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An online adaptive condition-based maintenance method for mechanical systems
Mechanical Systems and Signal Processing 24 (2010) 2985–2995
Contents lists available at ScienceDirect
Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/jnlabr/ymssp
An online adaptive condition-based maintenance method for mechanical systems Fangji Wu a,b,, Tianyi Wang b, Jay Lee b a b
State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics, Xi’an Jiaotong University, Xi’an 710049, China NSF I/UCR Center for Intelligent Maintenance System, University of Cincinnati, USA
a r t i c l e in fo
abstract
Article history: Received 14 August 2009 Received in revised form 3 April 2010 Accepted 9 April 2010 Available online 24 April 2010
This paper proposes an online adaptive condition-based maintenance method with pattern discovery and fault learning capabilities for mechanical systems. The method is mainly based on a subtype of neural network techniques called self-organizing map (SOM). It is able to reduce local clusters from the same pattern and optimize the SOM architecture to further decrease the calculation cost in matching patterns in the neuron fitting process. Moreover, distance analysis and statistical pattern recognition (SPR) on neurons of the SOM are combined to establish rules and criteria for conducting and controlling the discovery and learning process so continuous process as purging prototypes on the map can be avoided. An experiment on condition monitoring of a machine tool test bed demonstrates and validates the effectiveness of the proposed approach. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Condition-based maintenance Self-organizing map Statistical pattern recognition Machine tool
1. Introduction In modern industry, the tendency towards, and popularity of, utilizing condition-based maintenance (CBM) in order to minimize breakdowns and their impact upon performance, reduce maintenance costs, improve production efficiency, and ensure safety has attracted more and more attention and interest [1]. CBM is a maintenance paradigm that recommends maintenance decisions based on the information collected through condition monitoring. Currently, in order to determine and understand the ongoing physical behavior of machines, and further identify normal and abnormal patterns, various sensors have been developed and adopted to monitor and record information such as temperature, pressure, sound, and vibration [2]. To make use of this information, techniques in signal processing, feature selection, health assessment, fault diagnosis, and remaining useful life (RUL) prediction are continuously being developed, providing new tools to fulfill the requirements of CBM. More specifically, the development of a maintenance system with intelligent features in fault detection and knowledge accumulation for mechanical structures is an attractive academic pursuit for researchers while at the same time, becoming a powerful assistance to industry where it is almost impossible to manually analyze rapidly growing data to extract valuable decision-making information. Currently, in order to fulfill the need for fault identification to solve the practical problems of mechanical systems, many data mining methodologies, such as statistical methods, neural networks, decision tree, support vector machine (SVM), rough sets and various hybrid methods have been introduced and validated [3–7]. After training with these methods, specific rules or models can be established to reproduce a specified system behavior or represent the underlying Corresponding author at: State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics, Xi’an Jiaotong University, Xi’an 710049, China. Tel.: + 1 513 910 9752. E-mail address: [email protected] (F. Wu).
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mechanism, and then can further be used to detect and diagnose abnormal behaviors. These methods can be implemented for online applications for performance evaluation and decision-making. However, once new knowledge, such as unexpected patterns or novel rules, is discovered in previously mined databases, the knowledge discovery process stops unless more effective data mining methods are employed or more information is gathered. Even though sophisticated and complete knowledge is learned from historical databases, its limited ability to handle new data may still induce misjudgment or false alarms due to the unforeseen changes in the system dynamics. Especially, for condition monitoring activities, which require reliable, robust, and efficient fault mapping and identification abilities, the unlearned patterns may drastically affect the equipment health assessment and consequently fail to prevent system breakdowns due to an unpredicted failure. In reality, most knowledge discovery is an iterative and continuous process. The nature of condition monitoring requires an online and adaptive updating ability to accumulate knowledge such as operating patterns and faults. On the other hand, in reality, mechanical systems are usually non-linear systems with complex, dynamic characteristics, therefore raw data sampled in different operating conditions or fault situations rarely have a purely linear relationship. Due to the strength of artificial neural networks (ANN), such as the ability to easily deal with complex problems without sophisticated and specialized knowledge, the ability to carry out classifications, the ability to deal with non-linear systems and low operational response times after the learning phase, many methods based on ANN have been developed for online surveillance with knowledge discovery, novelty detection and learning abilities [8–10]. In this paper, an online adaptive pattern discovery and fault learning method for mechanical maintenance systems with a concentration on condition monitoring is proposed. This method is mainly based on a subtype of neural network called self-organizing map (SOM). SOM uses powerful pattern analysis and clustering methods, while at the same time providing excellent visualization capabilities. In order to reduce local clusters from the same pattern and improve classification, the map size estimation method is employed to optimize the SOM architecture and further decrease the calculation cost involved in matching patterns. Moreover, distance analysis and statistical pattern recognition (SPR) on the neurons of the SOM are combined to establish the rules and criteria to conduct and control the discovery and learning process to achieve online adaptive functionality. Furthermore, by selecting the proper timing for updating the map, this method does not need to keep purging previous prototypes on the map. In order to validate the proposed approach, its application in an experiment involving the condition monitoring of a machine tool test bed is introduced. The results demonstrate the effectiveness of the proposed approach. The contents of this paper are organized as follows. In Section 2, the SOM is briefly introduced. The scheme of the proposed approach as well as the fundamental methodologies involved, are presented in Section 3. Then, Section 4 shows the effectiveness of the proposed approach when applied for condition monitoring of a machine tool test bed. Finally, conclusions are drawn in Section 5.
2. Self-organizing map (SOM) SOM, first introduced by T. Kohonen, is a subtype of neural network techniques. The term ‘‘self-organizing’’ refers to the ability to learn and organize information without being given the corresponding class labels for the input pattern. SOM uses powerful pattern analysis and clustering methods, while providing excellent visualization capabilities at the same time. It implements an orderly mapping of a high-dimensional distribution onto a regular low-dimensional grid thereby allowing it to convert complex, non-linear statistical relationships between high-dimensional data into simple geometric relationships on a low-dimensional display [11,12]. A SOM usually consists of neurons from a few dozen up to several thousand. Each neuron is represented by a d-dimensional weight vector (also known as prototype vector or codebook vector) m= [m1,y,md], where d is equal to the dimension of the input vectors x= [x1,y,xd]. The neurons are connected to adjacent neurons by a neighborhood relation, which dictates the topology or structure of the map. The training of SOM is usually an iterative process. In each training step, one sample vector x from the input data set is chosen randomly and the distances between it and all the weight vectors of the SOM are calculated using some distance measure. The neuron possessing the vector that is closest to the input vector x is called the best-matching unit (BMU), denoted by mBMU: JxmBMU J ¼ minfJxmi Jg, i
ð1Þ
where || || is the distance measure, typically Euclidean distance. After finding the BMU, the weight vectors of the SOM are updated so that the BMU is moved closer to the input vector in the input space. The update rule for the weight vector of unit i at time t is mi ðt þ 1Þ ¼ mi ðtÞ þ aðtÞhci ðtÞ½xðtÞmi ðtÞ,
ð2Þ
where hci(t) and a(t) denote the neighborhood kernel around the winner unit c and the learning rate at time t, respectively. The topological neighbors of the BMU are treated similarly. This adaptation procedure stretches the BMU and its topological neighbors towards the sample vector. Eventually, a regular low-dimensional grid in an ordered fashion can be obtained.
