F Di Maio

J Hu

P Tse

M Pecht

K Tsui

E Zio

Ensemble-approaches for clustering health status of oil sand pumps

Keywords: Degradation, Fault detection, Fuzzy C-means, Hierarchical Tree, Ensembles of classifiers, Slurry pumps

Centrifugal slurry pumps are widely used in the oil sand industry, mining, ore processing, waste treatment, cement production, and other industries to move mixtures of solids and liquids. Wear of slurry pump components, caused by abrasive and erosive solid particles, is one of the main causes of reduction in the efficiency and useful life of these pumps. This leads to unscheduled outages that cost companies millions of dollars each year.

Traditional maintenance strategies can be applied, but they provide insufficient warning of impending failures. On the other hand, condition monitoring and on-line assessment of the wear status of wetted components in slurry pumps are expected to improve maintenance management and generate significant cost savings for pump operators. In this context, the objective of the present work is to develop and compare two unsupervised clustering ensemble methods, i.e., fuzzy C-means and hierarchical trees, for the assessment and measurement of the wear status of slurry pumps when available data is extremely limited. The idea is to combine predictions of multiple classifiers to reduce the variance of the results so that they are less dependent on the specifics of a single classifier. This will also reduce the variance of the bias, because a combination of multiple classifiers may learn a more expressive concept class than a single classifier.

Introduction

Detection of anomalies and faults in hydraulic pumps is an important task with implications for the safe, economical, and efficient operation of hydraulic systems. These systems are often embedded in hazardous plants, and are thus expected to operate with high levels of reliability, availability, and safety although they run in adverse environment that may lead to sudden break down due to excessive wear. For this reason, both equipment manufacturers and owners invest significant resources in maintenance programs designed to ensure that the required hydraulic system performance is maintained at maximum efficiency. In particular, equipment owners strive to avoid unplanned machine downtimes and costly component replacements and repairs that result from unexpected premature failures or gradual performance degradation caused by system wear [Mitchell, 1999;[START_REF] Hancock | A Hybrid Approach to Hydraulic Vane Pump Condition Monitoring and Fault Detection[END_REF].

This work evolved from a particular need in industry to monitor the health of a machine prone to sporadic catastrophic breakdowns. Previous maintenance and condition monitoring schemes provided insufficient warning of the impending failure. A system that could distinguish between normal machine operation and an impending mechanical failure was needed, i.e., a fault classifier had to be put in operation.

In general terms, fault classification methods can be divided into two categories [START_REF] Venkatasubramanian | A Review of Process Fault Detection and Diagnosis: Part I: Quantitative Modelbased Methods[END_REF]: model-based and pattern recognition techniques. In model-based methods, faults can be detected by performing some mathematical calculations. For example, in the case of interest here, the state-of-the-practice entails oil pump failures being diagnosed by expert analysis of the parameter values measured during the monitoring time and their comparison with the nominal power curve of every oil pump: drawing the actual power curve according to the measured parameters values, i.e., by manual analysis, allows the analyst to identify whether any fault exists. Indeed, failed pumps often show hollow pumping action and energy waste. Because of the nonlinearity of the wear behavior and the size of the input data and their uncertainties, this way of proceeding requires significant human, material, and financial resources while not guaranteeing the timely detection of faults, thus seriously affecting production [START_REF] Tian | Fault Detection of Oil Pump Based on Classify Support Vector Machine[END_REF]. On the other hand, pattern recognition methods offer a framework that can satisfy a number of basic requirements, such as short calculation time, high accuracy, and capability of dealing with large data sets representative of nonlinear wear behaviors [Zio, 2007]. Specially, soft computing approaches (e.g., Artificial Neural Networks and Fuzzy Logic systems) have shown superior robustness, speed, and accuracy compared to model-based methods [START_REF] Shahrtash | [END_REF].

In pattern recognition methods, the conceptual basis for the detection of failure onset is that different system faults initiate different patterns of evolution of the interested variables, as measured by properly placed sensors [START_REF] Zio | Neuro-fuzzy Pattern Classification for Fault Diagnosis in Nuclear Components[END_REF]. Pattern recognition methods entail three different stages: feature extraction, feature selection, and classification [START_REF] Sheng | Decision Tree-Based Methodology for High Impedance Fault Detection[END_REF]. A number of pattern recognition methods have been proposed that differ in the classification stage, e.g., hierarchical trees (H-trees) [START_REF] Breiman | Classification and regression trees[END_REF][START_REF] Ripley | Pattern Recognition and Neural Networks[END_REF][START_REF] Loh | Split selection methods for classification trees[END_REF], artificial neural networks (ANNs) [START_REF] Rumelhart | Parallel Distributed Processing[END_REF][START_REF] Ripley | Pattern Recognition and Neural Networks[END_REF]Zhang, 2000], and fuzzy logic (FL) systems [Zadeh, 1965;[START_REF] Klir | Fuzzy Sets and Fuzzy Logic: Theory and Applications[END_REF][START_REF] Zio | Neuro-fuzzy Pattern Classification for Fault Diagnosis in Nuclear Components[END_REF][START_REF] Wang | Vibration-based Fault Diagnosis of Pump Using Fuzzy Technique[END_REF][START_REF] Wang | Fault Diagnosis of Centrifugal Pump Using Symptom Parameters in Frequency Domain[END_REF].

H-trees evaluate the contribution of input features in determining the output classes of similarity. Generally, the most effective feature is selected as the first node of the tree, and its border value is used to create two different branches. Then, by the same criterion, the next most effective feature is found in each branch. This process is continued until the final nodes (leaves of the tree) obtained in all of the branches contain only the output classes. After creating the tree, a pruning process is performed to remove unnecessary nodes and decrease the size of the tree. Finally, within a supervised scheme, different sets of input features, obtained from various simulations, are fed to the tree in the test stage, and the outputs are compared with the known classes of each set to determine the accuracy of the tree. It is worth mentioning that there are different procedures for creating an H-tree. Different procedures may be applied to search for the best tree to solve a given problem, and then the best one can be selected by comparing the accuracy of the results and the time required to create the tree [START_REF] Shahrtash | [END_REF].

