Imaged wear debris separation for on-line monitoring using gray level and integrated morphological features

Wear 316 (2014) 19–29

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Wear journal homepage: www.elsevier.com/locate/wear

Imaged wear debris separation for on-line monitoring using gray level and integrated morphological features Tonghai Wu a,n, Hongkun Wu a, Ying Du a, Ngaiming Kwok b, Zhongxiao Peng b a b

Key Laboratory of Education Ministry for Modern Design and Rotor Bearing System, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, People's Republic of China School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney 2052, Australia

art ic l e i nf o

a b s t r a c t

Article history: Received 18 February 2014 Received in revised form 9 April 2014 Accepted 11 April 2014 Available online 29 April 2014

The characteristics of wear debris particles are valuable information sources for machine condition monitoring. A possible approach is to apply ferrography with computer vision techniques. However, when images are captured on-line, it is observed that particles tend to appear agglomerated and an effective image processing method is hence required. A particle extraction procedure is here developed by making use of advances in morphological segmentations. The reliability of particle separation is improved with both transmitted and reflected debris images. Furthermore, an iterative morphological scaling operation, incorporating gray and boundary based segmentation, is included to increase segmentation accuracy. The performance of the proposed method is tested using real-world wear debris images captured from the lubricant return line in a gearbox. Particle characteristics are found to follow closely the Weibull distribution. & 2014 Elsevier B.V. All rights reserved.

Keywords: Wear debris analysis Particle separation Image processing On-line ferrograph monitoring

1. Introduction The demand for effective and economic maintenance schedules has recently grown rapidly with the development of complex and expensive machines. In order to maximize their lifespans with minimum cost, condition-based machine maintenance is often required [1]. Practitioners can obtain estimates of the machine condition by measuring vibrations, temperatures, sounds and many other informative features. On the other hand, machine health can be inferred by observing the amount of wear. However, physical inspection of wear condition could be forbidding due to the need to stop the machine from its normal operation. Approaches based on characterizing the wear process by observing and analyzing the morphological features of debris are thus attractive potential on-line solutions [2]. For instance, in [3], adhesive or abrasive wear was classified using the area, perimeter and elongation parameters. In particular, when the machine is built with oil lubrication systems, it would be an economical practice to inspect the carried debris particles for their shapes and sizes [4]. Techniques that can be employed include spectroscopic oil-analysis, magnetic plug and filter inspection, and ferrography [5]. In most practical cases, machine parts are traditionally made up of metals for higher strength. Many of these materials are

n

Corresponding author. E-mail address: [email protected] (T. Wu).

http://dx.doi.org/10.1016/j.wear.2014.04.014 0043-1648/& 2014 Elsevier B.V. All rights reserved.

magnetizable and this character is advantageously made use of in ferrography [6]. It is a technique that enables the precipitation of tiny magnetic particles in liquids such as lubrication oil. By this way of capturing and analyzing debris particle morphologies, machine conditions due to wear can be inferred. When compared to methods such as trace, spectrum and filter [7], the ferrograph method is able to differentiate and recognize the sizes of particles by means of image processing techniques. Consequently, the use of quantitative image analysis in wear debris inspection has emerged a class of techniques for studying particle morphologies [8]. For example, computer based image analysis had been used to obtain and characterize particle boundaries [9]. It was reported in [10] that analytical ferrography is very useful in machine condition monitoring. Attempts had been made to classify imaged wear particles using soft computing methods including the neural network [11], ant-colony [12] and fuzzy c-means algorithm [13]. On the other hand, in previous applications of ferrography, most image based analyses were conventionally conducted with off-line processes using a still image. However, it is practically demanding that wear condition can be obtained on-line in order to provide a rapid and continuous indication of the machine condition [14]. By adopting the on-line philosophy [15], ferrograph can provide descriptions of wear particle characteristics based on their color statistics. In the image based analysis of wear debris, a fundamental requirement is to separate individual particles appearing in the captured image. In particular, particles carried in the lubrication oil tend to form into agglomerated chains and this makes separation a

