ann Arbor, MI ; USA ddjurdja@umich.edu Phone: Fax: junni@umich.edu Jay Lee, Professor The University of Wisconsin, Milwaukee Director of the Center for Intelligent Maintenance Systems (IMS) Cozzens-Cudahy Research Center 9100 North Swan Rd, Milwaukee, WI 534; USA Tel: Fax: jaylee@uwm.edu ABSTRACT Machines degrade as a result of aging and wear, which decreases their erformance reliability and increases the otential for faults and failures. In contemorary manufacturing it becomes increasingly imortant to redict and revent machine failures, rather than allowing the machine to fail and then fixing the failure. In this aer, methods of time-frequency signal analysis will be used to cature information from multile machine sensors. This information could be used to assess machine erformance degradation and subsequently take aroriate action. Signals emanating from three different sensors were collected when a shar and a worn tool have been mounted on a CNC lathe machine. Several combinations of sensors and signal features have been tried in order to demonstrate the ability to use the information from multile sensors and increase sensitivity to tool wear. 1. INTRODUCTION It becomes increasingly imortant in contemorary manufacturing to redict and revent machine failures, instead of allowing it to fail and then react to the failure. The imact of machine failure is such that this redict and revent (PAP) aradigm is increasingly referred and desired over the traditional fail and fix (FAF) aradigm. Therefore, there is a huge otential benefit in deloying a systemic methodology that will enable a near-zero-downtime erformance, [1]. Machines degrade as a result of aging and wear, which decreases their erformance reliability and increases the otential for faults and failures. The aradigm of machine degradation assessment was first introduced by Lee [], [3], who used a Cerebellar Model Articulation Controller (CMAC) neural network [4], [5], to roduce a quantitative confidence 1 All corresondence should be addressed to this author. 1 Coyright 00 by ASME

2 value (CV) index of machine degradation. This aroach enabled reventive maintenance through tracking and rediction of the CV index. The decreasing trend of this index was the quantitative indicator of machine degradation during its oeration. One can identify the following advantages of the CMAC based aroach to the roblem of machine degradation assessment and monitoring. a) Self-calibration: The CMAC neural networks have the ability to relatively quickly, without any outside intervention, learn the machine behavior during its normal oeration and detect the abnormal states, without those states being resented to it reviously. b) Wide range of alications and generalization: CMAC neural networks have the ability to learn any function (machine behavior) in the training oints to a desired tolerance. This ability allows one to use this aroach in a wide range of alications c) Sensor fusion: It is ossible to merge inuts from several sensors mounted on the machine and use them concurrently to assess the machine erformance. These three roerties enabled one to emloy the CMAC based aroach to continuous assessment and monitoring of the machine erformance. Nevertheless, this aroach has a number of weaknesses. Firstly, no signal rocessing method was alied to the CMAC inuts coming from the sensors attached to the machine. Raw signals were ut into the network, which otentially could hamer the very function of the neural network if large signals of several thousands of samles were used as inuts into the network. Therefore, this aroach was useful only for low-dimensional inut feature saces. Furthermore, the neural network architecture, as well as a wide range of CMAC neural network arameters need to be set by the user, and no general guidelines exist on how to do this. Currently, one must be an exert in the area of alication in order to choose these network roerties and arameters in order to get any meaningful results out of the CMAC network. Finally, the CV index has been calculated in a rather ad hoc way, leaving the user with the task to interret it and set thresholds that would trigger any action towards erforming maintenance and fixing the roblems identified by the CMAC network. This task becomes even more difficult if one takes into consideration that the CV index deends not only on the inuts into the CMAC neural network, but also on its architecture and arameters. In this aer, a new method for rocessing and extraction of features from sensor readings is roosed for machine-tool degradation assessment and monitoring. It is based on the time-frequency signal rocessing tools and statistical attern recognition. Imlementation of the newly roosed methods is demonstrated in caturing information from multile sensors mounted near the tool on a CNC lathe machine and using it to assess the tool condition. Signals were collected with a shar and a worn tool mounted on the machine, and several combinations of sensors and signal features have been tested in order to demonstrate the generality of the roosed methods, and