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effective alternative is motor current signature analysis [2-4]. However, vibration ..... homopolar component,” Mechanical Systems and Signal Processing, vol.
Classical Mechanics-Inspired Optimization Metaheuristic for Induction Machines Bearing Failures Detection and Diagnosis Charaf Eddine Khamoudj1,2, Fatima Benbouzid-Si Tayeb1, Karima Benatchba1 and Mohamed Benbouzid2,3 1

Ecole Nationale Supérieure d’Informatique, LMCS_Lab, Algiers, Algeria 2 University of Brest, FRE CNRS 3744 IRDL, Brest, France 3 Shanghai Maritime University, Shanghai, China [email protected], [email protected], [email protected], [email protected] Abstract—This paper deals with induction machines bearing failures detection and diagnosis using vibration and temperature signals. It proposes the use of a new Classical Mechanics-inspired Optimization (CMO) metaheuristic for data clustering. To ensure failure detection, transitions from a state to another is analyzed in order to form a transitional model between system states generated by the clustering. The performances of the proposed new metaheuristic are evaluated on the PRONOSTIA experimental platform data. Keywords—Induction machine, bearing failure, detection, diagnosis, Classical Mechanics-inspired Optimization (CMO) metaheuristic.

I. INTRODUCTION Failure detection and diagnosis in electromechanical systems are a priority within the overall operational safety field, in order to ensure the availability of the production tool and to avoid losses caused by unpredictable stopping. One of the sensitive components of these systems is the electrical machine and particularly the induction one, which is widely used in industry and more recently as a generator for renewable energies harvesting. However, its use generates electrical and mechanical constraints that unfortunately can lead to internal failures that must be detected and diagnosed at an early stage [1]. Induction machine rotors are statistically more vulnerable compared to the stator. Indeed, they are under high stresses, including thermal mechanical, and electrical stresses. Bearings are typically the most frequently failed component of an induction machine. In particular, bearing failure is caused by some misalignment in the drive train, which gives rise to abnormal loading that unfortunately accelerates bearing wear [1]. In this context, there is a crucial need for condition monitoring and operating state supervision. Conventional condition monitoring techniques require sensors deployment and computationally intensive signal processing techniques. A costeffective alternative is motor current signature analysis [2-4]. However, vibration analysis still remains the most common used condition monitoring technology used in industry for rotating equipment [5-6]. In [7], it is proposed a method for the monitoring of bearing performance degradation based on k-medoids clustering using the vibration signals collected in run-to-failure tests. It consists in extracting process of signals then obtaining the defect feature

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vectors by using a similarity measurement to train a k-medoids clustering model. In [8], an unsupervised feature of k-means clustering is used in the learning procedure for the automated diagnosis of defective rolling element bearings. Since k-means is sensitive to the choice of the initial centers, [9] propose to hybridize k-means with a genetic algorithm in order to define the starting solution to implement a bearing failure diagnosis method based on vibration signals. In [6], an interesting literature overview is proposed. It particularly deals with vibration signalsbased failure detection and diagnosis algorithms. Compared to these signal processing-based approaches, this paper proposes a metaheuristic-based approach for data (vibrations and temperatures) clustering in which each state of the induction machine is represented by a pattern allowing its condition monitoring. To ensure failure detection, transitions from a state to another is analyzed in order to form a transitional model between system states. This will be achieved by unsupervised data classification (clustering). In this context, data clustering is realized using a new Classical Mechanics-inspired Optimization (CMO) metaheuristic [10]. The performances of the proposed CMO metaheuristic are evaluated on the PRONOSTIA experimental platform data [1112]. II. CLASSICAL MECHANICS OPTIMIZATION METAHEURISTICBASED FAILURE DETECTION AND DIAGNOSIS In this work, bearing failures detection and diagnosis are based on measured vibrations and temperature. The proposed approach is based on theses measured signals unsupervised classification in classes using the CMO metaheuristic. This will allow creating a graphical representation of the measured data, where each class represents an operating state of the induction machine. These classes sequence over time provide bearings degradation evolution. In other words, given a starting class, we can predict the next class that represents the next operating state and therefore report whether it will be a failure state or not. CMO is a metaheuristic inspired by the natural phenomenon of bodies movement in a space. It is based on the classical mechanics laws, especially Newton third law (universal gravitation). This metaheuristic was originally developed to sole the image segmentation problem [10]. The CMO algorithm is composed of two main steps: 1) The first one finds equilibrium of the rotating satellites around planets

