Artificial Immune Systems in Condition Monitoring 1 ...

Artificial Immune Systems in Condition Monitoring Prof. Jens Strackeljan (*) , Prof. Sulo Lahdelma (**), Dipl.-Ing. Stefan Goreczka(*) (*) Otto-von-Guericke-Universität Magdeburg, Institute of Applied Mechanics, Germany (**) University of Oulu, Mechatronics and Machine Diagnostics Laboratory, Finland

Abstract: The immune system is a complex, robust, adaptive natural system that defends the body against foreign pathogens. It is capable of categorising all the cells within the body as self or nonself cells. There has been increasing interest in the last few decades to develop engineering tools called Artificial Immune Systems (AIS), which are inspired by the human immune system. The immune system, with its cell diversity and variety of information processing mechanisms, is a cognitive system comparable to the brain in terms of its complexity. Understanding the way how this organ solves its computational tasks can suggest new engineering solutions or new ways of looking at old problems. This paper discusses an on-going investigation into the usefulness of two applications of AIS algorithms, the AbNET and the AIRIS (Artificial Immune Recognition System), in solving problems in vibration diagnostics. Fault detection based on the specific immunity response algorithms seems to be adequate for characterising the particular nature of normal conditions as well as reacting to new and unexpected anomaly situations. The results of the investigation clearly indicate that raw data pre-processing and feature extraction are important parts in the development of automatic fault detection systems, and even an advanced AIS classifier cannot compensate for major deficits in feature generation. Generalised moments and norms obtained from higher order derivatives seem to be adequate methods for feature calculation. Keywords: Condition monitoring, artificial immune systems, roller bearing diagnostics, adaptivity, generalised norms, statistical feature, fractional derivative

1 Introduction Artificial Immune Systems (AIS) are a relatively new area of research. There has been an increasing interest to development algorithms and engineering tools inspired by natural and human immune system. The classical self/non-self model for the immune system as the classical approach dominating research activities over more than 40 years. There are many publications that discuss artificial immune systems applications in robotics, optimization, control, computer science and other areas. Various mechanisms or processes in the human immune system are investigated in the development of AIS. Negative selection is one that got earliest attention but there are also several other algorithms and methods available, e.g. Immune Network Model [1], clonal selection algorithm and Danger Theory [2,3] and artificial immune recognition systems [4,5,6]. In recent years, mechanical machinery systems have become increasingly complex and consequently the challenge of protecting these systems has become increasingly difficult. The early fault detection and predictive maintenance are extremely important for the cost savings they provide, especially in large and complex systems with many pieces of equipment. In a system of such complexity (because of its many connections and diversity of equipment) it is difficult to make a complete catalog of all the possible, and probable, anomalous situations. With its ability to detect and react to novel situations, the immune system seems to be an adequate source of 48

inspiration to develop algorithms for early detection of anomalous behavior in mechanical and electrical systems [7]. Many properties of the immune system are of great interest for engineers: x x x x x

uniqueness: each individual possesses its own immune system, with its particular vulnerabilities and capabilities; anomaly detection and recognition of faults: the immune system can detect and react to pathogens that the body has never encountered before. The harmful molecules that are not native to the body are recognized and eliminated by the immune system; distributed detection: the cells of the system are distributed all over the body and, most importantly, are not subject to any centralized control; imperfect detection (noise tolerance): an absolute recognition of the pathogens is not required, hence the system is flexible; OHDUQLQJ DQG PHPRU\ WKH V\VWHP FDQ ³OHDUQ´ WKH VWUXFWXUHV RI SDWKRJHQV VR WKDW IXWXUH responses to the same pathogens are faster and stronger. That is of high importance for applications in fault detection and preventive maintenance.

Objective of the present investigation was to study the potential of the Artificial Immune System philosophy to dynamically adapt and evolve a Health Monitoring System to explore, learn and absorb new machinery incipient fault detection and discovery knowledge in order to provide accurate health monitoring response in dynamic environments. This paper shows in the first part results from applying one of the most popular algorithms, AbNET [8] (Nunes de Castro, von Zuben) to this problem. The main features of the Antibody NETwork (AbNET) are competitive learning, automatic generation of an internal network structure and the binary representation of the connection strengths. The antibody repertoire will have to be constructed while a new antigen is presented. This feature leads to the growing architecture and it is based on the clonal selection principle. Antibodies are removed from the network if they fail to expand. This means that they do not match to any antigen population. These two phases are called the growing and pruning phase. The network has also selfregulatory features. AbNET attains a specific equilibrium size and generates a characteristic amount of antibodies. When the NET reaches the equilibrium size, the new candidate antibodies must compete with the antibodies already in the network to enter the repertoire. More information and a literature review are available in Vähäkangas [9]. There are a couple of applications of artificial immune systems in industrial fault diagnosis. Dasgupta and Forrest [1] have used an immunity-based algorithm for tool condition monitoring. 7KHPHWKRGLVLQVSLUHGE\WKHQHJDWLYHVHOHFWLRQSULQFLSOHDQG WKHµVHOI¶LV GHILQHGDV WKHQRUPDO cutting operation and the non-self is the deviation beyond the allowable variation of the cutting force. The system is tested by simulations. Shulin et al.[10] proposed the improved negative selection algorithm for the fault diagnosis of the rotating machinery. The proposed algorithm has been is successfully demonstrated in the on-line case. Wang et al.[11] proposed a new fault diagnosis method based on the negative selection algorithm for the rotating rectifiers in generators with the brushless excitation system. Real data from an industrial coal flotation process were used to investigate the ability of the negative selection algorithm to detect changes by Yang et al.[12]. A fault diagnosis system has to be capable of adapting to dynamic changes[13,14,15]. The system should be designed to learn new antigens continuously and preserve its previous knowledge [16]. Liang, Xu & Sun[17] developed the immune memory network-based fault diagnosis (IMNFD) for diagnosing rolling bearings. 49