ANNs are computing devices inspired by the function of nerve cells in the human brain and provide a powerful way to empirically model and forecast nonlinear systems based on data representative of their behavior [START_REF] Rumelhart | Parallel Distributed Processing[END_REF]. They are composed of many interconnected computing units, each performing a few simple operations and communicating the results to its neighboring units. ANNs can learn to perform the mapping of the input-output relationships underpinning system behavior by a process of training on many different examples of input and corresponding output states [START_REF] Hancock | A Hybrid Approach to Hydraulic Vane Pump Condition Monitoring and Fault Detection[END_REF]. A main limitation of ANNs is that the results they deliver are difficult to interpret physically, and thus the underlying model remains cryptic.

FL modeling is designed to handle imprecise linguistic concepts, such as "small", "big", "young", and "low", and deal with uncertainties [Zadeh, 1965;[START_REF] Zio | Neuro-fuzzy Pattern Classification for Fault Diagnosis in Nuclear Components[END_REF].

FL exhibits an inherent flexibility and has proven to be a successful modeling framework in a variety of industrial applications and pattern recognition tasks [START_REF] Wang | Vibration-based Fault Diagnosis of Pump Using Fuzzy Technique[END_REF][START_REF] Wang | Fault Diagnosis of Centrifugal Pump Using Symptom Parameters in Frequency Domain[END_REF]. One of the main strengths of fuzzy logic modeling compared with other schemes is its capability of dealing with imprecise data [START_REF] Marseguerra | Model Identification by Neuro-fuzzy Techniques: Predicting the Water Level in a Steam Generator of a PWR[END_REF].

As for the limitations of fuzzy logic, the main difficulties stand in the fuzzy partitioning of the input and output spaces and in the establishment of the fuzzy rules that are at the basis of the classification phase and may require a time-consuming, trial-and-error process. Moreover, the elicitation of rules from human experts can be an expensive, error-prone procedure.

H-trees, ANNs, and FL have already been applied to real classification problems in a supervised scheme that entails, first, the classifier to be trained on data from known faults and then to be used to classify new data. In the present work, supervised classification schemes were precluded due to the unavailability of a comprehensive database of failure data, which is necessary for the training stage. Thus, as we shall see, the approaches adopted for detection do not require training. In other words, the classifiers are implemented for fault detection in an unsupervised manner, where the training and test phases collapse into the same clustering phase, and the class assignment is automated from available data of unknown classes. In particular, the adopted unsupervised FL approach, i.e. fuzzy clustering, exploits the advantages of automated generation of fuzzy rules, low computational burden, and benefits from the high-level, human-like rule representation typical of fuzzy systems, which offer an appealingly powerful framework for tackling practical classification problems.

Moreover, because of the shortage of data, the robustness of the classification approaches is augmented by combining multiple classifiers so as to improve upon the performance of individual classifiers. The idea is to combine the predictions of multiple classifiers (for more details on the methodology, refer to Section 3.3) to reduce the variance of the results and the bias.

The paper is organized as follows. Section 2 presents a case study. The first part of Section 3 presents the procedures developed for the feature selection phase and the method with which the fuzzy rules are generated from the data set (Sections 3.2 and 3.3), respectively. The second part introduces an approach for fault detection based on binary h-Tree (Section 3.4). Section 4 reports the application to the classification of the oil pump into failed or safe status, based on the available vibration data. The motivation for this application comes from the interest of a producer of oil extracted from oil sands in developing a proper monitoring scheme to detect pump failures in a system aimed at moving large amounts of raw oil sand. The reason for the failures is not exactly known, although it has been conjectured that the main contribution to pump wear is the large flow of oil into the vanes and the presence of small particle of dirt and sand in the sucked fluid [LaBour, 1995;[START_REF] Frith | Comparison of an External Gear Pump Wear Model with Test Data[END_REF]. The monitoring scheme is expected to provide advance warning and lead time to prepare the appropriate corrective actions. Finally, a comparison of the two classification approaches proposed is provided, highlighting the advantages and limitations of the proposed methodologies.

The Case Study

In this research, experimental data were collected from a number of slurry pumps that are used to deliver a mixture of bitumen, sand, and small pieces of rock from one site to another. For each pump, vibration is monitored as a symptom of system health.

Vibration signals have been collected at the inlet and outlet of slurry pumps operating in an oil sand mine. The pump vibration data were collected by the mine staff and one of the authors using the Smart Asset Management System (SAMS) and then further analyzed using the proposed classification methods. SAMS is a PC-based virtual instrument used to perform machine health monitoring [Tse, 2002]. Its measurement platform provides a Graphical User Interface that allows the user to choose from different diagnostic techniques (e.g., higher order statistical analysis and orbit analysis) to conduct machinery fault diagnosis. It can be installed in a notebook PC or desktop computer for portable or continuous machine health monitoring. SAMS also provides an easy-to-use interface for data management, report generation, trend analysis, etc., to help the maintenance staff in the recording and planning of maintenance activities.

The data acquisition equipment (DAQ) consist of a National Instrument (NI) cDAQ 9172 and a DAQ module NI 9234. Their specifications are listed in Table 1. 1) that were mounted on the case of the pump and denoted as 'Casing Lower' and 'Casing Discharge', respectively. Accelerometers S3

and S4 were PCB 352C18 accelerometers (see Table 1) mounted on the suction and discharge pipes, respectively. All four accelerometers captured the vibration signals from

four different positions at a similar sampling frequency rate of 50 kHz.

In Figure 2, the layout of the oil extraction site is represented. It consists of two parallel lines, L1 and L2, each composed of four different pumps. The pumps located in L1 are called G1, G2, G3, and G5, whereas G1, G2, G3, and G4 are those located in L2.

Each pump is different in type, size, and working condition, i.e., ground elevation, process fluid, history, and wear. 2.