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difficult task. The separation or segmentation problem is equivalent to that encountered in isolating grain kernels [16], where binarization on the image was made before segmentation. In addition, it is still a challenging task with regard to aggregated particle disassociation in the image. One of the powerful imaged object segmentation methods, the watershed algorithm [17], was employed to solve this problem [18]. However, in this work, boundary information extracted from a transmitted image is limited to obtaining satisfied separation accuracy. The watershed algorithm is known for its generality to segment a wide class of objects from their texture and color [19]. On the other hand, improvements on the separation accuracy could be made by using marker controls [20]. It was reported in [21] that imaged bubble surfaces can be extracted from backgrounds with this method. Based on previous work [18], in order to provide a more reliable particle segmentation result for on-line wear debris analysis, a comprehensive method in cooperating both grayscale and boundary features should be available. In this research, an advanced ferrography approach is developed encompassing wear particle image acquisition, intensity based pre-processing [22], a marker controlled and recursive scaled watershed segmentation. Wear particles flowing in lubrication oils are imaged using transmitted and reflected lights. Their intensities are used in identifying particles in chains carried by the lubricant. Isolation of individual particles is carried out by the marker controlled watershed algorithm. A further accuracy improvement stage is included with recursive and different morphological scales. The reliability of the proposed method is verified by fitting the result statistics with the Weibull distribution as the reference for comparison [23,24]. The rest of this paper is organized as follows. In Section 2, treatments of the transmitted and reflected images are described. Then follows the description of the generation of internal and external markers. The use of these markers in the watershed algorithm is illustrated. The segmentation based on particle boundaries and the integrated segmentation stage will be demonstrated.

Image preprocessing

Reflecting image

Gray image

Section 3 presents the experimental results together with a discussion. A conclusion is drawn in Section 5.

2. Method A method for the segmentation of on-line imaged wear particles flowing in lubrication oils is developed. The approach makes use of images captured from both transmitted and reflected illuminations on the oil passage. Wear particles held in positions by the magnetizing forces were imaged. The transmitted image was first binarized and edges were extracted to indicate particles to be isolated. The reflecting image at its gray levels was processed by an improved watershed algorithm. The improvement in segmentation accuracy was made by using a marker controlled watershed process. The combined intermediate results were further fed to a multi-scale corrosion and conditional expansion algorithm to produce the final output. A conceptual diagram illustrating the proposed method is shown in Fig. 1 and detailed descriptions are given in the sequel. 2.1. Imaged wear debris particles The images captured from the on-line ferrograph system, equipped in a mine scraper gearbox lubrication path, include a reflected and a transmitted image [18], see Fig. 2. It can be seen from the on-line images that most wear debris gather in chains and clusters. Furthermore, the reflected image shown in Fig. 2 (b) has gray scales and contour information but is influenced by bubbles in the oil flow. The transmitted image in Fig. 2(c) provides most of the wear debris chain contours. The gray scales and contour information are complementary to each other, hence, this advantage can be utilized to aid in improving the particle segmentation performance. Before proceeding, two particularities for on-line monitoring need to be highlighted. First, on-line images are often vague

Transmitting image

Boundary-based segmentation

Binary image

Final outcomes Wear debris chain extraction

Gray-based coarse segmentation

Marking internal in gray

Dividing lines

Watershed transformation Superposition

MSCCE algorithm Termination criterion

Obtaining external mark

Watershed transformation

Dividing lines

Fig. 1. Proposed method for on-line imaged wear debris particle segmentation.

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On-line monitoring sensor

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Fig. 2. On-line wear particles imaged from a gearbox lubrication path. (a) Mine scraper gearbox equipped with an on-line wear debris imaging sensor suite. (b) Reflected image. (c) Transmitted image [18].

because of the presence of oil, and the image quality gets worse with the aging of the oil. This makes it difficult to distinguish wear debris from their background. Second, most debris, produced by similar wear mechanisms and from similar parts, often appear in similar gray levels in the image, making it difficult to separate and identify particles from each other. The above observation implies the fact that on-line gray features of wear debris are unavoidably weak and vague as compared with those images obtained from off-line procedures. This problem will be tackled by a preliminary segmentation procedure described below.