2. Basic Ideas of the AIS The artificial immune system (AIS) is a class of adaptive or learning computer algorithms inspired by the functioning of the biological immune system. It has been designed for and is applied to difficult problems such as intrusion detection, data clustering, classification and search problems. It is important to note that although the terminology and functioning of AIS are described using biological terms from the field of immunological research, they are taken as simplifications and abstractions and are not intended to be models or representative of immunological response systems [18]. A simplistic view of the immune system is that of an organ whose task is to detect pathogens (potentially harmful material or antigens) and respond by protecting the organism from them. The system is adaptive in that it improves in terms of antigen recognition over time. As more antigens with similar characteristics are observed, the more effective the system becomes at recognising and thus responding to the antigen. This response takes the form of an antibody whose task is to neutralise the pathogenic material. In this abstraction of immune function, the elements that perform anomaly detection are referred to as B cells and T cells. The cells are suited to specific antigens and perform recognition or matching in shape-space, which is nothing more than the features of antingen's attributes. The term used to describe the degree of similarity between a recognition cell and an antigen is called affinity. The adaptive ability of the immune system is a process called affinity maturation. During an immune response the recognition cell will perform a clonal expansion, which means that it generates many clones of itself in an attempt to gain a better match next time the antigen is encountered. A process called somatic hypermutation mutates the generated clones in proportion to the affinity between the recognition cell and the antigen. The clones produced have different receptors (features) to their parent, some of which are likely to provide a better match to the antigen observed. Competition and selection between the resulting clones then occurs where only those cells with highest affinity with the antigen are maintained. This process is called clonal selection. The immune system is said to have a form of memory in that through its interaction with antigens in the past, it is capable of remembering what a pathogen looks like and can better defend the organism in future. 2.1 The AbNET-Algorithm The great advantage of the immune system over the nervous system, is the existence of several well-established theories that reasonably explain immune functions, and allows the development of derived models. Some immune theories can be successfully applied in the development of a network architectures, called antibody network (AbNET), with the main features of competitive learning, automatic generation of the network structure and binary representation of the connection strengths (weights). The results obtained by former investigations show that the AbNET network is a promising tool for solving problems that are inherently binary. The existence of an antigen (Ag) population to be recognized by the antibody repertoire will be assumed. The antibody repertoire contains a single individual or any predetermined size at the beginning of the learning process, so that the repertoire will have to be constructed while submitted to the Ag population. For the sake of simplicity, the cells will be uniquely represented by their receptors (Ab), which should have the same length as the antigens. The antibody repertoire (Ab) will be modeled as a Boolean competitive network. The main features of the antibody network are as follows [1]: 50

x x x x

growing architecture, based on the clonal selection principle, network pruning, representing the death of non-stimulated cells (apoptosis), boolean connection strengths, competitive network, with unsupervised learning based on a mutation mechanism (Fig. 1).

In our cognitive paradigm (antigen recognition, learning and memory), it is desired to build an antibody network for maximal coverage of the antigen space. In the shape-space domain, the input patterns are the antigens (Ag), and the neurons are simply called cells. An antibody k (Abk) will be represented by the weight vector wk connecting the network inputs to a single output unit k. All these units are linear processing elements, i.e., they compute the weighted sum of their inputs. One distinct characteristic of this network is that its weights are binary, instead of real-valued. The initial architecture might be composed of a single output unit whose weights represent a hypothetical single antibody in the antibody network. A concentration level, determines the concentration of antigens for each antibody (j) in the network, and together with the antibody with highest affinity to the antigen, select an individual for cloning. The affinity between an antibody bitstring and an antigen bitstring is the number of complementary bits, as depicted in Figure 2 (exclusive-or operator XOR).

Fig. 1. Main steps of the AbNET-Algorithm.

Fig. 2. Affinity measurement between two bitstrings (Ab, Ag), here affinity is 6. 51

2.2 The AIRS - Algorithm The AIRS could be seen as one of the first AIS algorithms designed specifically and applied to classification and recognition problems with the following desirable algorithmic characteristics [18]: x

Self-regulation ± A problem common to the field of artificial neural networks is the selection of an appropriate topology or neuronal architecture. AIRS does not require the user to select an architecture, but instead the adaptive process discovers or learns an appropriate architecture through training.