1 G1 2 G2 1 G2 3 G3 2 G3 NA G5 1 G4 1
Each degradation pattern is composed of 30 intervals of records, each one lasting

1.3 [s]
, with pauses of 2 [s] in between (Figure 3). A preliminary analysis of the data showed that smooth and gradual degradation of the pump performance occurred (except for catastrophic failures), such that there was no significant deviation of the signal along the total 40 seconds of records. Thus, to lighten the computational burden of the data treatment, we have concentrated our analysis only on the records from the first 1.3 [s] (65000 points), discarding the remaining 29 intervals, assuming that the pump is either failed or healthy at time 0 [s].

Methods

As mentioned in the Introduction, pattern recognition methods entail three different stages: feature extraction, feature selection, and classification [START_REF] Sheng | Decision Tree-Based Methodology for High Impedance Fault Detection[END_REF]]. In the

S1 S2 S3 S4
following, these procedural steps are detailed with reference to the particular case study introduced in Section 2.

Feature extraction

Ten features were selected and extracted from the batches of vibration data collected by the accelerometers. For each of the 11 degradation patterns, the following M=10 indexes were evaluated (N is equal to 65000 sampling points):

(1) Peak value:

1,..., max max j j N n = =
(2) Mean:

1 1 N j j u n N = = ∑ (3) Standard deviation: 2 1 1 ( ) 1 N j j n u N σ = = - -∑ (4) Root mean square: 2 1 1 ( ) N j j RMS n N = = ∑ (5) Skewness: 3 1 3 ( ) ( 1) N j j n u SK N σ = - = - ∑ (6) Kurtosis: 4 1 4 ( ) ( 1) N j j n u KU N σ = - = - ∑ (7) Crest indicator: 1,..., 2 1 max 1 ( ) j j N N j j n CI n N = = = ∑ (8) Clearance indicator: 1,..., 2 1 max 1 ( | |) j j N N j j n CLI n N = = = ∑ (9) Shape indicator: 2 1 1 1 ( ) 1 | | N j j N j j n N SI n N = = = ∑ ∑ (10) Impulse indicator: 1 max | | 1 | | N j j n MI n N = = ∑ 3.2. Feature selection
The objective of feature selection is three-fold: to improve the performance of the classifier, provide faster and more cost-effective classification, and provide a better understanding of the underlying process that generated the data [START_REF] Guyon | An Introduction to Variable and Feature Selection[END_REF].

Depending on the nature of the regression technique, the presence of irrelevant or redundant features can cause the system to focusing attention on the idiosyncrasies of the individual samples while losing sight of the broad relational picture that is essential for generalization beyond the training set. This problem is compounded when the number of observations is also relatively small. If the number of variables is comparable to the number of training patterns (as in our case study), the parameters of the model may become unstable and are unlikely to be replicated if the study were to be repeated.

Feature selection seeks to remedy this situation by identifying a small subset of relevant features and using only them to construct the actual model. In this work, the selection of the most relevant features to be used in the classification phase is based on two standard approaches based on commonly used statistical tools: 1) box plots and 2) correlation plots.

Feature selection based on box plots analysis

Box plots provide an excellent visual summary of many important aspects of a distribution and are useful for identifying its outliers [START_REF] Massart | Visual Presentation of Data by Means of Box Plots[END_REF]. The conceptual basis for using box plots in distinguishing the most relevant features for classification is that things can be distinguished from each other based on their inconsistency [START_REF] Hsiao | On Classification from Outlier View[END_REF]. Outliers can in fact be used as a primary method for pattern classification: the more outliers a parameter distribution has, the more that parameter will be useful in defining clusters in the feature space defined by the considered parameter while avoiding cluster overlapping.

There are several steps in constructing a box plot. The first relies on the evaluation of the 25th, 50th, and 75th percentiles in the distribution of the 11 patterns.

Figures 4567show how these three statistics are used in our case study: for each extracted feature, we draw a box extending from the 25th percentile to the 75th percentile. The 50th percentile is drawn inside the box. We also put "whiskers" above and below each box to give additional information about the spread of data. Whiskers are vertical lines that end in a horizontal. They are drawn from the lowest and upper hinges to the lowest datum still within 1.5 Inter Quartile Range (IQR) of the lower quartile, and the highest datum still within 1.5 IQR of the upper quartile, respectively [START_REF] Massart | Visual Presentation of Data by Means of Box Plots[END_REF].

Finally, we represent outliers in our box plots by adding additional crosses beyond the whiskers. In conclusion, both analyses, e.g., box and correlation plots, seem to be useful tools applicable to systematically provide information on the relevant parameters to be selected for optimal performance of the successive classification tasks.

Classification

Fault detection may pose difficulties, because it entails the implementation of a classifier for labeling the component status as healthy or failed. In our application, the shortage of data forces us to resort to a combination of classifiers in an attempt to improve the detection-classification performance [START_REF] Freund | Experiments with a New Boosting Algorithm[END_REF]Schapire, 1999;Friedman, 2000]. Figure 12 illustrates the basic framework for the ensemble scheme adopted and that was applied with two different classification approaches (Sections 3.3.1 and 3.3.2). The key step was the formation of an ensemble of diverse classifiers from a single data set. In this work, four different classifiers were fed with different inputs taken from different sensors (S1, S2, S3 and S4), but all relative to the same degradation pattern.

The single classifier results were then combined by two different methodologies [Friedman et al., 2000]:

-Majority voting

• Each ensemble member votes for one of the classes.

• Predicts the class with the highest number of vote.

• In case of equal number of votes, the class is labeled as uncertain.

-Weighted voting • Make a weighted sum of the votes of the ensemble members.

• Weights depend on the performance of each independent classifier.

Classification results

Classification results

Classification results

Combined classification results

We proceeded to generate results using the two different approaches. We varied the type of single classifier implemented and compared their performances. In this Section, we focus on the two unsupervised classification approaches employed for fault detection: 1) unsupervised Fuzzy C-Means (FCM) algorithm and 2) Binary Hierarchical Clustering Tree (H-Tree).