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The Kohonen SOM has been considered as novelty detector [13,14]. Some researches and applications of automated novelty detection have been introduced [15,16]. These methods evaluate the distance between new/test dataset and map units of SOM trained with inputs from normal dataset, and calculate the relative position of new/test dataset to trained normal class boundary/threshold. These novelty detection approaches provide information about whether a dataset fits the same distribution as the data that was used to train the SOM. For condition-based maintenance, SOM-based novelty detection which places one threshold value around the data space for the concern of ‘‘normal/abnormal case’’ is not sufficient. Condition-based maintenance requires reliable, robust, and efficient fault mapping and identification abilities, especially for complex machinery systems which involve multi-components and/or multi-failure models. The SOM needs to be extended with online adaptive updating ability to accumulate knowledge such as operating patterns and faults besides the ‘‘normal/abnormal case’’ information, so that prompt and targeted measures can be taken to minimize breakdowns. Using prior existing knowledge, training diagnostic network, and carrying out on-line learning for establishing adaptive system for condition monitoring are necessary [17]. The Kohonen SOM is actually a static SOM with a fixed structure. The grid size and the number of nodes have to be determined a priori. This results in a significant limitation on the final mapping as it is not possible to know the most appropriate structure beforehand. Moreover, though a Kohonen SOM trained by sample vectors is able to provide a regular grid in ordered fashion, it is difficult to determine whether the map has been organized into a proper cluster structure in which projected sample vectors from same case are concentrated and neurons representing different cases are distinguishable without overlap. Therefore, several SOM variations, known as dynamic SOMs, have been introduced to overcome the aforementioned shortcomings and improve the performance. These models include growing cell structures (GCS) model, incremental grid growing (IGG) model, growing self-organizing map (GSOM) and evolving self-organizing map (ESOM) [18–22]. Although these dynamic models will obviously become more complex compared to static SOM, significant advantages could be gained from such dynamic models. The main advantage is their ability to grow a better structure to represent the application. This becomes a very useful aspect in applications such as data mining, in which it is not possible for the neural network designer or users to be aware of the inherent structure in the data. 3. Online adaptive SOM for pattern discovery and fault learning In this section, a SOM-based approach with online adaptive pattern discovery and fault learning capabilities is presented in detail. It can be taken as an alternative to dynamic SOM. However, in contrast to the aforementioned dynamic SOM with a local growth process for cell insertion or nodes generation from the boundary, the growing process of the proposed method is actually a global process which is determined by performance evaluation of the network structure using the input data. An overview of the proposed method is shown in Fig. 1. Firstly, based on the previous cases and datasets, the SOM is initialized. Secondly, a map size estimation method is employed to optimize the SOM architecture for clear classification. Newly acquired data then undergo a neuron fitting procedure during which the current performance of the system is evaluated and classified. If unknown conditions are discovered where the previous neural classifier is no longer valid, self-adaptive training algorithms will be activated to update the SOM and accumulate the knowledge. 3.1. SOM Initialization SOM initialization is a case-based process. A case is usually a specific problem that has been previously encountered and solved, and often must be documented for various purposes. The first type of knowledge that can be learned from cases is the class labels of different datasets which are essential in order for the decision boundaries to be drawn. The second type of knowledge that can be learned from cases is features or symptoms. Although features can be defined in different domains such as time domain, frequency domain and time–frequency domain, cases can help to select and prune them and reserve the representative features for distinguishing different patterns efficiently. The third type of knowledge is solutions of cases which can be used for post-process. After features are extracted and selected from labeled datasets of historic
Fig. 1. Flowchart of online adaptive SOM.
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cases, the feature matrix as input is then forwarded to train the initial SOM. In this stage, the static SOM approach is used, usually resulting in the creation of a small map in the beginning. In other words, the map size is predetermined and it is not necessary to consider whether the map has been organized into a proper cluster structure according to the historic data. 3.2. SOM Optimization After initialization, SOM is trained as an organized cluster structure where each cluster or neuron can be considered as a ‘‘class’’. However, class redundancy, which is induced by map size selection, may be found using traditional SOM. If the map size is too large, the distances between the neurons are small and the number of neurons from the same pattern increases. If the number of neurons representing the same pattern is large, the time needed for the quantitative analysis of the pattern discovery process increases exponentially. On the other hand, if the map size is too small, the neurons of different patterns may be too close to each other or at worst, overlapping and thus an incorrect classification will be easily induced since the distinguishing ability has been significantly limited. The natural approach to the class redundancy issue is adjusting the map size to group the similar neurons together and to represent them with a relatively more general pattern. Furthermore, the distances between final patterns should be maximized. Suppose that there exists a set of d-dimensional samples in feature space. The ith subset Si labeled ‘‘i’’ has Ni samples which are projected onto Mi neurons in the SOM and the kth neuron has nk samples projected onto it. In order to form well-separated, compact clusters in the final map, a criterion function is introduced: 8 Mi X > nk > < ra maxk fnk g ð3Þ , k¼1 > > : JC C J Z b DistðiajÞ i
j
where a is the threshold value, Dist is the Euclidean distance between two adjacent neurons, b is the threshold coefficient, and Ci ¼
Mi X nk mik , N k¼1 i
ð4Þ
where mik is weight vector of the kth neuron onto which Si is projected. This criterion function is used to limit the number of similar neurons and ensure adequate distances between patterns. Typically, the Euclidean distance between the first two adjacent neurons or the minimum Euclidean distance between any two patterns is employed to represent the Dist. By adjusting the map size and using the above criterion functions, the structure of labeled patterns can be optimized to a reasonable state. 3.3. Neuron fitting, fault identification and SOM learning After optimization, SOM is used to monitor the physical system for any deviations in its dynamics. The activity of online condition monitoring and fault identification is to assign the current transient pattern of the system to one of the known patterns in the map. This process is called neuron fitting. It tries to find the neuron that possesses closest similarity to current feature vectors of raw data. For SOM, the neuron fitting process can be simplified as finding the BMU using Eq. (1). In addition, the distance analysis should be applied before assigning a label to the current data as JxmBMU J o Dist,
ð5Þ
where Dist is the same as in Eq. (3). At the online monitoring stage, Eq. (5) is necessary since even the BMU defined with Eq. (1) may already have an unacceptable distance from the input vector. In the presence of novel operating conditions or fault situations, changes in the dynamics will cause a mismatch in the behaviors of neuron fitting to all existing classes. The objective of a learning scheme is to develop an adaptive procedure that not only detects changes in the dynamics but is also able to learn these changes for the purpose of identifying faults more efficiently. The learning strategy based on SOM can be described as: (1) proceed with neuron fitting and fault identification; (2) if neuron fitting to all existing classes fails, then label the novel data and integrate them into a historic database, and wait for next update; (3) if the requirement for updating is met, then SOM is automatically triggered to retrain and update itself with the newly detected and gathered novel data in database without the need for a user interaction. After the SOM is updated, the novel patterns are integrated into it, and it is then carried forward to the SOM optimization process. The optimized map with stronger pattern recognition abilities is then ready for online condition monitoring and fault identification. In online mode, timing for updating is critical. One hit or few hits in an unlabeled neuron may not arrive at the conclusion that the current system behavior falls into a new region which has not been specified before.