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Performance - Empirical evaluation of the technique on standard classification problems, as when compared to the empirical results of the best known classifiers, showed that AIRS is a competitive classification system. The results indicate that AIRS ranks in the top five to top eight in terms of its classification accuracy as compared with some of the best widely known classification systems, and in the case of [6] it is capable of achieving the best classification results known for some datasets.

x

Generalisation - Unlike techniques such as k-Nearest Neighbour that use the entire training dataset for classification, AIRS performs the generalisation through data reduction. This means that the resulting classifier produced by the algorithm represents the training data with a reduced or minimum number of exemplars. AIRS typically produces classifiers with half the number of training instances [19].

x

Parameter Stability - The algorithm has a number of parameters that allows the tuning of the technique to a specific problem in order to achieve improved results. A feature of the algorithm is that over a wide range of parameter values, the technique is capable of achieving results that are within a few classification accuracy percentage points of the results gained using an optimal parameter set.

The AIRS offers a compromise between the powerful functionality of the natural immune system and reasonable complexity at the implementation level. A detailed specification of the algorithm in pseudo code ids is indicated in [19]. For the purposes of this investigation, we use the AIRS2 algorithm derived from AIRS I. The general purpose of the AIRS algorithm is to prepare a pool of recognition or memory cells (data exemplars), which are representative of the training data with a specific class labelling. It is suitable for classifying unknown data. The lifecycle of the AIRS system is described in Figure 3. This step of the algorithm consists of preparing the data for use in the training process and preparing system variables. The training data are normalized so that each numeric attribute is in the range [0,1]. The affinity measure is a very important aspect. in each recognition system. It is required in different steps during the training of a working process. A typical measure used is the inverted Euclidean distance , although a weighted distance measure (Mahalanobis) is possible. The memory cell pool is the collection of recognition elements that make up the classifier produced at the end of the training scheme. Seeding the memory pool is an optional step and involves randomly selecting a number of antigens to become memory cells. The final step during initialisation is to prepare the affinity threshold (AT) system variable. The affinity threshold is the mean affinity between antigens in the training dataset. It can be calculated either from a sample of the training set or the entire training set. This calculated value is used later during the training scheme to determine whether the candidate memory cells that are prepared can replace the existing memory cells in the classifier.

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Fig. 3. Main steps of the AIRS algorithm [18]. The AIRS algorithm is a single-shot algorithm in that only one pass over the training data is required to prepare a classifier. Each antigen is exposed to the memory pool one at a time. The recognition cells in the memory pool are stimulated by the antigen and each cell is allocated a stimulation value (inverted affinity). The memory cell with the greatest stimulation is then selected as the best match memory cell for use in the affinity maturation process. When the training process is completed, the pool of memory recognition cells becomes the core of the AIRS classifier. The data vectors contained within the cells can be denormalized or left as they are for the classification process. Classification occurs using the k-Nearest Neighbour approach where the best k matches to a data instance are located and the class is determined via majority vote [18].

3

Problem Setting

The aim of the study was to develop an artificial immune system network for roller bearing fault diagnosis. The AbNET algorithm was selected as a starting point for the investigation in order to train AbNET to classify different faults and recognise them from the real world data that were collected from rotating machinery. 3.1

Test Rig 1

Test data were collected from a rotor test rig with a rotating shaft supported by rolling bearings. Beside the normal operation condition the test rig allows the operation in nine different fault states. All measurements were done by Lahdelma and Kivistö in the Mechatronics and Machine Diagnostic Laboratory of the University of Oulu. This same data and same test rig have already been used in earlier studies Juuso et al. [20,21]. It is a convertible small size device with 0.18 kW AC motor. Five different rotation speeds between 900±1140 rpm were used and measurements were taken with seven separate accelerometers simultaneously. Two sensors measured axial vibration and five accelerometers radial vibration in vertical direction. Measurements were taken in LabVIEW environment by using 24 bit A/D converter. Sample rate was 22050 Hz and number of samples was 16384. The test rig and measurements points are presented in Figure 4. The following faults were simulated with the test rig: x two rotor unbalances weight 6.1 g and weight 11 g, x bent shaft, 53

x x

three coupling misalignments between the motor and input shaft: misalignment 1, misalignment 2, misalignment 3, three bearing faults (rolling element fault, outer race fault, inner race fault).

This makes in total nine different faults, but for this investigation only one fault at time was simulated.

Fig. 4. The test rig [20].

3.1.1 Features The data collection was carried out according to the following routine: Each fault situation was measured 100 times at five different rotating speeds 15, 15.5, 17, 18.5 and 19 rps. The same procedure was repeated also for the normal fault-free operation. One measurement vector included data from all seven accelerometers. Two of them measured axial vibration and five radial vibrations in vertical direction. By doing this, there were five data sets containing 100 measurements for each of the nine fault types and the normal operation, 5000 measurements together (see Fig. 5). Meas. # Normal case Unbalance 6.1 g Unbalance 11 g Accelometer Accelometer Accelometer 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 ... 100

.... ... ... ... ... ... ... ...

Inner race Accelometer 1 2 3 4 5 6 7

Figure 5. Measurement matrix for the rotational speed 15 rps. Based on this schema, five features, recogniced as well suited in the previous studies, were calculated from the time signals of the seven accelerometers: kurtosis, rms, jerkpeak, v1 and v2. The acceleration measurements range was 3-10700 Hz. The average of the three highest value of the jerk signal in the measurement range was denoted by jerkpeak. Two root-mean-square velocities

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were calculated in 10-11000 Hz and 20-85 Hz frequency ranges, and denoted by v1 and v2. This results in the total number of 36 different features (rotating speed included as a feature).