2.2. Preliminary segmentation by gray-based watershed method Being sensitive to detailed feature identification, the watershed transformation algorithm would be an attractive solution to the current issue [19,21,25]. This method, motivated by observing flooded terrains, uses pixel gray scale to construct terrains of which the ridgelines can be extracted. The mathematical principle of watershed transformation can be found in [17], and is conceptually illustrated in Fig. 3. The figure illustrates two kinds of transforms employed. First, distance-based transform, Fig. 3(a), was conducted for a binary image focusing on contour information, a pre-transformation was performed to convert the binary into a gray-like form by using the distance of each pixel to the boundary, and then the terrains can be obtained by considering the distance value as depth, Fig. 3(b). The gray level form is illustrated in Fig. 3(c). It uses higher pixel gray values to represent deeper “water-pockets”, and thus produces the overall terrains to be “flooded” according to the pixels gray values. The altitude of each pixel is calculated and

normalized as aðx; yÞ ¼ 1 gðx; yÞ=255;

ð1Þ

where aðx; yÞ is the inverted and normalized image pixel magnitude gðx; yÞ at coordinate (x,y). Subsequently, with the obtained topographical image as shown in Fig. 3(d), the connecting boundaries of these “water-pockets” can be extracted as dividing lines. It is observed that six debris chains together with the background were transformed into isolated water-pockets and these pixels at the bottom were regarded as local minima. Therefore, directly applying watershed transformation to the initial gray image would introduce large errors in particle identification. In general, the pixel gray value varies continuously within the scope of a particle; however, some abrupt changes always occur on its boundary and the gradient on the boundary can be used to differentiate debris from each other and from the background. Therefore, the gradient feature of the initial image was used to enhance the boundary features. A gradient vector of a pixel at image coordinate (x,y) can be calculated as ∇gðx; yÞ ¼ ½Gx Gy T ¼ ½∂gðx; yÞ=∂x ∂gðx; yÞ=∂yT ;

ð2Þ

T

where ½ is the matrix transpose. The amplitude of the vector can be obtained with the simplifying equation J ∇gðx; yÞ J  jGx j þjGy j:

ð3Þ

Moreover, the direction of the maximum amplitude variation is

θðx; yÞ ¼ tan  1 ðGx =Gy Þ:

ð4Þ

Accordingly, the essence of a gradient transformation is to find suitable values of Gx and Gy. For a digital image, a gradient transformation is often obtained by using a template [26]. A 3  3

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Fig. 3. Two watershed transformations of an on-line particle image. (a) Distance-based transformation. (b) Topography illustration of distance-based transformation result. (c) Gray scale form of target image. (d) Topography illustration of gray scale image.

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Fig. 4. Demonstration of gray-based watershed transformation of a wear debris chain image. (a) Original color wear debris image. (b) Gray level image. (c) Gradient image. (d) Watershed based segmentation result. (e) Smoothed image by merging pixels with close gray levels. (f) Final segmentation result.

square “Sobel” template, in this case, was applied in both the vertical and horizontal directions. Pixel gradients having large values at the boundary of wear particles can facilitate identifying the outlines of each particle. However, local minima of the initial gray scale image remain the root cause of over-segmentations. Therefore, a morphological opening and closing operation was included to eliminate those minima as noise spikes and counteracted the noise sensitivity of the watershed method. A particular demonstration is provided for depicting the above process illustrated in Fig. 4, where the reflected image shown in Fig. 2 (b) was used. One chain was selected from the image in Fig. 4(a) as an example. The original color image was firstly transformed into grayscale form, in which the background was eliminated as shown in Fig. 4(b). A gradient transformation was conducted and the resultant gradient image is shown in Fig. 4(c). Furthermore, watershed transformation was performed on the gradient image. As seen in Fig. 4(d), severe over-segmentation appears when superposing the intricate dividing lines onto the initial image. Therefore, a smoothing filtering process with morphological openclose operation was applied to the gradient image and the result is depicted in Fig. 4(e). It can be seen that, with watershed transformation, the over-segmentation problem was partially mitigated, see Fig. 4(f).