The Unsupervised Fuzzy C-Means algorithm

Fuzzy C-Means (FCM) is one of the most popular fuzzy clustering methods [Bezdek, 1981;[START_REF] Leguizamon | Unsupervised Fuzzy C-Means Classification for the Determination of Dynamically Homogeneous Areas[END_REF][START_REF] Alata | Optimizing of Fuzzy C-Means Clustering Algorithm Using GA[END_REF]. The FCM method originated from hard C-Means clustering, allowing data points to belong to two or more clusters [START_REF] Klir | Fuzzy Sets and Fuzzy Logic: Theory and Applications[END_REF]. The clusters emerged from the minimization of the following objective function: Fuzzy partitioning is carried out through an iterative optimization of ( , ) J N C , with the update of memberships ij m ϕ and the cluster centers j c by:

2 , 1 1 ( , ) ( ) ij ij N C i j i j J N C m d x c ϕ = = = ∑∑ (
2( 1)
2( 1)

1 ij ij ij c j d m d ϕ ϕ ϕ - - - - = = ∑ (2) 1 1 ij ij n i i j n i m x c m ϕ ϕ = = = ∑ ∑ (3)
For further details, the interested reader may refer to [Bezdek, 1981].

Binary Hierarchical Tree

Hierarchical clustering groups data over a variety of scales by creating a cluster tree, also called a dendrogram. The binary hierachrical tree is not a single set of clusters, but rather a multilevel hierarchy where crisp clusters at one level are joined as crisp clusters at the next level, i.e., the pattern belongs to one and only one cluster. This allows us to decide the level or scale of clustering that is most appropriate for the application of interest. Although many other clustering methods exist, hierarchical clustering is one of the most commonly used methods in crisp clustering [START_REF] Breiman | Classification and regression trees[END_REF][START_REF] Ripley | Pattern Recognition and Neural Networks[END_REF][START_REF] Loh | Split selection methods for classification trees[END_REF].

A hierarchical clustering algorithm initially places each data point in a cluster by itself, and then it recursively and merges the clusters that are closest to each other according to some distance or similarity criterion until a single dendrogram is created.

Results

The classification systems introduced in Section 3 were developed using some of the data from a database of 11 degradation patterns of oil vane pumps, as described in Section 2. These degradation patterns are representative of different stages of progressive pump deterioration. Moreover, they refer to pumps that are different in type, size and working conditions i.e., ground elevation, process fluid, history, and wear. Thus, in order to analyze only pumps subjected to similar working conditions, we only selected the degradation patterns relative to G1 and G2 from lines L1 and L2. Finally, the total number of available degradation patterns to be classified is 7. The real health status of the pumps relative to the 7 degradation patterns is listed in Table 3. This list is only used at the end of the unsupervised fault detection process for comparison with the obtained results and performance evaluation of the classifiers. The attributes for the pump vibrational data were extracted from the current signals, as introduced in Section 3.1. A total of four feature sets, each composed of 7×10 values, were collected. Then, among these features, the most important were identified according to box plots and correlation plots. Finally, the classification tools of FMC and H-tree were fed with the values of selected features for building the clusters in an unsupervised manner.

In what follows, the results for all the considered combinations of approaches for feature selection and classification are reported.

Method I:

Feature Selection: Box Plot Analysis

Classifier: Fuzzy C-Means

The features to be fed to the FCM classification algorithm were selected by box plot analysis. In Section 3.2.1 we justified the choice of skewness and kurtosis as important features. The classification phase identified 2 clusters that can be useful for labeling the degradation patterns as relative either to failed or to healthy pumps. In this case, the classification results are shown in Figure 13. By analyzing the skewness and kurtosis values of the considered degradation patterns plotted on the scatter plot of Figure 12, it turns out that the main differences between the two identified clusters (represented by circles and crosses) are:

-Circles have skewness values close to zero and lower kurtosis values.

-Crosses have skewness values far from zero and higher kurtosis values.

Based on this consideration we have decided that:

-Degradation patterns with skewness values close to zero, i.e., vibrational data normally distributed, are relative to healthy pumps (the flow of abrasive and erosive particles can only generate white noise on the measurements).

-Degradation patterns with skewness values far from zero, i.e., vibrational data not normally distributed, are working in anomalous conditions (failed components highly deform the parameter distributions).

Thus, hereafter, circles are labels of degradation patterns for safe pumps, whereas crosses indicate the class of failed pumps.

Method II:

Feature Selection: Box Plot Analysis Classifier: Hierarchical Clustering Tree

In this application, the same features selected by the box plot approach and used in Method I have been fed into the h-Tree algorithm. The classification results are shown in Figure 14. To compare the effectiveness of Method I and Method II, the classification results based on the batch of four sensors, S1, S2, S3, and S4, from the 7 degradation patterns have been listed in Table 4. Based on the FCM classifier algorithm, when using majority voting, the correctness of the classification was 86%, with an uncertain assignment percentage equal to 14%; whereas, using weighted voting, the correctness of the estimations reached 100%. Resorting to h-Tree, only 57% of the data was classified correctly and 43% was uncertain, when using majority voting; the weighted voting approach raised the correct estimation percentage to 86%, but 15% of the data were misclassified. The analysis of Table 4 highlights that:

-Fault detection based on FCM performed better than h-Tree in all cases because it allowed building clusters with uncertain boundaries accommodating for different pump locations and different pump types and sizes.

-Cluster centers identified only by the FCM turned out useful during on-line fault detection for classifying a new developing degradation pattern into healthy/failed clusters according to the distances of the feature values from the centers.

Method III:

Feature Selection: Correlation Coefficients Classifier: Fuzzy C-means

The features to be fed into the single FCM algorithm have been selected by correlation plot analysis. In Section 3.2.2 we justified the choice of different input features for each single classifier. Classification results are shown in Figure 15 and summarized in Table 5. The features to be fed to the single FCM algorithm have been selected by correlation plot analysis. The classification results are shown in Figure 16 and summarized in Table 5, together with those obtained using Method III. By comparison with Table 4, it can be seen that:

-When relying on FCM, correct assignment performance is almost constant, irrespective of the feature selection approach used.