3.1.2 Data Pre-processing The AbNET algorithm uses binary inputs as antigens which should be recognized and classified. In consequence the available real-valued data are not directly suitable for the algorithm and has to be converted into the range [0,1]. AbNET need for training and testing a labeled data set. Training data was created by calculating mean values at each rotating speed (mean value of 100 measurements) separately and converting UHVXOWLQJ YDOXHV DQWLJHQ LQSXWV IRU HDFK IDXOW ZLWK IHDWXUHV WR ¶V DQG ¶V DV IROORZV ,f the mean value of the feature was lower than a defined level it was converted to zero. It was converted to 1 if the mean value was above the defined level. This defined level is the same that was used by Juuso for the definition of membership functions. The final training data set contained 50 different measurements or antigen inputs with 36 features. The test data was created in the same way but it contained all measurements with 36 features. It must be noted that training and test data were not totally independent.

Normal case

Features for A1 15 1 2 3 4 5 15,5 17 18,5 19

A2 ... A7 1 2 3 4 5 ... 1 2 3 4 5 ... ... ... ... ... ... ... ...

Unbalance 15 1 2 3 4 5 x 1 2 3 4 5 ... 1 2 3 4 5 6.1 g 15,5 ... ... 17 ... ... 18,5 ... ... 19 ... ... ... ... ... ... ... Inner race 15 1 2 3 4 5 x 1 2 3 4 5 ... 1 2 3 4 5 fault 15,5 ... ... 17 ... ... 18,5 ... ... 19 ... ...

Figure 6. Training data. 3.1.3

Results

After creating the training data set, AbNET was trained to identify faults from test data. As the training result, AbNET calculates the minimal antibody population or the weight matrix which can recognize and classifies the antigens (measurements). AbNET learning algorithm is very robust and the only parameter that really influences the algorithm is the affinity threshold İ (see Fig. 2). In the training phase, three different threshold values were tested: 3, 6 and 12. Antibodies were removed from the network (network pruning) if they failed to expand, which means that they did not match any of the elements contained in the antigen population. The network grew, if it did not reach the minimal size necessary to bind every antigen available in the Ag population, given affinity threshold İ. Table 1 shows the effect of the threshold. The smaller is the threshold the more antibodies are included in the weight matrix.

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Table 1. Training results. Threshold Size of the weight matrix Percentage of misclassified

3 36*29 6

12 26*12 0

6 36*22 2

For the purpose of testing each of the above trained three networks, the complete data set converted to binary values was used. Testing involved three distance thresholds, 2, 2,5 and 3, but the results shown here use only threshold 3 which gave the best results. Figure 7 shows the number of misclassified faults for the normal case (#1) and nine faults according to the list given before. It is clear that the smallest threshold gives the best results in the test. According to Table 1 it has the biggest number of antibodies. Figure 8 (left) shows how different antibodies succeed in recognising different faults. The higher the cone, the more cases the antibody recognises as the faults. This figure is drawn using the results got from the network which had the training threshold 3, the best network. All faults where the number of misclassification is small, seem to have several specific antibodies that recognise them and or only suited for this special detection task. To demonstrate the influence of the threshold, Figure 8 (right) shows in principal the same results, but now the training threshold is 12. Numerical values for the threshold 3 are listed in Table 2. 250

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Figure 8 shows that faults 8-10, which are related to bearing faults, are recognized almost perfectly. They are now analyzed in more details. Figure 9 shows that the 8 selected (bearing) antibodies recognise mainly faults in bearings, but very seldom other kinds of faults. The combinations of these antibodies seem to be different for different faults in bearing, as shown in Figure 9 (right). This is in good conformity with Figure 8 that shows that there are no misclassified bearing faults.

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Fig. 8. Faults vs. antibodies. The training threshold equals 3 (left) and 12 (right).

28 A n 21 t 20 i 19 b o 18 d 17 y 16 27

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Fig. 9. Faults vs. antibodies. Some antibodies recognise only faults in bearings, training threshold 3. (left). Right: Faults vs. antibodies. Different combinations of antibodies separate different faults in bearings. Table 2. Results of fault classification (29 antibodies, threshold 3).

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The results are comprehensible because the suitable of the features are different for specific fault types. Unbalance and misalignments generate a complete other vibration signature than a bearing fault and in consequence even the feature to detect the faults should differ. 3.2

Test Rig 2

In this investigation, time signals are from a second test rig, which allows the generation of different fault and condition states. For each state 50 samples with a fixed rotational frequency of 30 Hz were measured and stored for further digital pre-processing. The condition states are: Class1 - intact, Class 2 ± unbalance, Class 3 - outer race fault, Class 4 ± outer race fault and unbalance, and Class 5 ± outer race fault, unbalance and noise. A couple of relevant faults, such as unbalance, misalignment, bent shaft and mechanical looseness, can be detected by means of displacement and velocity, i.e. signals x x ( 0) and x x (1) . On the other hand it is well known that the early detection of bearing faults, as well as cavitation can be detected more efficiently with the acceleration signal. Often higher order derivatives provide more sensitive solutions, i.e. the ratios of calculated features between the faulty and non-faulty cases become higher [20, 21, 22, 23, 24, 25, 26]. The severity of faults can be assessed by comparing signals and features in different orders of derivation. For sinusoidal signals x

dD x dt D

x (D )

x(t )