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by applying the Earth-Moon system then groups each planet with its satellites as one body after the stabilization. 2) Formed bodies are then grouped by applying the Earth-Apple system; merging bodies according to the gravitational attraction. Each body in space has two gravitation fields computed according to its mass, which correspond to an attraction force applied. The first field is applied on the Earth-Moon system to keep the satellites in rotation around planets. The second one is applied on the Earth-Apple system, causing some bodies to fall on others applying the greatest attraction force. Before launching the CMO algorithm, it is necessary to transform the problem data into a space bodies system and define the distance ratio, which represents the parameter used to transform the distance between data into distance in space. A. Problem Transform into a Space Bodies System The distance ratio represents the main parameter of the CMO algorithm to define the intensification/diversification behavior of the algorithm, because it is used to transform the calculated bodies gravitational field radius into distance between data. Indeed, when the distance ratio is small, the algorithm becomes more intensive because the similarity measure is small and we obtain a little number of classes. If the distance ratio is very small, we obtain a unique class containing all the data. This is called a black hole class. If the distance ratio is very large, we do not obtain any grouped bodies because bodies gravitational fields are very small. To create planets and satellites, we regularly select m measurement files according to the used data aggregation function. The remaining n files will be considered as satellites. The number of planets m is calculated, according to planets and satellites numbers in the simulated space bodies system, as follows. ×

=

(1)

Where PlanetNbr and SatelliteNbr are given by the simulated solar system data. The satellites number n is calculated according to (2). =

−

(2)

The gravitational force function Fab between the different bodies a and b is calculated by the Newton third law using the Euclidean or the Manhattan distances according to the algorithm parameters. This force is calculated as follows. =

(3)

Where ma and mb represent masses and dab represents the distance between bodies. This distance is calculated after the simulation of the spatial distance using a triangular rule. The body mass is calculated, according to the number of its element, as follows. =

−

Where the unit mass is calculated by

(4)

=

(5)

The distance ratio is calculated by =



(6)

where the bodies distance is the real one in space and the files distance represents the transformed bodies distance. Moreover, we can use the greatest distances between bodies in space and the greatest distances between data to calculate the distance ratio. The algorithm allows processing isolated points. The user specifies the minimum number of points per class and a strategy for grouping isolated points is defined (with the closest class in the x-axis or the y-axis or according to the gravitational attraction function). Next, we gather data according to the two CMO algorithm steps (Earth-Moon and Earth-Apple systems) according to the gravitation force. The center of gravity of each body in this space is based on the centroids concept, where each class is represented by a virtual point that is its center. The main algorithm (Algorithm 1) is described as follow. Algorithm 1: Main Algorithm. Input Dataset B {measurement files} begin Calculate (m) {Apply (1) to calculate the planet number according the file number} Calculate (n) {Apply (2) to calculate the satellite number} Calculate (DistanceRatio) {Apply (4)} Select isolated points grouping method Find the Earth-Moon system equilibrium {Algorithm 2} Find the Earth-Apple system equilibrium {Algorithm 3} end.

B. Body Equilibrium using Earth-Moon System In this step, we look for the Earth-Moon equilibrium, characterized by the stabilization of the satellites movement around planets, when this movement is caused by the planets exerted gravitational attraction. Each planet p1 exerts an attraction force Fp1s on a satellite s, which is rotating around another planet p2 with an applied force Fp2s. If Fp1s > Fp2s, then the satellite s leaves its path around p2 and follows a new path around p1. For each planet-satellites group, the gravity center becomes the center of all satellites around this planet, and the attraction force is calculated accordingly. We repeat the two previous steps until the system equilibrium is reached, resulting in no satellites displacements between planets. Algorithm 2 illustrates the Earth-Moon system equilibrium flowchart. C. Body Equilibrium using Earth-Apple System In this step, we will build the final classes corresponding to the final obtained bodies. After the first stabilization, we consider every planet-moon set as one body. Then we calculate bodies gravitational fields (EarthApple system) to group them. Each body situated in the gravitational field of another one falls on it (two classes fusion) and the two bodies are considered as a single one.

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Algorithm 2: Find the Earth-Moon system equilibrium.

A. The PRONOSTIA Platform

var E: array [1..z] of real; {E is the data set} Planet: array [1..m,1..n] of integer; {Each row of this matrix represents the satellites turning around the corresponding planet, Planet(j, 1) represents the center of gravity of the same line} Satellite: array [1..n] of integer; {Each case i represents the corresponding planet of satellite i} m, n: integer; {m is the planet number and n is the satellite number } begin Calculate (m); Calculate(n); Initialize (Planet, Satellite); repeat for i = 1 to n for j = 1 to m if Earth Moon Gravitational Field (Planet(j)) > Distance(Planet(j),Satellite(i)) then if Force(Planet(j,1), Satellite(i)) > Force(Planet(Satellite(i),1),Satellite(i)) then Move (Satellite(i),j); {Release satellite i from his planet and assign it to planet j} end if end if next j next i Until system stabilization end.

PRONOSTIA is an experimentation platform devoted to test and to validate bearings failure (radial load) detection, diagnostic, and prognostic approaches. The platform, illustrated by Fig. 1, has been designed and realized at AS2M Department of FEMTO-ST Institute [11-12]. It provides experimental data on ball bearings deterioration throughout their lifetime, up to their total failure (Fig. 2). B. The Experimental Data Bearing horizontal and vertical vibration signals are collected via two accelerometers placed at 90° of each other around the bearing outer ring. The temperature signal is measured via a thermocouple placed in a hole close to the bearing outer ring. The vibration and temperature signals were sampled at 25.6 and 10Hz, respectively. In the PRONOSTIA platform, three different operating conditions were carried out, where the radial load and the speed were varied. Table 1 provides the complete operating conditions and their specifications [11]. The data from each experiment are stored in a folder composed of several files containing the measured signals for 10 minutes. The experiment stops at the moment of the bearing total failure, which results in measuring a vibration maximum value.