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If timing is not specified, and the updating time is disregarded, dynamic SOM will tend to eagerly overwrite previously learned data. Therefore, building a robust and reliable criterion for the updating time is necessary. In order to ensure that an adequate updating time is determined, the SPR method is introduced. It is a quantitative performance assessment tool that analytically compares the distribution of features and evaluates the overlap between the most recently observed signatures and those observed during previously learned operation. This overlap is expressed through the so-called performance confidence value (CV), which ranges from zero to one, with a higher CV signifying a higher overlap [23]. If the d-dimensional data x from a class follows the Gaussian distribution, the probability density function (PDF) can be expressed as 1 1 gðx; m, SÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp ðxmÞT S1 ðxmÞ , ð6Þ 2 ð2pÞd jSj where m is the center and S is the covariance matrix of PDF. Based on the maximum likelihood estimation (MLE), the best estimation of m and S is 8 n > 1X > > m^ ¼ x > > ni¼1 i < ð7Þ n X > > T ^ ¼ 1 > ^ ^ S ðx m Þðx m Þ > i i > : n1 i ¼ 1 where n is the number of observations. The CV between two datasets in L2 space can then be calculated by CV ¼
^ 1 Þ g2 ðx; m^ , S ^ 2 Þj jg1 ðx; m^ 1 , S L2 2 ^ 1 ÞJL2 Jg2 ðx; m^ , S ^ 2 ÞJL2 Jg1 ðx; m^ 1 , S 2
:
Based on the above, a feasible and straightforward criterion for updating time can be expressed as ( Ns Z l CVi r r i ¼ 1, . . . ,N
ð8Þ
ð9Þ
where NS is the number of hits in an unlabeled neuron, CVi is the CV between current behavior and the ith pattern behavior, N is the number of patterns and l and r are the threshold value. In practice, l should be decided according to the specific application, and factors such as running speed, inspection interval and response time will influence the selection. 4. Case study In order to further demonstrate and validate the proposed approach, an experiment on condition monitoring of a machine tool test bed is explained in this section. Machine tools are critical equipments in metal-cutting industry. It has become more demanding to operate a machine tool and along the same lines of argument, it has also become more challenging to maintain it. The test bed is a high-performance vertical machining center (VMC) with a driven spindle that can run up to 12,000 rpm. It is a general purpose machine tool which can be used for drilling, tapping, end-milling and surface-milling, etc. Vibration near the bearing installed in the spindle is recorded using a single axis piezoelectric accelerometer PCB 6241B11 which has a 750 g measurement rating with approximately 100 mV/g sensitivity. This accelerometer has been installed via magnet mount. The location of the sensor is shown in Fig. 2. The sensor signal digitizer is the National Instruments USB-9233 module. It has 4-channel input and is capable of simultaneously sampling up to 50 kHz, with a built-in anti-aliasing filter. In this case, the sampling frequency was set to 10 kHz. The initial machine tool test bed operating condition is considered as normal. The three states of defects were made to exhibit tool wear, loosened spindle bearing and tightened spindle bearing. Loosened spindle bearing was simulated by partially unscrewing bolts of spindle bearing housing cap as shown in Fig. 3(a) to reduce pre-load force. Normally tightened bolts are put in place with 120 lb force, and loosened bolts are assembled with 50 or 0 lb force. The outer rim of the spindle bearing housing cap was ground to reduce the thickness by 0.02 mm so that the pre-load force of the spindle bearing (measured by distance that creates pre-load force by the bearing housing cap) is increased from the standard 0.02 mm to 0.04 mm, so tightened spindle bearing can be simulated as shown in Fig. 3(b). Condition monitoring of machining center utilizes an ‘‘out-of-process’’ strategy, which means that bearing health is monitored while the machine tool is not in operation or normal production. This is a necessary characteristic chosen for the monitoring platform to remove the effects of variable factors (depth of cut, part material, and other in-cutting parameters), otherwise, numerous experiments (including time, resources and effort) would have been needed to develop accurate and robust models that would take these factors into account, which can be prohibitively more expensive in the long run. Instead, the routine procedure, done automatically, will force the machine to perform specific actions and movements at predefined operating conditions. The strategy is implemented as a fixed cycle feature test (FCFT) through a routine NC program. FCFT can simplify machine operation conditions by fixing the running speeds and guarantee comparable conditions such as machine temperature for decision making of condition-based maintenance. The normal operation of the condition monitoring system requires a daily self-test of the machine by running the routine NC program. At the
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Fig. 2. Location of the single axis accelerometer on machine spindle.
Fig. 3. (a) Loosened bolts on spindle bearing housing cap to reduce bearing pre-load force. (b) Ground outer rim of spindle bearing housing cap to increase bearing pre-load force.
development stage, however, it is necessary to quickly collect a large amount of data under various conditions of the machine in order to create the monitoring/diagnosis models. Therefore, it is necessary to accelerate the data collection by running the routine program many times in a day, especially when a new machine condition is induced during experiments. The signal was collected while the machine was running a routine program. In each routine cycle, the machine was operated in three speeds as: 2500 rpm (low speed), 4500 rpm (medium speed), and 6500 rpm (high speed). The recorded raw sensor data are continuous vibration signals over a period of more than 30 s, as shown in Fig. 4(a). With the vibration data and controller data synchronized, the vibration data can be segmented by retaining the segment that the speed is within 1% variation of the steady-speed (2500, 4500, 6500 rpm) using speed rate reading in the controller data as shown in Fig. 4(b). Therefore three data segments can be isolated from the raw data in each routine cycle and further processing will be applied to the desired segments. In the figure, LSS, MSS, and HSS refer to low speed segment, medium speed segment, and high speed segment, respectively. The extracted machine feature set is a combination of multiple features in time domain and frequency domain. For bearing, a defect on the inner or outer race will cause an impulse each time a rolling element contacts the defect. In frequency domain, an inner race defect can express itself as the characteristic frequency called inner race ball pass frequency (BPFI), and for an outer race defect it occurs at outer race ball pass frequency (BPFO). A defect on rolling element will cause an impulse each time the defect surface contacts the inner or outer races, which will excite the ball spin frequency (BSF) [24]. For spindle, defects such as unbalance will excite harmonic frequency components of shaft rotating frequency. In time domain, these defects can change the signal statistical characteristics accordingly. Table 1 lists bearing
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Fig. 4. Vibration and speed signals of spindle during routine procedure.
Table 1 Characteristic frequency orders of bearing defect statuses. Bearing model
FAG HC7014C
BPFI BPFO BSF
15.19 12.81 5.63
Table 2 Feature list of spindle vibration signal. F1 F2 F3 F4 F5 F6 F7 F8
Root-mean-square (RMS) of LSS RMS of MSS RMS of HSS Sum-of-square (SOS) of the three spectra (total energy of LSS, MSS, and HSS) SOS around 1st, 2nd, and 3rd order of LSS, MSS, and HSS, divided by F4 SOS around 1x, 2x, and 3x BPFI of LSS, MSS, and HSS, divided by F4 SOS around 1x, 2x, and 3x BPFO of LSS, MSS, and HSS, divided by F4 SOS around 1x, 2x, and 3x BSF of LSS, MSS, and HSS, divided by F4
1st order means shaft rotational frequency.
statuses and their corresponding frequency orders. The frequency order is the ratio between the characteristic frequency and the shaft rotating frequency. The features in Table 2 are computed from the spindle vibration signal and form an 8dimensional feature vector as input to SOM. Moreover, the values of a, b, l, and r should be decided. The a is used to limit the number of similar neurons. With a large a value, a pattern will turn out to be scattered in many neurons; on the contrary, with a small a value (close to 1), a pattern will be limited in only one neuron without the consideration of variation in the pattern. The b value can ensure adequate distances between patterns. With a large b value, the distance between patterns will be unnecessarily long and map size could be very large; if the b value is too small (close to 0), the patterns will be highly overlapped. The l value controls the number of hits in an unlabeled neuron and should be decided taking machine running speed, inspection interval, response time and so on into consideration. The value of r is between 0 and 1, with higher value signifying a higher similarity between current behavior and stored pattern behavior, and vice versa. In this case, after comprehensive consideration of all aforementioned factors, the values of a, b, l, and r are set as 2.5, 1, 50 and 0.6, respectively. The SOM is initialized first with data from Case 1 (C1) as normal and Case 2 (C2) as tool wear. The map size is predetermined as {12, 12} as shown in Fig. 5(a). If the kth neuron has nk samples projected onto it, the rendering area of
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Fig. 5. Optimization process of two cases SOM: (a) map size {12, 12}, (b) map size {8, 8}, (c) map size {4, 4}, (d) map size {3, 3}.