their ability to use information from multile sensors to increase sensitivity to tool wear. The signal rocessing and feature extraction methods roosed in this aer will be used in the future to erform machine degradation assessment and monitoring, with the goal of maintaining the desirable roerties a), b) and c) of the CMAC based aroach, while alleviating its weaknesses outlined above. The rest of the aer is organized as follows. The newly roosed combination of signal rocessing, feature extraction and attern recognition methods for rocessing and fusion of sensory readings is described in Section. Descrition of the exerimental rocedure used for validation of the newly roosed methods is also given in. Section 3 resents exerimental results of imlementation of the newly roosed methods described in Section. These results are discussed in Section 4. Conclusions of this work and guidelines for future work are given in Section 5.. METHODS.1. Signal Processing Methods Due to non-linearity and/or time deendency of the manufacturing rocess, signals emitted from rotary machines during oeration are usually highly non-stationary [6], which invokes the need for the use of non-stationary signal analysis tools [7]. Time-frequency signal analysis tools are therefore suitable for rocessing of signals used for machine degradation assessment and monitoring. Cohen s general class of time-frequency distributions (TFDs) for the signal s(t) is described as 1 j ( θt+ τω ) C( t, ω) = A( θ, τ ) φ( θ, τ ) e dθ dτ 4π (1) where * τ τ jθt A( θ, τ ) = s ( t ) s( t + ) e dt is the ambiguity function of the signal, and φ( θ, τ) is the timefrequency kernel [8]. The choice of the time-frequency kernel can be used to achieve desired roerties in the resulting timefrequency reresentation. The bilinear nature of the twodimensional signal transformation (1) causes the occurrence of cross-terms when multi-comonent signals are rocessed. Cross-terms are sometimes indistinguishable from the autoterms and can hamer the time-frequency based signal interretation and attern recognition [9]. The Reduced Interference Distribution (RID) time-frequency kernels introduced by Jeong and Williams [10], suress the TFD cross-terms by attenuating the signal terms away from the θ and τ axes in the ambiguity domain [11]. In addition to crossterm suression, the RIDs retain a number of other desirable mathematical roerties, which are not exhibited by other members of the Cohen s class of TFDs, [10]. The binomial time-frequency kernel [1] is one of the RID kernels and is used in this aer to rocess signals obtained

3 from the sensors. Following [13], RIDs R ( t, ω) of the signals are viewed as robability distribution functions and are rocessed into their time-shift invariant reresentations (TIRs) as T INV R ( t, ω ) = R( t ER[ t],ω) where E R[ ] denotes the mathematical exectation oerator regarding R ( t, ω) as the robability distribution function. Frequency-shift and scale invariance were not ursued, because invoking those roerties uon RIDs would interfere with their frequency content [15], [13] The frequency content of the signal carries imortant information about machine erformance and it should therefore be reserved for attern recognition... Feature Extraction Methods q When all moments E[ X Y ],, q N of a twodimensional random variable (X,Y) exist, its characteristic j( ux + vy ) function f ( u, v) = E[ e ], u, v C can be reresented as [8] n + q [ ] n j q q f ( u, v) = E X Y u v + o ( u + v ), n N + q= 0! q! () o( h ) where o ( ) is such that lim = 0. Due to the unique h 0 n h corresondence between characteristic functions and robability distribution functions, Eq. () imlies that moments of a robability distribution function can be used to describe it. TIRs of the RIDs can also be viewed as robability distribution functions and its moments i j i j T M = E t ω = t ω INV ( t, ω) dtd, i, j 0,1, n [ ],... i, j T R ω = INV R can be used in subsequent attern recognition, similar to what was done in [14] and [15]. It is aarent from () that moments of order u to n, comletely describe the -D olynomial that, among all the olynomials of order u to n, best aroximates the characteristic function of a robability distribution function. Thus, the first few moments of a robability distribution function give the best indication of its general roerties ([8],. 