-When relying on FCM, the percentage of uncertain estimations increases when the combination of single classifier results is made by a majority voting strategy.

-In general, fewer degradation patterns are assigned to the wrong class.

In conclusion, FCM performed better than H-tree regardless of which features were used as input for the single classifiers, because of the higher percentage of correct class assignment for all the classification methods analyzed. Indeed, h-Trees are not very accurate because they can only ideally deal with imperfect data, outliers, different scales, and irrelevant attributes [Friedman, 2000].

Estimation of the Pump Wear Function (PWF)

When components are well-maintained, it allows downtime to be reduced for the sake of plant safety and overall performance efficiency. Since machines often go through degradation before failure, monitoring and predicting the trend of their degradation and condition may allow for correction before failure. Indeed, when the conditions of a component or structure can be monitored, maintenance can be planned dynamically [Williams et al., 1994;Marseguerra et al., 2002]. By predicting the future evolution of the degradation state of a component or structure, it is possible to verify whether it can continue performing the required function. In practice, the estimate of the system state in terms of wear function may be difficult to obtain because the degradation state may not be directly observable and/or the measurements may be affected by noise and disturbances.

In this Section, a method for constructing dynamic models for system wear estimation is proposed. Instead of assuming a structure for the wear model and identifying its parameters, only an approximate linear model is used. This results in a simple model that can be used as a monitoring tool for online application. Addition of noise, ε, during state estimation is used to reflect inherent process variability. According to verified superior classification performance guaranteed by the features skewness (S)

and kurtosis (K) (Section 4), these two features relative to the same 7 degradation patterns under analysis are considered as inputs for modeling the Pump Wear Function PWF. Their values have been fitted to a linear model for estimating PWF, whose function turns out to be equal to:

( ) PWF , = 0.9 5.6 0.05 0.003

S K S K S K ε - + × + × - × × + (4)
The fitted plot is shown in Figure 17. As expected, the larger the value of skewness, the larger the pump wear; similarly, the larger the kurtosis value, the larger the pump wear. This confirms the adopted hypotheses for labeling the classified degradation patterns as either healthy or failed.

However, it has to be pointed out that at this research stage the estimated PWF (Eq. 4) can only be considered as a trial approximation of the real PWF. Additional vibrational data coming from the same type and size of pumps will confirm the accuracy of the PWF estimation of wear. Finally, experimental implementation of the wear monitoring system will be necessary to license the proposed monitoring scheme for tracking oil pump wear.

Conclusions

For effective maintenance, industry needs to monitor the health of a machine prone to degradation and sporadic catastrophic breakdowns. To achieve this aim, a system is needed that can distinguish between normal machine operation and an impending mechanical failure, i.e., a fault classifier.

In this application, the focus is on the wear of slurry pump components, caused by abrasive and erosive solid particles. Unscheduled outages of pumps cost oil sand companies millions of dollars each year. Traditional maintenance strategies provide insufficient warning of an impending failure.

In this work, we have presented two unsupervised clustering ensemble methods (h-Tree and FCM) and compared their performance in the assessment of the wear status of pumps when available data is extremely limited.

In particular, the adopted unsupervised FCM approach exploits the advantages of the automated generation of fuzzy rules, low computational burden, and the high-level, humanlike thinking and reasoning of fuzzy systems, which offer an appealingly powerful framework for tackling practical classification problems.

Finally, for prognostics, the future evolution of the degradation state of the component or structure is predicted by a simple dynamic model for system wear estimation to verify whether it can continue performing the required function.

Figure 1 :

 1 Figure 1: Samples of the measurement locations of a slurry pump.

Figure 2 :

 2 Figure 2: The oil extraction lines layout.

Figure 3 :

 3 Figure 3: Sketch of the degradation pattern structure.

Figure 4 :

 4 Figure 4: Box plots of the distributions of the 10 extracted features from sensor S1.

Figure 5 :Figure 6 :

 56 Figure 5: Box plots of the distributions of the 10 extracted features from sensor S2. peak mean std RMS Skewness Kurtosis CI CLI SI IMI

Figure 7 : 2 .

 72 Figure 7: Box plots of the distributions of the 10 extracted features from sensor S4.

Figure 8 :Figure 9 :

 89 Figure 8: Correlation coefficients for 45 combinations of the 10 features relative to sensor S1.

Figure 10 :

 10 Figure 10: Correlation coefficients for 45 combinations of the 10 features relative to sensor S3.

Figure 11 :

 11 Figure 11: Correlation coefficients for 45 combinations of the 10 features relative to sensor S4.

Figure 12 :

 12 Figure 12: Scheme of combination of different classifiers.

  is the sum of the square errors of the distance of each individual data point x i , i=1,2,…,N, to the center j c , j=1,2,…,C, of the given cluster (class) j. The minimization is done with respect to the membership ij m ϕ and the centers j c is the square of the distance between i x and j c , whereas ij m ϕ is the degree of membership of x i to cluster j. The value φ is any real number greater than 1, and it modulates the fuzziness of the clusters.

Figure 13 :Figure 14 :

 1314 Figure 13: Classification results using box plots and an unsupervised FCM classifier algorithm: circles are healthy pumps; crosses are failed pumps; dots are clusters centers.

Figure 15 :

 15 Figure 15: Classification results using correlation plots and unsupervised FCM classifier algorithm: circles are healthy pumps, crosses are failed pumps, and dots are cluster centers.