Fig. 6. Neuron fitting process of signal from (a) C1, (b) C2, (c) C3.
this neuron is Ak ¼ ðnk =NÞ1=2
ð10Þ
where N is the maximum number of samples projecting onto one neuron. Then, after initialization, the map is optimized to {3, 3} as illustrated in Fig. 5. In Fig. 5, TSI refers to ‘‘time from start of initialization’’ to provide the time information of SOM development. Fig. 6(a) shows the neuron fitting process when the signal from C1 hits the C1 neuron with 0.68 Dist, and Fig. 6(b) shows neuron fitting process when the signal from C2 hits the C2 neuron with 0.39 Dist. When the signal from Case 3 (C3), loosened spindle bearing, is acquired, it cannot fall into any of the existing classes, as shown in Fig. 6(c). For visualization, good fitting data is depicted as round symbol and bad fitting data as cross symbol in the figure. Since the distance analysis shows that it exceeds the setting threshold, it is determined to be from a new pattern. As the requirements for updating are met, the SOM is updated with a newly obtained database and optimized as illustrated in Fig. 7(a). However, the signal from Case 4 (C4), tightened spindle bearing, cannot fit well in the newly updated map with large distances between the three patterns, as shown in Fig. 7(b). Even BMU of the signal is in C2 region, the distance between the data and this BUM is 8.60 times of Dist, which means that the signal cannot fit well in this three patterns SOM map. A better map with stronger fault identification ability can then be obtained after updating as shown in Fig. 8, in which all the four cases are contained. After 18 days operation, the improper pre-load force (tightened) deteriorated the bearing condition and induced a change in machine dynamics that was expressed as vibration spectrum changes and a failure in
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Fig. 7. (a) SOM for three cases, (b) Neuron fitting of signal from C4.
Fig. 8. SOM for four cases.
Fig. 9. Final SOM after 18 days running with tightened bearing pre-load force.
neuron fitting. The SOM finally evolved from a two cases map into a five cases map as shown in Fig. 9. The information of updating time for the three updates is listed in Table 3. The traditional Kohonen SOM for three cases, four cases and five cases, with map sizes {12, 12} and {8, 8}, are illustrated in Figs. 10–12. The experiment on condition monitoring of the machine tool test bed validated the effectiveness of the proposed approach and illustrated that it is able to grow to represent novel patterns without users needing to predetermine the structure of the neuron network. Moreover, the criteria for controlling the discovery and learning process
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Table 3 Information of updating time for the three updates. Update 1 Update 2 Update 3
Maximum CV: 0.0671 Maximum CV: 0.2939 Maximum CV: 0.0016
NS: 50 NS: 50 NS: 50
Fig. 10. SOM for three cases: (a) map size {12, 12}, (b) map size {8, 8}.
Fig. 11. SOM for four cases: (a) map size {12, 12}, (b) map size {8, 8}.
Fig. 12. SOM for five cases: (a) map size {12, 12}, (b) map size {8, 8}.
make online adaptive functionality achievable, and make it possible for the updating time to be determined. Therefore, this method does not need to keep purging prototypes on the map. At the same time, it also provides an excellent visualization capability which is very meaningful for conditional monitoring.
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5. Conclusions The SOM-based approach for CBM with online adaptive pattern discovery and fault learning capabilities has been presented in this paper. The map is first initialized based on previous cases and corresponding datasets. Then, the SOM architecture is optimized through map size estimation for a clear classification. During condition monitoring, newly gathered data are transferred to the neuron fitting procedure to evaluate and classify the current performance of system. The growing process of the SOM is a global process which is determined by performance evaluation of the network structure on the input data. If unknown conditions are discovered where the previous neural classifier is no longer valid, self-adaptive training algorithms will be activated to update the map and accumulate the knowledge. Therefore, this method does not need to continuously purge prototypes on the map. Moreover, it can also provide excellent visualization capability which is very meaningful for conditional monitoring activity. The proposed method was applied to condition monitoring of a machine tool test bed, and it is shown as an effective tool for CBM of mechanical systems.
Acknowledgements The authors would like to thank Dr. Yuhe Liao and other researchers at Research Institute of Diagnostics and Cybernetics, Xi’an Jiaotong University for their kind support during the work of this paper. References [1] A.K.S. Jardine, D. Lin, D. Banjevic, A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mechanical Systems and Signal Processing 20 (2006) 1483–1510. [2] P. Ripka, A. Tipek, Modern Sensors Handbook, ISTE, London, UK, 2007. [3] B. Samanta, K.R. Al-Balushi, S.A. Al-Araimi, Artificial neural networks and support vector machines with genetic algorithm for bearing fault detection, Engineering Applications of Artificial Intelligence 16 (2003) 657–665. [4] M. Ge, R. Du, G. Zhang, Y. Xu, Fault diagnosis using support vector machine with an application in sheet metal stamping operations, Mechanical Systems and Signal Processing 18 (2004) 143–159. [5] L. Zhang, A.K. Nandi, Fault classification using genetic programming, Mechanical Systems and Signal Processing 21 (2007) 1273–1284. [6] Y. Lei, Z. He, Y. Zi, Q. Hu, Fault diagnosis of rotating machinery based on multiple ANFIS combination with GAs, Mechanical Systems and Signal Processing 21 (2007) 2280–2294. [7] M. Goebel, L. Gruenwald, A survey of data mining and knowledge discovery software tools, in: ACM SIGKDD, vol. 1, 1999, pp. 20–33. [8] N. Kasabov, Evolving fuzzy neural networks for supervised/unsupervised online knowledge-based learning, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 31 (2001) 902–918. [9] H. Marzi, Real-time fault detection and isolation in industrial machines using learning vector quantization, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 218 (2004) 949–959. [10] M. Markou, S. Singh, Novelty detection: a review–part 2: neural network based approaches, Signal Processing 83 (2003) 2499–2521. [11] T. Kohonen, The self-organizing map, Neurocomputing 21 (1998) 1–6. [12] J. Vesanto, J. Himberg, E. Alhoniemi, J. Parhankangas, Self-organizing map in matlab: the SOM toolbox, in: Proceedings of the Matlab DSP Conference 1999, vol. 1, Espoo, Finland, 1999, pp. 35–40. [13] A. Ypma, R.P.W. Duin, Novelty detection using self-organizing maps, Progress in Connectionist Based Information Systems 2 (1998) 1322–1325. [14] O. Taylor, J. Tait, J. MacIntyre, Improved classification for a data fusing Kohonen self organizing map using a dynamic thresholding technique, in: Proceedings of IJCAI-99, The 16th International Joint Conference on Artificial Intelligence, vol. 2, July 31–August 6, 1999, pp. 828–832. [15] D.A. Clifton, et al., Automated Novelty Detection in Industrial Systems, in: Studies in Computational Intelligence (SCI), vol. 116, 2008, pp. 269–296. [16] M.L.D. Wong, L.B. Jack, A.K. Nandi, Modified self-organizing map for automated novelty detection applied to vibration signal monitoring, Mechanical Systems and Signal Processing 20 (2006) 593–610. [17] A. Adgar, C. Emmanouilidis, J. MacIntyre, P. Mattison, K. McGarry, G. Oatley, O. Taylor, The application of adaptive systems in condition monitoring, International Journal of Condition Monitoring and Diagnostic Engineering Management 1 (1) (1998) 13–17. [18] D. Alahakoon, S.K. Halgamuge, B. Srinivasan, Dynamic self-organizing maps with controlled growth for knowledge discovery, IEEE Transactions on Neural Networks 11 (2000) 601–614. [19] J. Blackmore, R. Miikkulainen, Incremental grid growing: encoding high-dimensional structure into a two-dimensional feature map, in: IEEE International Conference on Neural Networks, vol. 1, San Francisco, CA, USA, 1993, pp. 450–455. [20] B. Fritzke, Growing grid—a self-organizing network with constant neighborhood range and adaptation strength, Neural Processing Letters 2 (1995) 9–13. [21] D. Deng, N. Kasabov, On-line pattern analysis by evolving self-organizing maps, Neurocomputing 51 (2003) 87–103. [22] B. Fritzke, Growing cell structures-a self—organizing network for unsupervised and supervised learning, Neural Networks 7 (1994) 1441–1460. [23] D. Djurdjanovic, J. Lee, J. Ni, Watchdog agent—an infotronics-based prognostics approach for product performance degradation assessment and prediction, Advanced Engineering Informatics 17 (2003) 109–125. [24] B.D. Forrester, Advanced vibration analysis techniques for fault detection and diagnosis in geared transmission systems, Ph.D. Thesis, Swinburne University of Technology, Melbourne, Australia, 1996.