55)..3. Pattern Recognition Methods Since time-frequency moments M, described in Section. tend to be asymtotically Gaussian [13], one can model the machine behavior through the arameters of a multivariate Gaussian distribution function describing the distribution of the time-frequency moments collected during different stages of machine oeration (training rocess). Usually, one can observe Order of the moment E[ X Y ], q N i j q, is equal to +q. a high degree of correlation between the moments M,, and the uncorrelated ortion of the information contained in the time-frequency moments can be extracted through the use of the well-known Princial Comonent Analysis (PCA), [16]. For the sake of comleteness, the PCA rocedure emloyed in this aer will be briefly resented. Let us assume that at a given machine oeration stage S (in this aer, only the normal machine behavior and machine oeration with a worn tool are considered), the signal features X are characterized by the multivariate Gaussian distribution with mean µ S and the covariance matrix K S. The symmetric matrix K S can now be reresented as r T T K S = λ ivivi = VΛV (3) i=1 where r is the rank of the covariance matrix K S, λ i, i = 1,,..., r are the non-zero eigenvalues of K S, v i are the corresonding unit norm eigen-vectors and λ1 0 0 = [ v ] Λ = 0 λ V v v 1 r ; λr Due to the ositive semidefiniteness of K S, all its eigenvalues are real and greater than, or equal to zero. Each eigenvalue λ i, i = 1,,..., r deicts the amount of the covariance matrix energy rojected in the direction of the corresonding eigenvector v i. When there exists a high degree of correlation among the comonents of X, only a few of the eigenvalues in Λ account for most of the energy 3 in the covariance matrix K S. Thus, assuming that eigenvalues λ i, i = 1,,..., r are arranged in descending order, (3) can be reresented as T T K S = λ ivivi = VPΛ PVP (4) i=1 where λ1 0 0 [ ] 0 λ V = v v v Λ = 1 ; λ is the number of the rincial comonents of K S, λ i, i =1,,..., are the largest eigenvalues of K S, and v i are the corresonding unit norm eigen-vectors. A query item X ~ can now be transformed into a - comonent random variable Y ~ given as i j 3 One can interret this as only a few eigenvectors and eigenvalues accounting for most of the variability within the data class describing the machine state S. 3

4 Y ~ ~ 1/ = T ( X µ S ), T = Λ If X ~ belongs to the class of signals from machine state S, then Y ~ should be normally distributed with zero mean and variance I, where I is the unity matrix of order. Thus, for each query item X ~, its adherence to the class S can be assessed through the Euclidean norm of the vector Y ~, which in turn corresonds to assessment and classification based on the Mahalanobis distance of the query item from the training classes [17]..4. al Procedure Signals have been collected using a microhone, a vibration sensor and a force sensor mounted near the tool holder of a CNC lathe machine. A samling rate of 0 khz was used for all three sensors. 4 signals of length 0.5 ms (5000 samles each) have been collected when a shar tool was used, and another 4 when a worn tool was mounted on the machine. The state of the tool was assessed using the ISO standard rocedures, [18]. The TIRs of the RIDs of the signals have been roduced as described in Section.1, and their moments of order u to 15 have been calculated as described in Section.. Figure 1 and Figure show several RIDs of the signals that have been collected and Figure 3 shows the moments of the TIRs of the signals from Figure 1. As can be seen in Figure 3, the size of the moments diminishes raidly with the increasing order of the moments, and in this case it seemed that the ad hoc chosen number of moment orders was sufficient to describe the TIRs of the RIDs. Nevertheless, in the future, the issue of the number of moments necessary to describe a time-frequency distribution should be solved in a more systematic way. V assessed through the Mahalanobis distance of the signal features from the training signals, as described in Section.3. Figure 4 and Figure 5 show results of these exeriments. Figure 1. Plots of binomial RIDs of signals coming from the force sensor (lots a and d), vibration sensor (lots b and e) and microhone (lots c and f) when a shar tool was used. Darker areas denote areas of higher signal energy. RIDs on lots a, b and c on one hand, and RIDs on lots d, e, and f on the other hand, have been collected simultaneously (simultaneous readings of the force sensor, microhone and vibration sensor). 3. RESULTS Two sets of exeriments have been conducted. In the first set of exeriments, only the signals from normal rocess oeration were resented to the classifier, and the cutting rocess degradation was assessed based on the drift of the newly arrived signals away from those observed during the training eriod (normal cutting rocess). In the second set of exeriments, both the normal cutting rocess signals and the signals collected during oeration with the warn cutting tool were resented to the classifier, and it was tested in erforming a classical tool war monitoring task through recognizing the tool condition associated with the newly arrived signals s assessing the drift away from the shar tool machine oeration In the first set of exeriments, the first 1 signals collected when a shar tool was mounted on the machine have been used to train the classifier and assess the mean and covariance matrix of the signal features during machine oeration with a shar tool. Then, those signals along with the remaining 36 signals (total of 48 signals) were used to assess the drift of machine behavior from this normal machine state. The drift was Figure 4 shows Mahalanobis distances of the TIR moments of the signal RIDs for signals collected during the machine oeration with a worn tool (first 4 items) and with a shar tool (the second 4 items). In the first exeriment, TIR moments of order 1 through 3 (8 moments) from all three sensor signals have been used (total of 4 features). Results of exeriments, 3 and 4 were obtained using TIR moments of order 1 through 5 (6 moments) of the signal RIDs from only the force, sound and vibration sensors, resectively (i.e. there was no sensor fusion, and in each case, the total of 6 features was used for classification). Figure 5 simultaneously shows the first two rincial comonents for each of the 48 signals used in the four exeriments described above. It visually illustrates the class searation when different combinations of signals and signal features are used. s 1,, 3 and 4 in Figure 4 corresond to lots a, b, c and d, resectively, in Figure 5. 4

5 Figure. Plots of binomial RIDs of signals coming from the force sensor (lots a and d), vibration sensor (lots b and e) and microhone (lots c and f) when a worn tool was used. Darker areas denote areas of higher signal energy. RIDs on lots a, b and c on one hand, and RIDs on lots d, e, and f on the other hand, have been collected simultaneously (simultaneous readings of the force sensor, force sensor and microhone). Figure 3. Moments of the TIRs of the RIDs of the signals obtained when a shar tool was mounted on the machine. Plots a-f of the moments shown in this figure corresond to the TIR moments of the RIDs in lots a-f of Figure 1, resectively. The TIR moments are ordered in such a way that ositions 1 to 135 on the abscise corresond to moments E [t], E [ω ], E [ t ], E [ tω], E [ ω ], E t ], E [ t ω],, E ω ], resectively. [ 3 [ s in distinguishing between a shar and a worn tool The second set of exeriments was carried out with 1 training items added to the revious training set in order to inform the classifier about the worn tool machine oeration and test it in detecting this abnormal machine state. The 4 training signals (1 from the oeration with a shar tool and 1 from the oeration with a worn tool) have been added to the remaining 4 signals that were not used in training, and the ability of the classifier to use the Mahalanobis distance from the classes in the training set to distinguish between the two states of machine tool has been tested. Four exeriments have been conducted with the training set described above. In the first exeriment, TIR moments of order u to 3 from all three sensors have been used (total of 4 features). In the second, third and fourth exeriment, TIR moments of order 1 through 5 of the signal RIDs (total of 6 features) from the force, sound and vibration sensor readings, resectively, have been used. Figure 6 shows Mahalanobis signal distances calculated as described in Section from training signals collected during the machine oeration with a shar tool and the training signals collected during the machine oeration with a warn tool. As in Figure 4, the first 4 items reresent machining oeration with a worn tool, and the second 4 items reresent machining oeration with a shar tool. In the first exeriment, no misclassifications have been observed (100% correct classification). In the second exeriment, 10 misclassifications occurred (79.% correct classification), and in the third and fourth exeriment only one misclassification occurred (97.9% correct classification). More detailed classification results are given in Table 1. 5

6 Figure 4. Mahalanobis distances of the TIR moments of the RIDs of the signals collected during the machine oeration with a worn tool (items numbered 1 through 4) and with a shar tool (items numbered 5 through 48). In the first exeriment, TIR moments of order 1 through 3 from all three sensor signals have been used. Figure 6. Mahalanobis distances for exeriments 1,, 3 and 4 from section 3.. Plots a, b, c and d corresond to exeriments 1,, 3 and 4, resectively. The solid lines denote Mahalanobis distances from the training signals on the shar tool machine oeration, while the dotted lines denote Mahalanobis distances from the training signals on the worn tool machine oeration. Table 1. Classification results for exeriments 1,, 3 and 4 from Section 3.. Figure 5. Plots of the first two rincial comonents for each of the 48 signals used in the tests from Figure 4. s 1,, 3 and 4 in Figure 4 corresond to lots a, b, c and d, resectively. The circles denote rincial comonents of the TIR moments roduced from the signals collected during machine oeration with a shar tool, while the asterisks denote rincial comonents of the TIR moments roduced from the signals collected during machine oeration with a worn tool. Shar tool Worn Tool oeration Oeration Total Training Items Total Items (100%) 4 (100%) 1 (100%) 38 1 (87.50%) 17 (70.83%) (79.17%) 47 3 (95.83%) 4 (100%) 3 (97.9%) 47 3 (95.83%) 4 (100%) 4 (97.9%) 1 0 (0%) 0 (0%) 0 (0%) 10 3 (1.50%) 7 (9.17%) (0.83%) 3 1 (4.17%) 0 (0%) 1 (.08%) 4 1 (4.17%) 0 (0%) 1 (.08%) Correctly Classified Misclassified 6