2.2.1. Marking wear debris as internal markers In order to solve the over-segmentation problem, a markercontrolled watershed method was employed to introduce a priori identification of wear debris from their backgrounds before conducting particles separation [12,22]. The essence of this process is to find internal and external markers to denote, respectively, the particle and the background. An improved maker-watershed process is proposed for gray level segmentation and is illustrated as below with the example image in Fig. 4(b). In an on-line wear debris image, wear particle areas are of interest and those particles are marked as internal. The background area is marked as the external one. The internal pixels have lower gray levels in the image, and thus they are used to create the inner markers by merging those minimum pixels in accordance to ^ yÞ ¼ maxfgðx; yÞ; τg; gðx;

ð5Þ

^ yÞ is the transformed pixel and τ is a threshold. where gðx; Generally, a fixed value is preferable because the sampling happens under a fixed light condition in a sensor. Furthermore, for the preliminary segmentation, over-segmentation is intolerable due to incomplete information and some integers from 40 to 60 were tested but no obvious differences in their segmentation accuracy were found. Therefore, a relatively large threshold value τ ¼50 was adopted empirically where the gray levels were in [0, 255].

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Fig. 5. Watershed segmentation by using the marker-controlled method. (a) Initial gray level image. (b) Minima in the initial gray image. (c) Internal marker identification. (d) Dividing lines as internal markers. (e) Gradient image superimposed with internal and external markers. (f) Improved gradient image by eliminating minimums. (g) Watershed transformation result. (h) Image superimposed with the identified markers.

Results of the above process are illustrated in Fig. 5. With an initial gray image, Fig. 5(a), the pixels of the local minima were highlighted as shown in Fig. 5(b). By applying merging to the initial gray image, local pixels around those minima were merged, and thus some image patches were identified and filled with black as seen in Fig. 5(c). These regions were denoted as the internal markers of wear debris and were assigned with the same gray value as the pixels inside them. It should be noted that these internal markers only denote an estimation of wear debris pixel locations. 2.2.2. Marking the external marker Contrary to the internal markers, the corresponding external marker must fall in the background region. The dividing lines among those identified internal marker areas are here regarded as part of the background, and therefore can be hypothesized as external markers. Ideally, internal and external markers would be located in different areas without any overlap, and thus can be separated using the watershed transformation. To do this, pixel patches marked with internal markers were transformed into their binary form to eliminate the influences from intensity variations. Then, a distance transformation was performed on the processed internal patches and followed by a watershed transformation to obtain their dividing lines. The outcome is shown in Fig. 5(d). The dividing lines of wear debris regions were found in the background and were regarded as external markers. 2.2.3. Applying final segmentation Identified internal and external markers were superimposed onto the initial gradient image to separate wear debris, as seen in Fig. 5(e). The regions overlapped with the internal markers were recognized as wear debris and thus the corresponding pixels were assigned with the minimum value of the global gray range, and the

remaining pixels were updated by increasing their gray values by one-tenth of the global gray level range [8]. Consequently, the marked regions were distinctively enhanced. The resultant image is shown in Fig. 5(f). A watershed transformation was applied to the updated gradient image and the dividing lines were extracted as shown in Fig. 5(g). By superimposing these division lines onto the target image, the result was obtained as shown in Fig. 5(h). Each initial marker represents a specific watershed region, thus the number of markers was made equal to the final number of watershed regions. As shown in the segmentation results, the debris chain was divided into two parts. These are the object areas marked by numbers 1, 3 and 5, and “background” area marked by numbers 2 and 4. It should be noted that the mentioned background area is not the background of the debris chain, but the area marked as “background” which is distinctive from object areas 1, 3, and 5. 2.3. Segmentation based on boundary-based morphology A morphological method for boundary identification, namely, corrosion and expansion, is an efficient and accurate method for particle separation approach. Corrosion means to eliminate the outer pixels of wear debris by layers with a specific structural element for identifying the eliminated layer of pixels. The size of the matrix structural element determines the amount of pixels to be corroded for each corrosion cycle, and in the current case, an element in 3  3 pixels had been adopted. The total corrosion cycles to complete one separation was defined as the corrosion scale, which decides not only the remaining area but also the corrosion rate. Accordingly, by constantly eroding the area of wear debris chains in on-line images, the aggregated areas were continually reduced in size until they were eventually separated. The condition for termination was specified in advance to retain separated areas from being eroded till they vanished. The area processed by