Contents lists available at ScienceDirect
Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/jnlabr/ymssp
An online adaptive condition-based maintenance method for mechanical systems Fangji Wu a,b,, Tianyi Wang b, Jay Lee b a b
State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics, Xi’an Jiaotong University, Xi’an 710049, China NSF I/UCR Center for Intelligent Maintenance System, University of Cincinnati, USA
a r t i c l e in fo
abstract
Article history: Received 14 August 2009 Received in revised form 3 April 2010 Accepted 9 April 2010 Available online 24 April 2010
This paper proposes an online adaptive condition-based maintenance method with pattern discovery and fault learning capabilities for mechanical systems. The method is mainly based on a subtype of neural network techniques called self-organizing map (SOM). It is able to reduce local clusters from the same pattern and optimize the SOM architecture to further decrease the calculation cost in matching patterns in the neuron fitting process. Moreover, distance analysis and statistical pattern recognition (SPR) on neurons of the SOM are combined to establish rules and criteria for conducting and controlling the discovery and learning process so continuous process as purging prototypes on the map can be avoided. An experiment on condition monitoring of a machine tool test bed demonstrates and validates the effectiveness of the proposed approach. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Condition-based maintenance Self-organizing map Statistical pattern recognition Machine tool
1. Introduction In modern industry, the tendency towards, and popularity of, utilizing condition-based maintenance (CBM) in order to minimize breakdowns and their impact upon performance, reduce maintenance costs, improve production efficiency, and ensure safety has attracted more and more attention and interest [1]. CBM is a maintenance paradigm that recommends maintenance decisions based on the information collected through condition monitoring. Currently, in order to determine and understand the ongoing physical behavior of machines, and further identify normal and abnormal patterns, various sensors have been developed and adopted to monitor and record information such as temperature, pressure, sound, and vibration [2]. To make use of this information, techniques in signal processing, feature selection, health assessment, fault diagnosis, and remaining useful life (RUL) prediction are continuously being developed, providing new tools to fulfill the requirements of CBM. More specifically, the development of a maintenance system with intelligent features in fault detection and knowledge accumulation for mechanical structures is an attractive academic pursuit for researchers while at the same time, becoming a powerful assistance to industry where it is almost impossible to manually analyze rapidly growing data to extract valuable decision-making information. Currently, in order to fulfill the need for fault identification to solve the practical problems of mechanical systems, many data mining methodologies, such as statistical methods, neural networks, decision tree, support vector machine (SVM), rough sets and various hybrid methods have been introduced and validated [3–7]. After training with these methods, specific rules or models can be established to reproduce a specified system behavior or represent the underlying Corresponding author at: State Key Laboratory for Manufacturing Systems Engineering, Research Institute of Diagnostics and Cybernetics, Xi’an Jiaotong University, Xi’an 710049, China. Tel.: + 1 513 910 9752. E-mail address: [email protected] (F. Wu).
0888-3270/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2010.04.003
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mechanism, and then can further be used to detect and diagnose abnormal behaviors. These methods can be implemented for online applications for performance evaluation and decision-making. However, once new knowledge, such as unexpected patterns or novel rules, is discovered in previously mined databases, the knowledge discovery process stops unless more effective data mining methods are employed or more information is gathered. Even though sophisticated and complete knowledge is learned from historical databases, its limited ability to handle new data may still induce misjudgment or false alarms due to the unforeseen changes in the system dynamics. Especially, for condition monitoring activities, which require reliable, robust, and efficient fault mapping and identification abilities, the unlearned patterns may drastically affect the equipment health assessment and consequently fail to prevent system breakdowns due to an unpredicted failure. In reality, most knowledge discovery is an iterative and continuous process. The nature of condition monitoring requires an online and adaptive updating ability to accumulate knowledge such as operating patterns and faults. On the other hand, in reality, mechanical systems are usually non-linear systems with complex, dynamic characteristics, therefore raw data sampled in different operating conditions or fault situations rarely have a purely linear relationship. Due to the strength of artificial neural networks (ANN), such as the ability to easily deal with complex problems without sophisticated and specialized knowledge, the ability to carry out classifications, the ability to deal with non-linear systems and low operational response times after the learning phase, many methods based on ANN have been developed for online surveillance with knowledge discovery, novelty detection and learning abilities [8–10]. In this paper, an online adaptive pattern discovery and fault learning method for mechanical maintenance systems with a concentration on condition monitoring is proposed. This method is mainly based on a subtype of neural network called self-organizing map (SOM). SOM uses powerful pattern analysis and clustering methods, while at the same time providing excellent visualization capabilities. In order to reduce local clusters from the same pattern and improve classification, the map size estimation method is employed to optimize the SOM architecture and further decrease the calculation cost involved in matching patterns. Moreover, distance analysis and statistical pattern recognition (SPR) on the neurons of the SOM are combined to establish the rules and criteria to conduct and control the discovery and learning process to achieve online adaptive functionality. Furthermore, by selecting the proper timing for updating the map, this method does not need to keep purging previous prototypes on the map. In order to validate the proposed approach, its application in an experiment involving the condition monitoring of a machine tool test bed is introduced. The results demonstrate the effectiveness of the proposed approach. The contents of this paper are organized as follows. In Section 2, the SOM is briefly introduced. The scheme of the proposed approach as well as the fundamental methodologies involved, are presented in Section 3. Then, Section 4 shows the effectiveness of the proposed approach when applied for condition monitoring of a machine tool test bed. Finally, conclusions are drawn in Section 5.
2. Self-organizing map (SOM) SOM, first introduced by T. Kohonen, is a subtype of neural network techniques. The term ‘‘self-organizing’’ refers to the ability to learn and organize information without being given the corresponding class labels for the input pattern. SOM uses powerful pattern analysis and clustering methods, while providing excellent visualization capabilities at the same time. It implements an orderly mapping of a high-dimensional distribution onto a regular low-dimensional grid thereby allowing it to convert complex, non-linear statistical relationships between high-dimensional data into simple geometric relationships on a low-dimensional display [11,12]. A SOM usually consists of neurons from a few dozen up to several thousand. Each neuron is represented by a d-dimensional weight vector (also known as prototype vector or codebook vector) m= [m1,y,md], where d is equal to the dimension of the input vectors x= [x1,y,xd]. The neurons are connected to adjacent neurons by a neighborhood relation, which dictates the topology or structure of the map. The training of SOM is usually an iterative process. In each training step, one sample vector x from the input data set is chosen randomly and the distances between it and all the weight vectors of the SOM are calculated using some distance measure. The neuron possessing the vector that is closest to the input vector x is called the best-matching unit (BMU), denoted by mBMU: JxmBMU J ¼ minfJxmi Jg, i
ð1Þ
where || || is the distance measure, typically Euclidean distance. After finding the BMU, the weight vectors of the SOM are updated so that the BMU is moved closer to the input vector in the input space. The update rule for the weight vector of unit i at time t is mi ðt þ 1Þ ¼ mi ðtÞ þ aðtÞhci ðtÞ½xðtÞmi ðtÞ,
ð2Þ
where hci(t) and a(t) denote the neighborhood kernel around the winner unit c and the learning rate at time t, respectively. The topological neighbors of the BMU are treated similarly. This adaptation procedure stretches the BMU and its topological neighbors towards the sample vector. Eventually, a regular low-dimensional grid in an ordered fashion can be obtained.