Figure 16

 16 Figure 16 Results using correlation plots and H-tree: circles are healthy pumps, and crosses are failed pumps.

Figure 17 :

 17 Figure 17: Pump wear function.

Table 1 : Measurement Equipment

 1

	Equipment	Model	Specification
	1 DAQ Device	NI cDAQ 9172	Max. support module = 8
	2 DAQ Module	NI 9234	Resolution = 24 bit
			Input range = +/-5V
			Sampling rate = up to 51.2 kHz per channel
	3 Smart Asset Maintenance	Version 2.3.8
	System (SAMS)
	4 Notebook Computer	IBM T60	Intel Core Duo processor 1.66 GHz
			Windows XP Professional
	5 Accelerometer	PCB 352A60	Mounted on positions Casing Lower and Casing Discharge
			Sensitivity = 10.2 mV/g
	6 Accelerometer	PCB 352C18	Mounted on positions Suction Pipe and Discharge Pipe
			Sensitivity = 9.7 mV/g

Vibrations were measured by four accelerometers mounted in four different positions so that there were a total of four different vibration signals captured. They are denoted as S1, S2, S3, and S4. As shown in Figure

1

, accelerometers S1 and S2 were PCB 352A60 accelerometers (see Table

Table 2 : List of Available Degradation Patterns for Each Pump in L1 and L2. NA=Not Available L1 Available degradation patterns L2 Available degradation patterns G1

 2

Table 3 : Actual Health Status of the Pumps Relative to the 7 Degradation Patterns Considered (H=healthy, F=failed)

 3

	Degradation pattern	1	2 3	4	5	6	7
	Actual health status	H H F H H H H

Table 4 : The Comparative Classification Results Using Unsupervised FCM and H-tree, with Box Plots as Selecting Methods for the Input Features (H=healthy, F=failed, ?=uncertain)

 4

	Degradation pattern	1	2 3	4	5	6	7 Correct Uncertain
	FCM (majority voting)	H ? F H H H H	86%	14%
	FCM (weighted sum)	H H F H H H H	100%	0%
	h-Tree (majority voting)	? H ? H ? H H	57%	43%
	h-Tree (weighted sum)	H H F H F H H	86%	0%

Table 5 : The Comparative Classification Results Using Unsupervised FCM and PC+HT, with Correlation Plots as the Selecting Methods for the Input Feature Variables (H=healthy, F=failed, ?=uncertain)

 5

	Degradation pattern	1	2 3	4	5	6	7 Correct Uncertain
	FCM (majority voting)	? H F H H ?	H	71%	29%
	FCM (weighted sum)	H H F H H H H	100%	0%
	HT (majority voting)	H H F H ? H H	86%	14%
	HT (weighted sum)	H H F H F H H	86%	0%


Michael Houseman

Trying to Make a Difference with "Ritual Design"

Trying to Make a Difference with "Ritual Design"

The papers presented at the Ritual Design panel were largely oriented towards pushing the "ritual dynamics" envelope: granted that ritual innovation is the norm rather than the exception, just how innovative can a ritualist afford to be? What myriad forms can ritual creativity take? This accounts in part for the diverse and somewhat outlandish character of some of the topics: ritual activities at a Marian shrine in India, Christmas celebrations among "ordinary" Swiss families, Masonic rites in France, but also newly crafted funerary ceremonies, as well as various Neopagan, New Age, on-line, fictional, and artistic ritualisations involving such unlikely non-human entities as digital parishioners (and their ghosts), reprogrammable cellular memories, Vulcan Starfleet officers, and Cinderella look-alike goddesses. The whole shebang was both intellectually challenging and great fun, and there is no way that I am going to be able to stuff all that exuberant toothpaste back into the rigorous analytical tube from whence it came.

From the onset, the notion of "ritual design" was used to subsume a wide range of innovative processes: incremental transformation, deliberate revival, speculative re-creation, intentional invention, and so forth. One happy result of this was that the various case-studies discussed were tacitly posited as theoretically equivalent, the implication being that it was analytically expedient to consider them all as instances of ritual practice.1 However, while this was self-evident for some cases, for others, such as "human potential"-based teacher training, artistic initiatives on All Souls' Day, or the use of on-line ceremonial prescripts, it was much less so, although the ways in which these latter activities diverged from more canonical sorts of ritual events remained unclear. The problems raised by such possible divergences, barely addressed during the panel sessions, continue to badger me: might attending to ritual design point to essential differences between distinct modes of ritualisation, or even to the limits of ritualisation itself? This question lies at the heart of the envelope-pushing issue: how far can ritual dynamics press on in the "dynamic" direction before "ritual" gets left behind?

In other words, are there important conceptual distinctions worth making within the field of ritual design: should some kinds of innovation be deemed more radically innovative than others? In a nutshell, the question is Gregory Bateson's: what difference makes a difference?2 Is there some empirical novelty pertaining to ritual design that implies a significant discrimination on the level of ritual theory? One possible candidate is simply the presence of change. However, as a discriminating criterion, this is a total non-starter. As has often been stressed, all ritual performances are continually evolving over time, existing patterns of ceremonial action being progressively reshaped as a function of ongoing transformations in the larger social field. Jan Snoek's account of changing Masonic rites, and especially Matthias Frenz's analysis of contested space at the Marian sanctuary of Velankanni, provided examples of this type of ongoing ritual reconfiguration. Moreover, on another, less historical level, no two ritual performances are ever strictly alike, if for no other reason than because from one performance to the next, the participants are either different people or the same people who, for any number of reasons (such as their participation in prior ritual performances), don't act in exactly the same way. I cannot but wield the sacrificial knife differently, both from the way you do and from the way I used to when I was younger -to say nothing of the fact that the goat to be immolated is different every time. Because rituals are not undertaken theoretically, but by particular persons in particular times and places, they always incorporate a measure of creativity and improvisation.

In this light, practitioners' claims of ritual invariance are worthy of attention. In many cases, as in both the above-mentioned examples, ritual participants maintain that the modifications their rituals may have undergone are but contingent aspects of ceremonial events whose essential nature has remained unchanged. The ability to make such assertions is upheld by considerable cultural work, pertaining, among other things, to the organisation of the ritual performances themselves. This is not the place to elaborate further on this idea. Let it suffice to remark that such statements amount to saying that, while innovation may be present (indeed, it is often readily admitted to), it is in no way constitutive of the ritual's efficacy as such: it is held to contribute only very marginally to what makes the ritual in question the extra-ordinary enactment that it is deemed to be.