X sinZt we obtain

S Z D X sin(Z t D ) 2

X D sin(Z t MD ), ........................ (1)

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Z D X , and the change of the

phase angle is MD . Real order derivatives increase the number of signal alternatives. Figure 10a shows the raw acceleration signal x(2) obtained from an accelerometer with a time length of 0.5 s and a sampling rate of 131072 Hz. All the time signals used in this paper were acquired with these settings. It could be seen in the corresponding amplitude spectra that frequency components up to 40 kHz are present. Figure 10e shows the signal x(2) in the case of unbalance, generated by a disk with an unbalance of 3.6 kgmm. The signal has a clear sine-shape with an additional noise level, which is comparable to the level in Figure 10a [27]. All the other signals in Figure 10 are derived from these acceleration signals. In Figures 10b and 10f both the time signals x(4) are very similar. The reason is obvious, because these signals only differ in the low frequent unbalance component at 30 Hz. On the other hand, unbalance could be clearly identified in the x(1) signal, which is generated by the integration of x(2). The velocity increases considerably in the case of unbalance (Figs. 10c and 10g). According to the ISO 2372 standard, the vibration rms value of approx. 30 mm/s is far away from any acceptable level. Figure 11 shows time signals from the two other classes: outer race fault and a combination of this with the unbalance. While the signals x(4) and x(2) from the outer race fault have a typical structure with relative constant peaks (Figs. 11a and 11b), the combinations of outer race and unbalance are less structured (Figs. 11e and 11f). The reason is the time dependent load that occurs during the contact between the roller and the damaged area caused by unbalance. This effect leads to slightly higher peaks than in the pure outer race fault situation.

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outer race and unbalance (Fig. 11f). The selected noise level masks the typical fault structure in the x(2) signal completely (Fig. 12). The signal x(4) is adequate to indicate the fault while the signals x(1) and x(0) highlight the unbalance. time signal

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3.2.2 Feature extraction There are a couple of different feature which are well established in condition monitoring. A systematic approach is given by features which are calculated by means of a generalised moment about the origin: W

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«««««««««. (2)

i 1

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p

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W

4

which corresponds to the signal x(4). The moment V M D 1 , and the moment V M D corresponds to the kurtosis of the signal. These norms can be used for detecting unbalance, misalignment, bent shaft and mechanical looseness. For bearing faults, displacement and velocity should be replaced by acceleration or higher derivatives. The generalised moments and norms have been used for diagnosing faults in a roller contact on a rough surface [29]. Kurtosis WV M D4 (4) is normalized and as a dimensionless number therefore not affected by attenuation in the signal transmission path, for example, from the source of vibration to the sensor. For roller bearing fault detection the fourth moment provides a reasonable compromise between insensitive low order moments and the very sensitive high orders. Figure 13 demonstrates the influence of the order of derivatives on two features, crest factor and kurtosis, for all 5 classes. x(1)

x(1)

6

4

intact unb outer unb+outer unb+outer+noise

2.4 2.2

crest factor

crest factor

5

3 2

2 1.8 1.6

1 0 0

1.4 0.5

1

1.5 kurtosis x(2)

2

2.5

3

1.5

1.6

1.7 kurtosis x(2)

1.8

2

3 kurtosis x(4)

4

3 kurtosis

3.5

20 8 7

crest factor

crest factor

15

10

6 5 4 3

5

2 10

20 30 kurtosis x(4)

40

50

1

60

10

50

8

40

crest factor

crest factor

0 0

30 20

6 4 2

10 0 0

5

50

100

150 200 kurtosis

250

0 2

300

2.5

4

Fig. 13. Feature map for all 5 condition states using kurtosis and crest factor as a feature for the signals x(1), x(2) and x(4). The notations are unb=unbalance, and outer=outer race fault [27]. 62

When using x(4) for class 4 (outer race fault + unbalance) and class 5 (outer race fault+unbalance+noise), the variation of kurtosis is very high with maximum values about 250 (Fig. 13 bottom left). Class 3 (only outer race) has much less variation, since the load is more stationary in the absence of unbalance. The time signals x(4) of class 1 (intact) and class 2 (unbalance) lead to kurtosis values of 3 with very low variation (bottom right), i.e. the signals are very close to Gaussian signals. The component caused by the unbalance weakens with derivation. Velocity x(1) eliminates all high frequency components. As a result, all kurtosis values are between 1.5 and 3. In the unbalance case, velocity is very close the sine-shaped signals: kurtosis goes to 1.5 and crest factor to ξʹǤ Unbalance is detected in the combined case also when noise is included. In the intact case, slight unbalance can be seen with these features as well. For the combined fault with noise, the feature values are very similar to the values of the intact case. Strong noise moves the signal towards the Gaussian signal. This example clearly indicates that an optimum setting of the derivative is only possible for individual fault detection. The use of one fixed value for the order for the combination of faults will lead to a compromise setting. The experiments indicate that the kurtosis value of an intact bearing is close to 3 and that kurtosis in general provides a measure of the occurrence of peaks in a signal. 3.2.3 Classification results with ARIS The AIRS algorithm and different other classifiers have been applied as benchmarks on the five class data set with 250 samples in total. 10-fold cross-validation has been used to test the accuracy of the algorithms. The results of this investigation are shown in Table 3. The AIRS2Parallel algorithm has been chosen in weka [30] with its user-defined parameters (seed: 1, affinityThresholdScalar: 0.2, clonalRate: 10.0, hypermutationRate: 2.0, totalResources: 150.0, stimulationValue: 0.9, numInstancesAffinityThreshold: 1, memInitialPoolSize: 1, knn: 3, numThreads: 2, mergeMode: 1). In total only 14 samples were mis-classified when the acceleration x(2) signal was used with kurtosis and crest factor as features.