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The Kohonen SOM has been considered as novelty detector [13,14]. Some researches and applications of automated novelty detection have been introduced [15,16]. These methods evaluate the distance between new/test dataset and map units of SOM trained with inputs from normal dataset, and calculate the relative position of new/test dataset to trained normal class boundary/threshold. These novelty detection approaches provide information about whether a dataset fits the same distribution as the data that was used to train the SOM. For condition-based maintenance, SOM-based novelty detection which places one threshold value around the data space for the concern of ‘‘normal/abnormal case’’ is not sufficient. Condition-based maintenance requires reliable, robust, and efficient fault mapping and identification abilities, especially for complex machinery systems which involve multi-components and/or multi-failure models. The SOM needs to be extended with online adaptive updating ability to accumulate knowledge such as operating patterns and faults besides the ‘‘normal/abnormal case’’ information, so that prompt and targeted measures can be taken to minimize breakdowns. Using prior existing knowledge, training diagnostic network, and carrying out on-line learning for establishing adaptive system for condition monitoring are necessary [17]. The Kohonen SOM is actually a static SOM with a fixed structure. The grid size and the number of nodes have to be determined a priori. This results in a significant limitation on the final mapping as it is not possible to know the most appropriate structure beforehand. Moreover, though a Kohonen SOM trained by sample vectors is able to provide a regular grid in ordered fashion, it is difficult to determine whether the map has been organized into a proper cluster structure in which projected sample vectors from same case are concentrated and neurons representing different cases are distinguishable without overlap. Therefore, several SOM variations, known as dynamic SOMs, have been introduced to overcome the aforementioned shortcomings and improve the performance. These models include growing cell structures (GCS) model, incremental grid growing (IGG) model, growing self-organizing map (GSOM) and evolving self-organizing map (ESOM) [18–22]. Although these dynamic models will obviously become more complex compared to static SOM, significant advantages could be gained from such dynamic models. The main advantage is their ability to grow a better structure to represent the application. This becomes a very useful aspect in applications such as data mining, in which it is not possible for the neural network designer or users to be aware of the inherent structure in the data. 3. Online adaptive SOM for pattern discovery and fault learning In this section, a SOM-based approach with online adaptive pattern discovery and fault learning capabilities is presented in detail. It can be taken as an alternative to dynamic SOM. However, in contrast to the aforementioned dynamic SOM with a local growth process for cell insertion or nodes generation from the boundary, the growing process of the proposed method is actually a global process which is determined by performance evaluation of the network structure using the input data. An overview of the proposed method is shown in Fig. 1. Firstly, based on the previous cases and datasets, the SOM is initialized. Secondly, a map size estimation method is employed to optimize the SOM architecture for clear classification. Newly acquired data then undergo a neuron fitting procedure during which the current performance of the system is evaluated and classified. If unknown conditions are discovered where the previous neural classifier is no longer valid, self-adaptive training algorithms will be activated to update the SOM and accumulate the knowledge. 3.1. SOM Initialization SOM initialization is a case-based process. A case is usually a specific problem that has been previously encountered and solved, and often must be documented for various purposes. The first type of knowledge that can be learned from cases is the class labels of different datasets which are essential in order for the decision boundaries to be drawn. The second type of knowledge that can be learned from cases is features or symptoms. Although features can be defined in different domains such as time domain, frequency domain and time–frequency domain, cases can help to select and prune them and reserve the representative features for distinguishing different patterns efficiently. The third type of knowledge is solutions of cases which can be used for post-process. After features are extracted and selected from labeled datasets of historic
Fig. 1. Flowchart of online adaptive SOM.
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cases, the feature matrix as input is then forwarded to train the initial SOM. In this stage, the static SOM approach is used, usually resulting in the creation of a small map in the beginning. In other words, the map size is predetermined and it is not necessary to consider whether the map has been organized into a proper cluster structure according to the historic data. 3.2. SOM Optimization After initialization, SOM is trained as an organized cluster structure where each cluster or neuron can be considered as a ‘‘class’’. However, class redundancy, which is induced by map size selection, may be found using traditional SOM. If the map size is too large, the distances between the neurons are small and the number of neurons from the same pattern increases. If the number of neurons representing the same pattern is large, the time needed for the quantitative analysis of the pattern discovery process increases exponentially. On the other hand, if the map size is too small, the neurons of different patterns may be too close to each other or at worst, overlapping and thus an incorrect classification will be easily induced since the distinguishing ability has been significantly limited. The natural approach to the class redundancy issue is adjusting the map size to group the similar neurons together and to represent them with a relatively more general pattern. Furthermore, the distances between final patterns should be maximized. Suppose that there exists a set of d-dimensional samples in feature space. The ith subset Si labeled ‘‘i’’ has Ni samples which are projected onto Mi neurons in the SOM and the kth neuron has nk samples projected onto it. In order to form well-separated, compact clusters in the final map, a criterion function is introduced: 8 Mi X > nk > < ra maxk fnk g ð3Þ , k¼1 > > : JC C J Z b DistðiajÞ i
j
where a is the threshold value, Dist is the Euclidean distance between two adjacent neurons, b is the threshold coefficient, and Ci ¼
Mi X nk mik , N k¼1 i
ð4Þ
where mik is weight vector of the kth neuron onto which Si is projected. This criterion function is used to limit the number of similar neurons and ensure adequate distances between patterns. Typically, the Euclidean distance between the first two adjacent neurons or the minimum Euclidean distance between any two patterns is employed to represent the Dist. By adjusting the map size and using the above criterion functions, the structure of labeled patterns can be optimized to a reasonable state. 3.3. Neuron fitting, fault identification and SOM learning After optimization, SOM is used to monitor the physical system for any deviations in its dynamics. The activity of online condition monitoring and fault identification is to assign the current transient pattern of the system to one of the known patterns in the map. This process is called neuron fitting. It tries to find the neuron that possesses closest similarity to current feature vectors of raw data. For SOM, the neuron fitting process can be simplified as finding the BMU using Eq. (1). In addition, the distance analysis should be applied before assigning a label to the current data as JxmBMU J o Dist,
ð5Þ
where Dist is the same as in Eq. (3). At the online monitoring stage, Eq. (5) is necessary since even the BMU defined with Eq. (1) may already have an unacceptable distance from the input vector. In the presence of novel operating conditions or fault situations, changes in the dynamics will cause a mismatch in the behaviors of neuron fitting to all existing classes. The objective of a learning scheme is to develop an adaptive procedure that not only detects changes in the dynamics but is also able to learn these changes for the purpose of identifying faults more efficiently. The learning strategy based on SOM can be described as: (1) proceed with neuron fitting and fault identification; (2) if neuron fitting to all existing classes fails, then label the novel data and integrate them into a historic database, and wait for next update; (3) if the requirement for updating is met, then SOM is automatically triggered to retrain and update itself with the newly detected and gathered novel data in database without the need for a user interaction. After the SOM is updated, the novel patterns are integrated into it, and it is then carried forward to the SOM optimization process. The optimized map with stronger pattern recognition abilities is then ready for online condition monitoring and fault identification. In online mode, timing for updating is critical. One hit or few hits in an unlabeled neuron may not arrive at the conclusion that the current system behavior falls into a new region which has not been specified before.