What about deliberate innovation? Intuitively, this seems a more likely possibility: taking a conscious decision to modify one's ritual behaviour surely betokens a watershed of sorts. Well, not really. To begin with, as Simone Heidbrink had occasion to remark during a discussion, basing a conceptual distinction on speculations regarding participants' states of mind is a hazardous undertaking at best: how does one go about evaluating the extent of their premeditated intention to introduce change? But, above all, the fact is that most, if not all ritual innovations, such as those already alluded to, involve a fair amount of conscious deliberation on the part of those concerned. Indeed, rituals are social practices and, as such, their evolution typically entails such mindful activities as confrontation, factionalism, wilful intimidation, soliciting support, negotiation, and compromise. I am tempted to suggest that, as a rule, people are at least as thoughtful about their rituals as they are, say, about their cooking. Ceremonial changes, like culinary experiments, may be prompted by boredom, elicited by others' desires, or dictated by happenstance (having no rice, I use pasta; in the absence of a cow, I sacrifice a cucumber); they never "just happen". To use a more contemporary vocabulary, ritual innovation, as suggested, for example, by Roland Hauri-Bill's survey of family Christmas rituals in Switzerland, is an inherently reflexive, context-dependant process.

A third imaginable criterion for a radical distinction within the framework of ritual design is purposeful invention. It seems reasonable to expect a newly created ritual to be of a markedly different nature than one hallowed by enduring practice. Although I initially imagined this to be the case, the introductory talks by the panel's co-organisers, Gregor Ahn and Kerstin Radde-Antweiler, as well as the discussion that followed, convinced me of just how difficult it is to draw a line between innovation and invention in so far as ritual design is concerned. First of all, as Gregor Ahn made clear, this distinction depends a great deal on one's point of view, for what may appear to be a freshly forged ceremony for an outside party may be conceived by its practitioners as a reworking of an already existing rite. In addition, the very process of ritual crafting, because it invariably incorporates some sort of ritual transfer, makes such a discrimination highly problematic. Typically, "invented" rituals are composed by relating bits and pieces, gathered from a variety of sources, to a more or less familiar ritual schemata or frame. This also came out clearly, for example, in Thomas Quartier's account of contemporary funeral design in the Netherlands. Moreover, as Kerstin Radde-Antweiler showed for newly minted rituals posted on personal web-sites, pre-existing ritual schemata and their attendant, often exotic religious traditions can be convoked in the absence of any substantive knowledge by even the slightest, most superficial of references. As a consequence, no newly conceived ritual can be said to be totally original; it always refers, either explicitly or implicitly, directly or obliquely, to some pre-existing ceremonial performance. 3 The same applies to made-up rituals in fictional accounts (e.g. the cinematographic re-embodiment rites analysed by Gregor Ahn), to novel on-line ceremonies (e.g. vendor-machine worshipping in Simon Jenkins' Church of Fools), and to ritual enactments drawing simultaneously on several different cultural traditions (e.g. the Milky Way Phantasy described by Inken Prohl and "Ger-manic" Neopagan rites outlined by Rene Gründer). In short, as several panel members insisted, rituals are never concocted from scratch.

So wherein lies the difference that makes a difference? It is not novelty itself (all rituals change), nor is it deliberate innovation (all ritual change is intentional), nor even outright invention (all rituals are to some extent derivative). Another possibility, if creativity is indeed a constant feature of ritual, is that this difference pertains to the positive or negative role that innovation is expected to play in ritual performance.

As previously mentioned in connection with Masonic ceremonies and Marian devotions at Velankanni, many rituals disregard, impugn, or challenge the changes they nevertheless undergo. Both participants' accounts and ritual organisation itself bear witness to the fact that innovation is held to be largely contingent; it is not presumed to be constitutive of the performance's distinctive effectiveness as ritual. This makes sense, given that this efficacy is alleged to proceed above all from the accomplishment of certain fairly mysterious acts (by the standards of everyday behaviour) -carrying the Virgin's chariot, prostrating oneself before Mary's standard, wearing emblematic aprons, etc. -handed down by more authoritative Others (ancestors, divinities, cult founders, church leaders, etc.) and having operative value in and of themselves.

Other rituals, on the contrary, explicitly endorse and encourage innovation. They proceed from the notion that creativity is a necessary, pivotal feature of ritual practice, essential to its effectiveness as such. This applies, for example, to the New Age "spiritualised practices" described by Anne-Christine Hornborg, to the Milky Way Phantasy pilgrimages presented by Inken Prohl, and to the Neopagan ceremonies discussed by Kerstin Radde-Antweiler and René Gründer. In all these cases, ritual potency is deemed to rely less on the faithful repetition of certain conventional items of behaviour than on the participants' experiencing certain equally conventional, albeit somewhat enigmatic, feelings and motivations -unconditional love, the vibration of universal prayer, an intimate connection with nature, spiritual community, etc. -ascribed, here also, to more authoritative Others (one's "inner" Self, extra-terrestrial fantasy-castle princesses, Celtic druids, ancestral Norsemen, etc.). Although, in fact, practitioners make use of a limited number of recurrent images, formulae, spatial setups, and scenarios, they are expected to exercise considerable imagination and creativity in accommodating their ceremonial practices to their personal sensibilities and circumstances. This is because participants do not envisage their ritual activities as ends in themselves (archetypal actions), but as the means whereby certain exemplary emotional and intentional dispositions may become their own. In this perspective, established religious traditions, the participants' own or others, are seen as providing not models to follow, but resources to be inventively explored. Hence the byword of ritual traditions of this type, the symmetrical inverse of assertions to the effect that rituals never change: "Do whatever works best for you".