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Fig. 6. MSCCE segmentation results. (a) Original chain. (b) 1st scale erosion. (c) 1st scale expansion. (d) 1st scale segmentation line. (e) 2nd scale erosion. (f) 2nd scale expansion. (g) 2nd scale segmentation line. (h) 3rd scale erosion. (i) 3rd scale expansion. (j) 3rd scale segmentation line. (k) 4th scale erosion. (l) 4th scale expansion. (m) 4th scale segmentation line. (n) 5th scale erosion. (o) segmentation result. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

corrosion was defined as the core of the separated area. The core was also marked as the centers of potential wear debris, and the amount of overall cores denotes the number of the separated wear debris. Eroding an area to a core with a size similar to that of the structural element is defined as ultimate corrosion. Furthermore, conditional expansion means to obtain complete boundaries of wear debris by expanding the areas from the cores with two predefined conditions as follows: (a) not exceeding the boundaries of the initial wear debris chains and (b) not overlapping and touching separated areas. Contacting lines produced by expansion form dividing lines for individual particles. Specifically, dimensional diversity of aggregating particles is one of the protruding features of on-line imaged wear debris particles. According to a recent study [18], ultimate corrosion would result in vanishing of small debris and consequently introduce an error in particle counting. Therefore, a multi-scale corrosion and conditional expansion (MSCCE) method was developed in Ref. [18] to adaptively separate particles in different sizes. A specific demonstration in Fig. 6 illustrates the boundary segmentation process using the MSCCE method. To facilitate comparison, the same debris chain images as those used in gray-based separation were adopted. It is shown that a debris image (in binary form) containing one chain is the object for undertaking a MSCCE segmentation, as given in Fig. 6(a). The original areas were corroded with the first scale and the resultant cores due to corrosion can be found in Fig. 6(b). Then conditional expansion was followed to obtain new dividing lines. The images after expanding and the new dividing line are shown in Fig. 6(c) and (d), respectively. After processing with the second corrosion scale, the resultant images of corrosion, expansion, and dividing lines are presented in Fig. 6(e), (f) and (g), respectively. More MSCCE segmentations had been consecutively

conducted before the termination criterion was fulfilled, as shown in Fig. 6(h)–(n). By superimposing all dividing lines onto the target image, the final segmentation was obtained as shown in Fig. 6(o). It can be observed from the result in Fig. 6(o) that some erroneous dividing lines (marked by red circles) were produced, which resulted in both extra areas and error splitting. The main cause of these errors is due to the high irregularity of the particle profiles, apparent dimension differences and the complexity of aggregation of wear debris. Therefore, the boundary information alone is not adequate to separate wear debris from their aggregations. 2.4. Integrated segmentation approach An integrated approach using both gray- and boundary-based methods developed in this work for wear debris particle chain segmentation is summarized and its performance illustrated. First, both initial reflected and transmitted images are pre-processed into gray and binary images, respectively. Second, the gray level image is adopted for gray-based segmentation, where wear debris chain instead of the whole image is considered. Control markers including internal and external ones are marked on the target chain image, and by superimposing these two kinds of control tags onto the target binary image, dividing lines for gray-based separation are generated. Third, with the superimposed binary image with the above dividing lines, boundary-based segmentation is carried out. Results can be achieved by superimposing these newly produced dividing lines onto the initial images. The imaged wear debris chain in Fig. 6(a) was used to illustrate the overall integrated approach. The results are shown in Fig. 7. As seen in Fig. 7(b), the resultant image processed by the graybased segmentation contained several separated areas in the chain. Then, these separated areas were corroded with the first