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If timing is not specified, and the updating time is disregarded, dynamic SOM will tend to eagerly overwrite previously learned data. Therefore, building a robust and reliable criterion for the updating time is necessary. In order to ensure that an adequate updating time is determined, the SPR method is introduced. It is a quantitative performance assessment tool that analytically compares the distribution of features and evaluates the overlap between the most recently observed signatures and those observed during previously learned operation. This overlap is expressed through the so-called performance confidence value (CV), which ranges from zero to one, with a higher CV signifying a higher overlap [23]. If the d-dimensional data x from a class follows the Gaussian distribution, the probability density function (PDF) can be expressed as 1 1 gðx; m, SÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp ðxmÞT S1 ðxmÞ , ð6Þ 2 ð2pÞd jSj where m is the center and S is the covariance matrix of PDF. Based on the maximum likelihood estimation (MLE), the best estimation of m and S is 8 n > 1X > > m^ ¼ x > > ni¼1 i < ð7Þ n X > > T ^ ¼ 1 > ^ ^ S ðx m Þðx m Þ > i i > : n1 i ¼ 1 where n is the number of observations. The CV between two datasets in L2 space can then be calculated by CV ¼
^ 1 Þ g2 ðx; m^ , S ^ 2 Þj jg1 ðx; m^ 1 , S L2 2 ^ 1 ÞJL2 Jg2 ðx; m^ , S ^ 2 ÞJL2 Jg1 ðx; m^ 1 , S 2
:
Based on the above, a feasible and straightforward criterion for updating time can be expressed as ( Ns Z l CVi r r i ¼ 1, . . . ,N
ð8Þ
ð9Þ
where NS is the number of hits in an unlabeled neuron, CVi is the CV between current behavior and the ith pattern behavior, N is the number of patterns and l and r are the threshold value. In practice, l should be decided according to the specific application, and factors such as running speed, inspection interval and response time will influence the selection. 4. Case study In order to further demonstrate and validate the proposed approach, an experiment on condition monitoring of a machine tool test bed is explained in this section. Machine tools are critical equipments in metal-cutting industry. It has become more demanding to operate a machine tool and along the same lines of argument, it has also become more challenging to maintain it. The test bed is a high-performance vertical machining center (VMC) with a driven spindle that can run up to 12,000 rpm. It is a general purpose machine tool which can be used for drilling, tapping, end-milling and surface-milling, etc. Vibration near the bearing installed in the spindle is recorded using a single axis piezoelectric accelerometer PCB 6241B11 which has a 750 g measurement rating with approximately 100 mV/g sensitivity. This accelerometer has been installed via magnet mount. The location of the sensor is shown in Fig. 2. The sensor signal digitizer is the National Instruments USB-9233 module. It has 4-channel input and is capable of simultaneously sampling up to 50 kHz, with a built-in anti-aliasing filter. In this case, the sampling frequency was set to 10 kHz. The initial machine tool test bed operating condition is considered as normal. The three states of defects were made to exhibit tool wear, loosened spindle bearing and tightened spindle bearing. Loosened spindle bearing was simulated by partially unscrewing bolts of spindle bearing housing cap as shown in Fig. 3(a) to reduce pre-load force. Normally tightened bolts are put in place with 120 lb force, and loosened bolts are assembled with 50 or 0 lb force. The outer rim of the spindle bearing housing cap was ground to reduce the thickness by 0.02 mm so that the pre-load force of the spindle bearing (measured by distance that creates pre-load force by the bearing housing cap) is increased from the standard 0.02 mm to 0.04 mm, so tightened spindle bearing can be simulated as shown in Fig. 3(b). Condition monitoring of machining center utilizes an ‘‘out-of-process’’ strategy, which means that bearing health is monitored while the machine tool is not in operation or normal production. This is a necessary characteristic chosen for the monitoring platform to remove the effects of variable factors (depth of cut, part material, and other in-cutting parameters), otherwise, numerous experiments (including time, resources and effort) would have been needed to develop accurate and robust models that would take these factors into account, which can be prohibitively more expensive in the long run. Instead, the routine procedure, done automatically, will force the machine to perform specific actions and movements at predefined operating conditions. The strategy is implemented as a fixed cycle feature test (FCFT) through a routine NC program. FCFT can simplify machine operation conditions by fixing the running speeds and guarantee comparable conditions such as machine temperature for decision making of condition-based maintenance. The normal operation of the condition monitoring system requires a daily self-test of the machine by running the routine NC program. At the
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Fig. 2. Location of the single axis accelerometer on machine spindle.
Fig. 3. (a) Loosened bolts on spindle bearing housing cap to reduce bearing pre-load force. (b) Ground outer rim of spindle bearing housing cap to increase bearing pre-load force.
development stage, however, it is necessary to quickly collect a large amount of data under various conditions of the machine in order to create the monitoring/diagnosis models. Therefore, it is necessary to accelerate the data collection by running the routine program many times in a day, especially when a new machine condition is induced during experiments. The signal was collected while the machine was running a routine program. In each routine cycle, the machine was operated in three speeds as: 2500 rpm (low speed), 4500 rpm (medium speed), and 6500 rpm (high speed). The recorded raw sensor data are continuous vibration signals over a period of more than 30 s, as shown in Fig. 4(a). With the vibration data and controller data synchronized, the vibration data can be segmented by retaining the segment that the speed is within 1% variation of the steady-speed (2500, 4500, 6500 rpm) using speed rate reading in the controller data as shown in Fig. 4(b). Therefore three data segments can be isolated from the raw data in each routine cycle and further processing will be applied to the desired segments. In the figure, LSS, MSS, and HSS refer to low speed segment, medium speed segment, and high speed segment, respectively. The extracted machine feature set is a combination of multiple features in time domain and frequency domain. For bearing, a defect on the inner or outer race will cause an impulse each time a rolling element contacts the defect. In frequency domain, an inner race defect can express itself as the characteristic frequency called inner race ball pass frequency (BPFI), and for an outer race defect it occurs at outer race ball pass frequency (BPFO). A defect on rolling element will cause an impulse each time the defect surface contacts the inner or outer races, which will excite the ball spin frequency (BSF) [24]. For spindle, defects such as unbalance will excite harmonic frequency components of shaft rotating frequency. In time domain, these defects can change the signal statistical characteristics accordingly. Table 1 lists bearing
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Fig. 4. Vibration and speed signals of spindle during routine procedure.
Table 1 Characteristic frequency orders of bearing defect statuses. Bearing model
FAG HC7014C
BPFI BPFO BSF
15.19 12.81 5.63
Table 2 Feature list of spindle vibration signal. F1 F2 F3 F4 F5 F6 F7 F8
Root-mean-square (RMS) of LSS RMS of MSS RMS of HSS Sum-of-square (SOS) of the three spectra (total energy of LSS, MSS, and HSS) SOS around 1st, 2nd, and 3rd order of LSS, MSS, and HSS, divided by F4 SOS around 1x, 2x, and 3x BPFI of LSS, MSS, and HSS, divided by F4 SOS around 1x, 2x, and 3x BPFO of LSS, MSS, and HSS, divided by F4 SOS around 1x, 2x, and 3x BSF of LSS, MSS, and HSS, divided by F4
1st order means shaft rotational frequency.
statuses and their corresponding frequency orders. The frequency order is the ratio between the characteristic frequency and the shaft rotating frequency. The features in Table 2 are computed from the spindle vibration signal and form an 8dimensional feature vector as input to SOM. Moreover, the values of a, b, l, and r should be decided. The a is used to limit the number of similar neurons. With a large a value, a pattern will turn out to be scattered in many neurons; on the contrary, with a small a value (close to 1), a pattern will be limited in only one neuron without the consideration of variation in the pattern. The b value can ensure adequate distances between patterns. With a large b value, the distance between patterns will be unnecessarily long and map size could be very large; if the b value is too small (close to 0), the patterns will be highly overlapped. The l value controls the number of hits in an unlabeled neuron and should be decided taking machine running speed, inspection interval, response time and so on into consideration. The value of r is between 0 and 1, with higher value signifying a higher similarity between current behavior and stored pattern behavior, and vice versa. In this case, after comprehensive consideration of all aforementioned factors, the values of a, b, l, and r are set as 2.5, 1, 50 and 0.6, respectively. The SOM is initialized first with data from Case 1 (C1) as normal and Case 2 (C2) as tool wear. The map size is predetermined as {12, 12} as shown in Fig. 5(a). If the kth neuron has nk samples projected onto it, the rendering area of
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Fig. 5. Optimization process of two cases SOM: (a) map size {12, 12}, (b) map size {8, 8}, (c) map size {4, 4}, (d) map size {3, 3}.