Table 3. Classification accuracy for different orders of derivative x x(1) x(2) x(4

Corr. Classified Corr. Classified Corr. Classified Corr. Classified

153 190 236 130

61.2% 76.0% 94.4% 52.0%

More detailed information gives the confusion matrix were all errors a listed per class. One could see that there is no problem in classifying samples of the classes 2,3 and 5. All 50 training samples of each class were classified correctly. Mis-classified values in deciding between classes were generated between the Class1 ± intact and Class 5 ± outer race fault, unbalance and noise. The high additive noise level leads to an overlap of the samples in the feature map (Fig. 14, kurtosis approx. 3 and crest factor between 4 and 5). There is no change to improve the accuracy with these features and the signal x(2) . To obtain an error-free result, one could use the signal x(4) to separate both classes without any problems. The significant difference in the feature space between the two classes is illustrated in the lower left-hand part of Figure 13. For fault identification, the classification has to be performed as a two-stage process. At the first step the unknown sample passes through the five-class classifier. The decision will be a crisp classification result in one of the predefined classes. If class 1 or 5 is selected, the derivative signal x(4) has to be calculated in a 63

two-class problem. In this investigation, random noise was taken as a disturbance. However, in real applications, a careful analysis is needed: signal components, which could easily be considered noise, can provide important information. For example, friction has been detected by the norms of x(4) in the supporting rolls of a lime kiln [31, 32]. Table 4. Confusion matrix C1 (1)

C2 (2)

(4)

x

(1)

C3 (2)

(4)

x

x

x

(1)

x

C4 (2)

x

(4)

x

x

(1)

x

C5 (2)

x

(4)

x

x

x

x

(1)

(2)

(4)

x

x

x

x

x

x

C1

35

33

38

33

0

0

0

13

15

0

0

0

0

4

0

1

0

13

12

3

C2

0

0

0

20

33

46

50

23

0

0

0

1

17

4

0

3

0

0

0

3

C3

14

0

0

4

0

0

0

6

36

50

50

31

0

0

0

6

0

0

0

3

C4

0

1

0

4

28

14

0

8

0

0

0

1

13

35

50

21

9

0

0

16

C5

0

15

6

6

3

0

0

4

0

1

0

2

9

0

0

22

38

34

44

16

x(2) 8

crest factor

7 6 5 4 3 2 1

2

3 kurtosis

4

5

Fig. 14. Feature map for all 5 condition states using kurtosis and crest factor as a feature for the signal x(2) . The red box identify the problem area where a classification leads to a errors. A standard decision tree C 4.5 was used to compare the results with other classifiers. The classification accuracy was 91.6% i.e. lower than in the case of the AIRS algorithm.

4. Conclusions This paper presents the results of two different Artificial Immune System algorithms for diagnosing machinery faults. The AbNET results are comparable with the earlier ones gained with other methods using the same data. The results are promising in view of the detection of roller bearing faults. Damaged roller bearings are separated from normal fault-free operation and other simulated fault classes. There are still problems and mis-classifications with other fault classes, such as 64

unbalance, bent shaft and misalignment, because the features of these faults are similar. The fault classes cannot be established without better and more extensive measurements. The main problem, however, lies in data pre-processing. Better results could be achieved by finding a more suitable method for encoding the real-valued feature data to binary values. The ARIS does not have this drawback. The internal structure of the algorithm qualifies the method for recognition tasks. The results are promising and classification accuracy is slightly better than with a standard decision tree or a bayes classifier. This mis-classification rate is related to the well-known problem that raw data pre-processing and feature extraction are essential parts of developing automatic fault detection systems. The AIS as an advanced classifier could not compensate for major deficits in feature generation. For this important step, a couple of advanced signal processing and feature extraction methods to be chosen according to task are available in order to detect different faults. Generalised moments and norms obtained from higher or real order derivatives provide informative features for diagnosing faults in a roller contact. The feature calculated from x(2) gives the best overall performance in a five-class classification. A complete error-free classification needs the features of x(4), which indicate well the intact case and the outer race fault with and without additional noise. The approach of intelligent indices [31,32] could solve the problem. The combination of fault-specific indices calculated from different order derivatives take the effects of adapted signal processing into consideration. An approach for optimising pre-processing parameters is shown in [33]. Derivation reduced the effect of noise by amplifying higher frequency components from bearing faults more than the noise components. The results clearly show that the detection of fault combinations needs an adapted signal pre-processing technique in order to obtain the best sensitivity for specific faults. A general setting of parameters will lead to a compromise that will reduce classification accuracy. On the other hand, the investigation clearly illustrates that the correct way of profiting from the mechanisms developed by nature is to obtain algorithmic inspiration from them, but at the same time finding ways of implementation that are more appropriate to a specific problem. Clone proliferation is a costly biological operation, whereas in the software of an anomaly detection system it is merely a virtual and less time-consuming operation and could be used more extensive ly. This is a good example of why one should receive inspiration from nature but not copy it blindly.