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Fig. 7. Integrated segmentation. (a) Original chain in binary form. (b) Gray-based segmentation result in binary form. (c) 1st scale erosion. (d) 1st scale expansion. (e) 1st scale segmentation line. (f) 2nd scale erosion. (g) 2nd scale expansion. (h) 2nd scale segmentation line. (i) Segmentation result. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

scale until resultant cores emerged as seen in Fig. 7(c), which was collectively marked by a red circle. Condition expansions from these cores were conducted to obtain new dividing lines, as shown in Fig. 7(d). The dividing lines after expansion processes are given in Fig. 7(e). It is seen from Fig. 7(d) that two regions specially filled with neighboring gray levels were separated. Likewise, the images of corroded cores, expanded regions, and the resultant dividing lines after processing with the second corrosion scale are presented in Fig. 7(f), (g) and (h), respectively. In addition, red circles are placed in the image to highlight the newly separated cores. By superimposing the dividing lines obtained from the two processes onto the target image, the final segmentation was achieved and is shown in Fig. 7(i).

methods are shown in Fig. 9(a)–(c), respectively. The outcomes of the above methods are assessed visually. Generally, it can be seen that the integrated method improves the accuracy significantly by compensating for the incomplete and over segmentation problems of the individual methods. However, the integrated method still inherits intrinsic shortcomings from the previous morphological method. An example of such limitations is an error dividing line marked as “E” in Fig. 9(c). On the other hand, for on-line monitoring purposes, a relatively higher tolerance for error identification is allowable. This is because a large amount of samples can be obtained in a short time period. Besides, due to the resolution of the sensor, the method will lose its accuracy when particles are smaller than 50 μm or in severe overlapping. For this reason, the developed system has been used for gearbox monitoring.

3. Results and discussion 3.1. Segmentation results 4. Evaluation of segmentation performance A practical application of the integrated segmentation was conducted on the images as shown in Fig. 2. The whole process is illustrated in Fig. 8. The gray level image in Fig. 8(b) was obtained from initial reflected image in Fig. 8(a). Fig. 8(c) shows the outcome of the gray-based separation, from which each debris chain was extracted by the dividing lines as shown in Fig. 8(d). After that, a boundary-based segmentation was applied to segment the individual chains of the transmitted image in Fig. 8(e). The binary form of the transmitted image was superimposed with the dividing lines from the gray-based segmentation, as shown in Fig. 8(f). With the MSCCE process, wear debris with different sizes were separated iteratively as shown in Fig. 8(g), together with the dividing lines shown in Fig. 8(h). Finally, the outcome of the proposed segmentation method was obtained as shown in Fig. 8(i). 3.2. Discussion To examine the effectiveness of the proposed wear particle segmentation method, the results obtained by the integrated method were compared with two intermediate processing results using the gray-based method and the previously developed boundary-based method [18]. Fig. 9 shows the results of the same initial image using the different segmentation methods. The results of the gray-based and boundary-based and the integrated

4.1. Evaluation of the integrated method by hypothesis testing The analysis on the segmentation effects of the integrated method was made on the basis of subjective observations as suggested by conventional ferrography. A further verification is necessary for on-line applications. Generally, there are two choices for the current issue under consideration. One is to compare with other standard measurements, and the other is through hypothesis testing with previously developed or widely acceptable mathematical models. The problem with the former is that different criteria and data ranges are concerned with different instruments, such as a spectrometer or a particle counter. It is not feasible or meaningful to make a comparison among these different measuring principles. Therefore, hypothesis testing is adopted in this work as a solution. It is regarded that wear condition is highly correlated with the sizes of wear particles and a large amount of research works had reported findings on possible distributions of wear debris sizes. Some fundamental probability models were proposed with a large quantity of debris samples [5]. On this basis, an improved model of Weibull function [27] is better known for its use in the analysis of fatigue wear. A later study in [7] revealed that a two-parameter Weibull function is more suitable for wear debris separation evaluation.