Fig. 6. Neuron fitting process of signal from (a) C1, (b) C2, (c) C3.
this neuron is Ak ¼ ðnk =NÞ1=2
ð10Þ
where N is the maximum number of samples projecting onto one neuron. Then, after initialization, the map is optimized to {3, 3} as illustrated in Fig. 5. In Fig. 5, TSI refers to ‘‘time from start of initialization’’ to provide the time information of SOM development. Fig. 6(a) shows the neuron fitting process when the signal from C1 hits the C1 neuron with 0.68 Dist, and Fig. 6(b) shows neuron fitting process when the signal from C2 hits the C2 neuron with 0.39 Dist. When the signal from Case 3 (C3), loosened spindle bearing, is acquired, it cannot fall into any of the existing classes, as shown in Fig. 6(c). For visualization, good fitting data is depicted as round symbol and bad fitting data as cross symbol in the figure. Since the distance analysis shows that it exceeds the setting threshold, it is determined to be from a new pattern. As the requirements for updating are met, the SOM is updated with a newly obtained database and optimized as illustrated in Fig. 7(a). However, the signal from Case 4 (C4), tightened spindle bearing, cannot fit well in the newly updated map with large distances between the three patterns, as shown in Fig. 7(b). Even BMU of the signal is in C2 region, the distance between the data and this BUM is 8.60 times of Dist, which means that the signal cannot fit well in this three patterns SOM map. A better map with stronger fault identification ability can then be obtained after updating as shown in Fig. 8, in which all the four cases are contained. After 18 days operation, the improper pre-load force (tightened) deteriorated the bearing condition and induced a change in machine dynamics that was expressed as vibration spectrum changes and a failure in
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Fig. 7. (a) SOM for three cases, (b) Neuron fitting of signal from C4.
Fig. 8. SOM for four cases.
Fig. 9. Final SOM after 18 days running with tightened bearing pre-load force.
neuron fitting. The SOM finally evolved from a two cases map into a five cases map as shown in Fig. 9. The information of updating time for the three updates is listed in Table 3. The traditional Kohonen SOM for three cases, four cases and five cases, with map sizes {12, 12} and {8, 8}, are illustrated in Figs. 10–12. The experiment on condition monitoring of the machine tool test bed validated the effectiveness of the proposed approach and illustrated that it is able to grow to represent novel patterns without users needing to predetermine the structure of the neuron network. Moreover, the criteria for controlling the discovery and learning process
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Table 3 Information of updating time for the three updates. Update 1 Update 2 Update 3
Maximum CV: 0.0671 Maximum CV: 0.2939 Maximum CV: 0.0016
NS: 50 NS: 50 NS: 50
Fig. 10. SOM for three cases: (a) map size {12, 12}, (b) map size {8, 8}.
Fig. 11. SOM for four cases: (a) map size {12, 12}, (b) map size {8, 8}.
Fig. 12. SOM for five cases: (a) map size {12, 12}, (b) map size {8, 8}.
make online adaptive functionality achievable, and make it possible for the updating time to be determined. Therefore, this method does not need to keep purging prototypes on the map. At the same time, it also provides an excellent visualization capability which is very meaningful for conditional monitoring.
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5. Conclusions The SOM-based approach for CBM with online adaptive pattern discovery and fault learning capabilities has been presented in this paper. The map is first initialized based on previous cases and corresponding datasets. Then, the SOM architecture is optimized through map size estimation for a clear classification. During condition monitoring, newly gathered data are transferred to the neuron fitting procedure to evaluate and classify the current performance of system. The growing process of the SOM is a global process which is determined by performance evaluation of the network structure on the input data. If unknown conditions are discovered where the previous neural classifier is no longer valid, self-adaptive training algorithms will be activated to update the map and accumulate the knowledge. Therefore, this method does not need to continuously purge prototypes on the map. Moreover, it can also provide excellent visualization capability which is very meaningful for conditional monitoring activity. The proposed method was applied to condition monitoring of a machine tool test bed, and it is shown as an effective tool for CBM of mechanical systems.
Acknowledgements The authors would like to thank Dr. Yuhe Liao and other researchers at Research Institute of Diagnostics and Cybernetics, Xi’an Jiaotong University for their kind support during the work of this paper. References [1] A.K.S. Jardine, D. Lin, D. Banjevic, A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mechanical Systems and Signal Processing 20 (2006) 1483–1510. [2] P. Ripka, A. Tipek, Modern Sensors Handbook, ISTE, London, UK, 2007. [3] B. Samanta, K.R. Al-Balushi, S.A. Al-Araimi, Artificial neural networks and support vector machines with genetic algorithm for bearing fault detection, Engineering Applications of Artificial Intelligence 16 (2003) 657–665. [4] M. Ge, R. Du, G. Zhang, Y. Xu, Fault diagnosis using support vector machine with an application in sheet metal stamping operations, Mechanical Systems and Signal Processing 18 (2004) 143–159. [5] L. Zhang, A.K. Nandi, Fault classification using genetic programming, Mechanical Systems and Signal Processing 21 (2007) 1273–1284. [6] Y. Lei, Z. He, Y. Zi, Q. Hu, Fault diagnosis of rotating machinery based on multiple ANFIS combination with GAs, Mechanical Systems and Signal Processing 21 (2007) 2280–2294. [7] M. Goebel, L. Gruenwald, A survey of data mining and knowledge discovery software tools, in: ACM SIGKDD, vol. 1, 1999, pp. 20–33. [8] N. Kasabov, Evolving fuzzy neural networks for supervised/unsupervised online knowledge-based learning, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 31 (2001) 902–918. [9] H. Marzi, Real-time fault detection and isolation in industrial machines using learning vector quantization, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 218 (2004) 949–959. [10] M. Markou, S. Singh, Novelty detection: a review–part 2: neural network based approaches, Signal Processing 83 (2003) 2499–2521. [11] T. Kohonen, The self-organizing map, Neurocomputing 21 (1998) 1–6. [12] J. Vesanto, J. Himberg, E. Alhoniemi, J. Parhankangas, Self-organizing map in matlab: the SOM toolbox, in: Proceedings of the Matlab DSP Conference 1999, vol. 1, Espoo, Finland, 1999, pp. 35–40. [13] A. Ypma, R.P.W. Duin, Novelty detection using self-organizing maps, Progress in Connectionist Based Information Systems 2 (1998) 1322–1325. [14] O. Taylor, J. Tait, J. MacIntyre, Improved classification for a data fusing Kohonen self organizing map using a dynamic thresholding technique, in: Proceedings of IJCAI-99, The 16th International Joint Conference on Artificial Intelligence, vol. 2, July 31–August 6, 1999, pp. 828–832. [15] D.A. Clifton, et al., Automated Novelty Detection in Industrial Systems, in: Studies in Computational Intelligence (SCI), vol. 116, 2008, pp. 269–296. [16] M.L.D. Wong, L.B. Jack, A.K. Nandi, Modified self-organizing map for automated novelty detection applied to vibration signal monitoring, Mechanical Systems and Signal Processing 20 (2006) 593–610. [17] A. Adgar, C. Emmanouilidis, J. MacIntyre, P. Mattison, K. McGarry, G. Oatley, O. Taylor, The application of adaptive systems in condition monitoring, International Journal of Condition Monitoring and Diagnostic Engineering Management 1 (1) (1998) 13–17. [18] D. Alahakoon, S.K. Halgamuge, B. Srinivasan, Dynamic self-organizing maps with controlled growth for knowledge discovery, IEEE Transactions on Neural Networks 11 (2000) 601–614. [19] J. Blackmore, R. Miikkulainen, Incremental grid growing: encoding high-dimensional structure into a two-dimensional feature map, in: IEEE International Conference on Neural Networks, vol. 1, San Francisco, CA, USA, 1993, pp. 450–455. [20] B. Fritzke, Growing grid—a self-organizing network with constant neighborhood range and adaptation strength, Neural Processing Letters 2 (1995) 9–13. [21] D. Deng, N. Kasabov, On-line pattern analysis by evolving self-organizing maps, Neurocomputing 51 (2003) 87–103. [22] B. Fritzke, Growing cell structures-a self—organizing network for unsupervised and supervised learning, Neural Networks 7 (1994) 1441–1460. [23] D. Djurdjanovic, J. Lee, J. Ni, Watchdog agent—an infotronics-based prognostics approach for product performance degradation assessment and prediction, Advanced Engineering Informatics 17 (2003) 109–125. [24] B.D. Forrester, Advanced vibration analysis techniques for fault detection and diagnosis in geared transmission systems, Ph.D. Thesis, Swinburne University of Technology, Melbourne, Australia, 1996.