References 1. D Dasgupta and S Forrest, 1999, µ$UWLILFLDO LPPXQH V\VWHPV LQ LQGXVWULDO DSSOLFDWLRQV¶ Proceedings of the Second International Conference on Intelligent Processing and Manufacturing of Materials (IPMM), Honolulu, Hawaii, July 10-15, pp. 257-267. 2. U Aickelin and S Cayzer, 2002, µ7KH'DQJHU7KHRU\DQGLWV$SSOLFDWLRQWR$UWLILFLDO,PPXQH 6\VWHPV¶ 3URFHHGLQJV RI WKH VW ,QWHUQDWLRQDO &RQIHUHQFH RQ $UWLILcial Immune Systems (ICARIS 2002), Canterbury, UK, pp. 141-148. 3. P Matzinger, 1994, µ7ROHUDQFH GDQJHU DQG WKH H[WHQGHG IDPLO\¶ $QQXDO 5HYLHZV LQ Immunology, Vol. 12, pp. 991-1045. 4. A Watkins and L Boggess, 2002, 'A New Classifier Based on Resource Limited Artificial Immune Systems', Proceedings of Congress on Evolutionary Computation, Honolulu, USA, May 12-17, pp. 1546-1551. 65

5. A Watkins, J Timmis, and L Boggess, 2004, 'Artificial Immune Recognition System (AIRS): An Immune-Inspired Supervised Learning Algorithm', Genetic Programming and Evolvable Machines, Vol. 5, No. 3, pp. 291-317. 6. J H Carter, 2000, 'The Immune System as a Model for Pattern Recognition and Classification ', Journal of the American Medical Informatics Association, Vol. 7, No. 1, pp. 28-41. 7. J Strackeljan and K Leiviskä, µArtificial Immune System approach for the Fault Detection in Rotating Machinery¶, Proceedings of CM 2008 ± MFPT 2008, Edinburgh, UK, pp. 879-889. 8. L Nunes de Castro and F J von Zuben, 1999, µ$UWLILFLDO ,PPXQH 6\VWHPV 3DUW - Basic 7KHRU\DQG$SSOLFDWLRQV¶, Technical report TR-DCA 1. 96 p. 9. V Vähäkangas, 2007, µ$UWLILFLDO,PPXQH6\VWHPVLQ)DXOW'LDJQRVLV¶, MSc. Thesis. University of Oulu, Department of Process and Environmental Engineering, Oulu, Finland. 61 p. 10. L Shulin, Z Jiazhong, S Wengang and H Wenhu, 2002, µ1HJDWLYH-selection algorithm based DSSURDFKIRUIDXOWGLDJQRVLVRIURWDU\PDFKLQHU\¶, Proceedings of the American Control Conference 2002, Anchorage, Alaska, 8-10 June, pp. 3955-3960. 11. T Wang, N Liu, C Xie and K Sun, 2006, µ6WXG\RI)DXOW'LDJQRVLVLQ%UXVKOHVV0DFKLQHV Based RQ$UWLILFLDO,PPXQH$OJRULWKP¶,2006 IEEE International Symposium on Industrial Electronics (ISIE´06), Montreal, 9-13 July, pp. 1779-1782. 12. X Yang, C Aldrich and C Maree, 2007, µ'HWHFWLQJFKDQJHLQG\QDPLFSURFHVVV\VWHPVZLWK LPPXQRFRPSXWLQJ¶, Minerals Engineering, Vol. 20, No. 2, pp. 103-112. 13. A Boukerche et. al., 2004, µ$QDUWLILFLDOLPPXQHEDVHGLQWUXVLRQGHWHFWLRQPRGHOIRU computer DQGWHOHFRPPXQLFDWLRQV\VWHPV¶3DUDOOHO&RPSXWLQJ9RO. 30, No. 5-6, May-June, pp. 629646 . 14. D Bradly and $7\UHOOµ,PPXQRWURQLFV+DUGZDUH)DXOW7ROHUDQFH,QVSLUHGE\WKH ,PPXQH6\VWHP¶3URFeedings of the 3rd International Conference on Evolable Systems,LNCS 1801, Springer, pp.11-20. 15. C P J Branco, J A Dente and R V Mendes, 2003, µ8VLQJ,PPXQRORJ\3ULQFLSOHVIRU)DXOW 'HWHFWLRQ¶,(((7UDQVDFWLRQVRQ,QGXVWrial Electronics, Vol. 50, No. 2, pp. 362-373. 16. G C Luh and W Chen, 2005, µ,PPXQHPRGHO-EDVHGIDXOWGLDJQRVLV¶ Mathematics and Computers in Simulation, Vol. 67, No. 6, pp. 515-539. 17. L Liang, G Xu and T Sun, 2006, µ,PPXQH0HPRU\1HWZRUN-%DVHG)DXOW'LDJQRVLV¶ Proceedings of the Sixth International Conference on Intelligent Systems Design and Applications (ISDA'06), IEEE Computer Society, Jinan, China, October 16-18, pp. 517-522. 18. J Brownlee, 2005, µArtificial Immune Recognition System (AIRS) a review and analysis¶, Faculty of Information and Communication Technologies (ICT), Swinburne University of Technology, Technical Report ID: 1-02. 19. D Goodman, L Boggess and A Watkins, 2002, µArtificial Immune System Classification of Multiple-Class Problems¶ Intelligent Engineering Systems Through Artificial Neural Networks: Smart Engineering System Design: Neural Networks, Vol. 12, pp. 179-184. 20. E Juuso, M Kivistö and S Lahdelma, 2004, µ,QWHOOLJHQW&RQGLWLRQ0RQLWRULQJ8VLQJ9LEUDWLRQ 6LJQDOV¶(XURSHDQ6\PSRVLXPRQ,QWHOOLJHQW7HFKQRORJLHV+\EULG6\VWHPVDQG7KHLU Implementation on Smart Adaptive Systems, Verlag Mainz, Aachen. ISBN 3-86130-368-X, pp. 381-390. 21. S Lahdelma and E Juuso, 2008,¶6LJQDO3URFHVVLQJLQ9LEUDWLRQ$QDO\VLV¶3URFHHGLQJVRI)LIWK International Conference on Condition Monitoring & Machinery Failure Prevention Technologies CM 2008 ± MFPT 2008, Edinburgh, UK, 15-18 July, pp. 867-878. 22. S Lahdelma and V Kotila, 2003, µ5HDO2UGHU'HULYDWLYHV± 1HZ6LJQDO3URFHVVLQJ0HWKRG¶LQ Finnish), Kunnossapito, Vol. 17, No. 8, pp. 39-42. 66