7 4. DISCUSSION It is aarent from Figure 4 that Mahalanobis distances of the TIR moments of the signal RIDs for the signals collected during machine oeration with a shar tool (item numbers 5 through 48) are smaller than those of the TIR moments of the signal RIDs obtained when the tool was worn (item numbers 1 through 4). This increase in Mahalanobis distances when tool conditions drift away from the ones that were observed during training, can be used for early detection and reventive maintenance, which is the ultimate goal in Intelligent Maintenance Systems, [1]- [3]. Furthermore, one can see that the signals that are numbered as item numbers 40 and above demonstrate an increasing trend in their Mahalanobis distances from the training set. The reason for this trend is that these signals have been collected when a significantly thinner workiece was cut than that cut during the training rocess. This caused a change in the rocess arameters and their increased variability because of the reduced stiffness of the workiece, which was readily mirrored in the raising and increasingly variable Mahalanobis distances of the TIR moments of the signals collected during that time. One can also note that the difference in Mahalanobis distances of the TIR moments between the two classes of machine oeration considered in this aer, increases when a combination of sensors is used ( 1 in Section 3.1), rather than when information from only a single sensors is emloyed (s, 3 and 4 in Section 3.1). This imrovement in the sensitivity of the classifier to a change in tool condition is even more visible in Figure 5. It is also aarent from exeriments, 3 and 4 that the vibration and sound sensor signals show a higher sensitivity to lathe toolwear, when comared to that of the force sensor signal. This is in concordance with the conclusions of the study about aroriate sensor selection that ranked the force sensor sensitivity to lathe tool wear below those of the sound and vibration sensors, [19]. The exeriments described in Section 3. demonstrate the ability of the classifier described in this aer to discriminate between a shar and a worn tool once signals collected during machine oeration with both a shar and a worn tool have been resented to it during the training rocess. Results of these exeriments reinforce observations made about the exeriments from Section 3.1. Namely, Mahalanobis distances show a shar change once a transition is made from one class of signals to another, and they aarently cature the change in rocess arameters that occurred when signals were collected. Furthermore, one can see from Table 1 that the classifier erformance imroved and became erfect once information from multile sensors was utilized. 5. CONCLUSIONS AND FUTURE WORK In this aer, a new aroach to machine degradation assessment and monitoring is roosed. It is based on the timefrequency signal rocessing tools and statistical attern recognition. Several exeriments with signals collected from sensors mounted on a CNC lathe machine are erformed in order to demonstrate how this aroach can utilize multile sensor fusion to facilitate an increase in the sensitivity to the changes in the rocess arameters. Furthermore, the generic nature of the time-frequency and statistical attern recognition tools allows the methods roosed in this aer to be alied to a variety of signals and situations, without significant human intervention, such as that necessary when CMAC based aroach is used. Nevertheless, further work is necessary to fully uncover and exloit the otentials of the methods roosed in this aer. Firstly, more signals must be collected under constant rocess arameters, and not with a significantly varying workiece diameter, as was done when signals used in this aer were collected. Also, the Mahalanobis distances roduced, as described in Section 3.3, should be statistically interreted in order to assess the confidence index of the machine erformance. Asymtotic normality of the time-frequency moments used in this aer can be emloyed in accomlishing this task. Finally, in order to fully demonstrate its abilities, the newly roosed aroach should be tested in alications other than rotary machine monitoring. Possible areas of alication are in welding, or gear-shift erformance assessment and monitoring. ACKNOWLEDGEMNT This research was suorted in art by The Engineering Research Center for Reconfigurable Manufacturing Systems (RMS) at the University of Michigan, Ann Arbor as well as NSF Industry/University Cooerative Research Center for Intelligent Maintenance Systems (IMS) at the Univ. of Wisconsin-Milwaukee and the Univ. of Michigan-Ann Arbor.. REFERENCES [1] [] J. Lee, Measurement of Machine Performance Degradation Using a Neural Network Model, Comuters in Industry, [3] J. Lee, Machine Performance Monitoring and Proactive Maintenance in Comuter-Integrated Manufacturing: Review and Persective, Int. Journal of Comuter Integrated Manufacturing, 1995, Vol. 8, No. 5, [4] J. S. Albus, A New Aroach to Maniulator Control: The Cerebellar Model Articulation Controller (CMAC), Transactions of ASME, Journal of Dynamic Systems, measurement and Control, Setember 1975,.0-7. [5] J. S. 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