My suggestion, then, is that ritual design is structured around two poles representing two rather different modes of ritualisation: change-eschewing on the one hand, and change-embracing on the other, the former organised around the repetition of complex actions, the latter around the re-actualisation of complex dispositions. 4 There were some interestingly ambiguous cases among the materials presented. For example, it is very difficult to position the rituals composed by contemporary funeral designers in the Netherlands (Thomas Quartier's talk), mostly because descriptions of the ceremonies themselves were lacking, as was also the case for Roland Hauri-Bill's Swiss Christmas celebrations. A particularly intriguing case, presented by Erik de Maaker, was that of Dutch artists who created various installations on All Souls' Day in order to elicit people's feelings and to provide them "with the ritual means to commemorate the dead". As the testimonies show, at least some participants were deeply moved. Human-like statues of white wax, for example, lit from within by burning candles that caused them to slowly melt, evoked both bodily deterioration and the presence of souls. However, this is precisely what art is supposed to do: induce complex emotional and intentional states in others. For an artistic installation to also make sense as ritual, the exemplary feelings occasioned by the artists' works would have to provide the participants with the grounds for undertaking exceptional enactments of their own whose performance is presumed to be able to affect them in extra-ordinary ways. In the annual Milky Way Phantasy described by Inken Prohl, for example, artistic performances are pursued to create an "aesthetic sensation" among the participants that sustains their ceremonial building of a fairy-tale castle, in whose construction the participants are able to "feel the Gods". In this perspective, the All Souls' installations made use of what we might call the idiom of ritual, but fell short of full-fledged ritualisation. Some works, however, came closer than others. In "Objects of Remembrance", for instance, the artist provided bereaved individuals with a collection of disparate objects from which one was chosen and placed, along with a written message to or about the deceased, in a memorial box destined, for the space of an evening, to be displayed and shared with others. One would need to know more about exactly how objects were selected and messages were written, as well as the ways in which 4 For a fuller account of the distinction between these two ritual modes, see Houseman 2007. It is perhaps worth noting the extent to which Simon Jenkins' online Church of Fools abounds in stipulated, often equivocal gestures: kneeling, the "hallelujah" pantomime, injunctions to "please use 'tear hair out' gesture as we think of them", shaking hands with co-participants who are invisible to all except themselves, etc. As ritual (and not as a spectacle or a play for example), I would situate it firmly in the action-centred, change-disregarding ceremonial camp.

participants (and others) talked about what was being done, to be able to judge to what degree installations such as this allowed people to forge not only a renewed connection with their departed intimates, but also a renewed ritual relationship with them.

The half-baked, two-pole model of ritual design proposed above is, of course, not the final answer to anything. I have introduced it mainly as a way of underlining certain of the theoretical issues raised by the notion of "ritual design": What are its limits? What conceptual distinctions does it imply? Specifically, how should we discriminate among "designed" ceremonial practices that range from Marian pilgrimages to spiritual therapies for developing one's inner potential to yet other instances of contrived expressive behaviour? I would like to conclude by encouraging those who would tackle such questions, especially the last of them, to avoid a number of easy answers. I can think of at least three.

One is to say that it's all ritual, loosely defined as symbolic practice. Using "ritual" in such a casual way, "as a metaphor for all kinds of experience" (as Felicia Hughes-Freeland rightly remarked in another panel session), may be fine for practitioners, but a real cop-out for those who make a living conceptualising about this sort of thing. The fact is that for "ritual" and its related terms to have any analytical (as opposed to evocative) value they must be closely defined. There are risks involved, but hey, they're only academic. 5 A second type of evasive manoeuvre consists in being satisfied with labels: let's call some things "ritual" and other things, say, "ceremony", or some things "ritual" and other things "ritualised". All this is well and good if we know (and say) exactly what we mean by such categories; if not, their introduction amounts to a pragmatic stop-gap solution (I study ritual, you work on ceremonies) to theoretical quandaries that remain intact.

A third easy way out is to take an insufficiently thought-out relativist position: if "they" call it ritual, then it should be considered ritual. The problem, of course, is that as a rule, "they" don't call anything "ritual". "They" make use of any number of local terms, often pertaining to quite different realms of experience, to refer to what we researchers, for either ethnocentric or theoretical reasons (it's either one or the other), lump together as "ritual". It should be noted in passing that taking this into account has a troubling implication when applied to contemporary Western societies: that fact that we Westerners do or don't call certain practices "ritual" is not particularly relevant in determining that which should be legitimately studied as such.

One alternative to these overly simplistic approaches, I would suggest, is to begin, somewhat artificially, by positing certain manifestly heterogeneous phenomena, such as change-dismissing and change-promoting ceremonial practices, as "ritual" in the strictest, fullest sense of the word. This shifts the analytical burden squarely onto the shoulders of the researcher, where it belongs. The question then becomes a potentially constructive one: what conceptualisation of "ritual" do we need in order to be able to account for both their similarities and their divergences as the interdependent features of a single model? I have tried to show that the concept of "ritual design" raises pressing questions about the very nature of ritual practice. In precluding the easiest of (false) solutions to these questions, all the while having no conclusive answers to offer, I have tried my best to paint us all not so much into an analytical corner, as to the edge of a conceptual cliff. So please let me end on a positive note by borrowing from a legendary blooper: the time has come for ritual studies to take a big step forward!

Similarly, other concepts recently introduced within the ritual dynamics paradigm, such as "ritual transfer"(Langer et al.

2006) or "patchwork ritual" (Radde-Antweiler 2006), have been mobilised chiefly to legitimise heretofore marginalised or discredited ceremonial phenomena; their use thus tends to emphasise continuities rather than discontinuities.

Bateson 1972: 453.

Such self-referential circuits cannot but contribute to validating the newly "invented" practices in question as instances of "ritual".

I personally find the "polythetic" or "fuzzy set" approach to the definition of ritual (for example Snoek 2006) to be uncomfortably close to this loose "it's all ritual" strategy. Specifically, it tends to turn a useful methodological precept that allows people to talk together without being hampered by arduous definitional issues, into a dull conceptual tool.