23. S Lahdelma and E Juuso, 2007, µ$GYDQFHGVLJQDOSURFHVVLQJDQGIDXOWGLDJQRVLVLQFRQGLWLRQ PRQLWRULQJ¶,QVight, Vol. 49, No. 12, pp. 719±725. 24. S Lahdelma and E Juuso, 2008,¶6LJQDO3URFHVVLQJLQ9LEUDWLRQ$QDO\VLV¶3URFHHGLQJVRI)LIWK International Conference on Condition Monitoring & Machinery Failure Prevention Technologies CM 2008 ± MFPT 2008, Edinburgh, UK, 15-18 July, pp. 867-878. 25. S Lahdelma and V Kotila, 2005, µComplex Derivatives A 1HZ6LJQDO3URFHVVLQJ0HWKRG¶ Kunnossapito, Vol. 19, No. 4, pp. 39-46. 26. S Lahdelma and E Juuso, 2007, µ$GYDQFHGVLJQDOSURFHVVLQJDQGIDXOWGLDJQRVLVLQFRQGLWLRQ PRQLWRULQJ¶,QVight, Vol. 49, No. 12, pp 719±725. 27. S Lahdelma, E Juuso and J Strackeljan, 2010 µUsing Condition Indices and Generalised Norms for Complex Fault Detection¶, in A Seeliger and P Burgwinkel (Ed.) Tagungsband zum AKIDA 2010, Aachen, Germany, November. 15 p. 28. S Lahdelma and E Juuso, 2008, µ9LEUDWLRQ$QDO\VLVRI&DYLWDWLRQLQ.DSODQ:DWHU7XUELQHV¶ Proceedings of the 17 World Congress, The International Federation of Automatic Control, Seoul, Korea, July 6-11, pp. 13420-13425. 29. S Lahdelma, E Juuso and J Strackeljan, 2008, µ9LEUDWLRQ$QDO\VLVZLWK*HQHUDOLVHG1RUPVLQ &RQGLWLRQ 0RQLWRULQJ¶ AKIDA, Tagungsband zum 7. Aachener Kolloquium für Instandhaltung, Diagnose und Anlagenüberwachung, 18-19 November 2008, Aachen, Germany, A. Seeliger & P. Burgwinkel. Aachener Schriften zur Rohstoff- und Entsorgungstechnik, Band 70, Verlag R. Zillekens, pp. 583-593. 30. Waikato Environment for Knowledge Analysis, online available: // http://www.cs.waikato.ac.nz/~ml/weka/ 31. S Lahdelma and E Juuso, 2010, µ*HQHUDOLVHG OS 1RUPV LQ 9LEUDWLRQ $QDO\VLV RI 3URFHVV (TXLSPHQWV¶ 3URFHHGLQJV RI WK ,QWHUQDWLRQDO &RQIHUHQFH RQ &RQGLWLRQ 0RQLWRULQJ Machinery Failure Prevention Technologies CM 2010 ± MFPT 2010, Stratford-upon-Avon, UK, June 22-24. 13 p. 32. E Juuso and S Lahdelma, 2010, µ,QWHOOLJHQW 6FDOLQJ RI )HDWXUHV LQ )DXOW 'LDJQRVLV¶ Proceedings of 7th International Conference on Condition Monitoring & Machinery Failure Prevention Technologies CM 2010 ± MFPT 2010, Stratford-upon-Avon, UK, June 22-24. 15 p. 33. S Goreczka and J Strackeljan, 2010, µAutomatic Parameter Setting for the Signal Processing in Rolling Bearing CM¶, Proceedings of 7th International Conference on Condition Monitoring & Machinery Failure Prevention Technologies CM 2010 ± MFPT 2010, Stratford-upon-Avon, UK, June 22-24. 10 p.

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