After every fusion, we repeat the previous two steps until the overall system is stable and all the bodies are far from each other. Algorithm 3 illustrates the Earth-Apple system equilibrium flowchart.

NI DAQ card

Pressure regulator

Cylinder Pressure

Force sensor

Bearing tested

Accelerometers

Algorithm 3: Find the Earth-Apple system equilibrium. use result of Algorithm 1 begin repeat for i = 1 to n for j = 1 to m if Gravitational Field Earth-Apple (Planet(i)) > Distance(Planet(i),Planet(j)) then Move (Planet(j),i); {move all data of body j to body i} Recalculate the new center of gravity; Remove line j from Planet matrix; m = m – 1; end if next j next i Until system stabilization end.

AC Motor

Speed sensor

Speed reducer

Torquemeter

Coupling

Fig. 1. Overview of the PRONOSTIA platform [11-12].

III. VALIDATION ON EXPERIMENTAL DATA For validation purposes, we consider the vibration and temperature data from the experimental platform PRONOSTIA [11-12]. This platform is well recognized and is regularly used for failures diagnosis and prognosis approaches [13-14].

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Fig. 2. Normal and degraded bearings [11].

Thermocouple

TABLE 1. PRONOSTIA DATASETS VERSUS OPERATING CONDITIONS SPECIFICATIONS. Dataset Radial Load (N) Speed (rpm) Learning sets

Test sets

measurement file becomes a body in space represented by one measurement.

Operating Conditions Condition 1

Condition 2

Condition 3

4000

4200

5000

1800

1650

1500

B1_1

B2_1

B3_1

B1_2

B2_2

B3_2

B1_3

B2_3

B3_3

B1_4

B2_4

B1_5

B2_5

B1_6

B2_6

B1_7

B2_7

D. CMO Metaheuristic Application The proposed CMO metaheuristic is now applied on the PRONOSTIA platform experimental datasets by simulating the solar system. In this case, the number of planets m is calculated using (1) based on a solar system with 167 satellites and 8 planets. =

C. Measurements Management and Processing To properly manage measurements, they are stored in a database, using the MS-SQL-Server system, which plays the management role and query the data using SQL statements for selection, sorting, insertion, deletion, modification, and aggregation. Measurements processing from the files requires a run through at each execution. They remain in a crude state and the cited operations are not allowed leading to reprocessing the data using the algorithm at each execution. Each file is composed of a number of measurements in a time interval. To optimize the algorithm progressing time, measurements have been aggregated per file considering the aggregated file as a single measurement. This has been achieved using a classical aggregation function such as data standard deviation and data mean. In this context, each

×

(7)

For detection and diagnosis purposes, each experiment dataset should be set according to the proposed metaheuristic. To illustrate the proposed CMO metaheuristic performances, the learning set B1_1 and the test one B1_3 are used. Figures 3 and 4 highlight the clustering of the measured signals after data aggregation per file using a standard deviation function. Data are grouped into classes where each class elements have the same color and typically represents the induction machine (bearing) operating state. These two figures clearly highlight the clustering high performances of the proposed CMO metaheuristic. This will obviously lead to increased failure detection and diagnosis performances and accuracy. Figures 5 and 6 show the bearing degradation over time of datasets B1_1 and B1_3, respectively. These results clearly highlight the ability of the proposed classical mechanicsinspired metaheuristic not only for bearing degradation initiation detection but also tracking its evolution over time. This is a key feature for the estimation of the bearing remaining useful life.

Fig. 3. File measurements clustering by CMO for dataset B1_1.

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Fig. 4. File measurements clustering by CMO for dataset B1_3.

Fig. 5. Bearing degradation evolution for dataset B1_1.

Fig. 6. Bearing degradation evolution for dataset B1_3.

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The proposed approach achieved results are not limited to two classes, which represent the normal operating state and the failure one. With this approach, for each experiment we get several classes that represent the bearing degradation over time in a macroscopic view. It is therefore possible, during the bearing operation, to diagnose its state of health and predict its next states until failure. IV. CONCLUSION

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This paper has proposed a new metaheuristic for induction machines bearing failures detection and diagnosis using vibration and temperature signals. It is a classical mechanicsinspired optimization metaheuristic for data clustering. The performances of the proposed metaheuristic have been evaluated using the PRONOSTIA experimental platform data. The achieved results clearly highlight the clustering high performances, which will obviously lead to increased failure detection and diagnosis performances and accuracy. In addition, it has been shown the ability of the proposed classical mechanics-inspired metaheuristic not only for bearing degradation initiation detection but also tracking its evolution over time. This is a key feature that will be used in future investigations for bearings remaining useful life estimation.

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