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Fig. 8. Demonstration of full-integrated separation procedures with on-line images. (a) Initial reflected image. (b) Gray level image. (c) Gray-based separation result. (d) Preliminary dividing lines. (e) Initial transmitted image [18]. (f) Binary image superimposed with preliminary dividing lines. (g) Morphological segmentation results. (h) Complementary dividing lines. (i) Final separation result.

A two-parameter Weibull function can be given as PðdÞ ¼ 1  expð  ððd  δÞ=BÞ Þ; A

ð6Þ

where d is the particle diameter indicator, P(d) is the probability of

finding a particle smaller than d, A and B are parameters adjusting the distribution, and δ is the lower range limit. Various diameter indices are used for characterizing an irregular particle. The equivalent circle dimension (ECD) that is

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E

A’

A

C’

C

B’

B

D

D’

Fig. 9. Comparison of segmentation method with and without integration. (a) Gray-based method. (b) Boundary-based method. (c) Integrated method.

Fig. 10. The distributions of the ECD values and the corresponding Weibull fitting curves from the segmentation results using (a) the binary segmentation and (b) the integrated segmentation approach.

popularly adopted in most existing measurements is selected as a diameter indicator in our test case. With the above premise, the hypothesis is as follows:

employed to find the joint distribution of all samples. It takes the form as follows: N

H0: the ECD calculated from the separated wear debris follows the two-parameter Weibull distribution in Eq. (6). H1: the ECD calculated from the separated wear debris does not follow the two-parameter Weibull distribution. To conduct the hypothesis test, a two-step procedure is followed for parameter estimation and the setup of the decision criterion.

LðA; BÞ ¼ Mðd1 ; d2 ; …; dN Þ ¼ N! ∏ f ðdi Þ;

ð7Þ

i¼1

where LðA; BÞ is the maximum likelihood function, N denotes the amount of samples, Mðd1 ; d2 ; …; dN Þ is the joint probability distribution of samples d1 ; d2 ; …; dN , and f ðdi Þ is the probability density of PðdÞ in Eq. (6). The maximum likelihood of this function can be obtained with the derivation of the two target variable parameters. In the current ^ BÞ ^ study, the estimated representative of ðA; BÞ is denoted by ðA; and can be calculated from

4.1.1. Parameter estimation In Eq. (6) two unknown parameters, A and B, need to be estimated from the sample data. An approach by regression estimates was reported in determining these two parameters [24]. However, this method is vulnerable to a large error when initial sample data has large deviations. For an unbiased estimation of these parameters, the maximum likelihood function approach [23] was

∂ lnðLðA; BÞÞ=∂A ¼ 0;

∂ lnðLðA; BÞÞ=∂B ¼ 0;

ð8Þ

where " #1 N ^  1 ∑ lnðd  δÞ A^ ¼ hðAÞ ; i Ni¼1

ð9Þ

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" #1=A^ 1 N A^ ^ ∑ ðd  δÞ ; B¼ Ni¼1 i

4.2. Case studies ð10Þ

Category

Number of particles

The above hypothesis test was applied to examine the segmentation results generated using the proposed method. The equivalent circle diameter (ECD) was used as the target feature of isolated wear particles to be examined in this test. The samples of ECD extracted from the image in Fig. 9 were used as initial data. Two proposed methods including the individual boundary-based and the integrated separations were employed in making a comparison. In the results, 62 initial samples were obtained by using the boundary segmentation and 89 samples obtained by using the integrated segmentation method. The distributions of these two results are shown in Fig. 10. With the above initial data, the following procedures were conducted to test the above hypothesis. First, we estimated the parameter of the Weibull function by the maximum likelihood. ^ BÞ, ^ were calcuUsing Eqs. (8)–(11), the estimated parameters, ðA; lated and the results were ð1:73; 67:18Þ for the data from Fig. 9(a) and ð1:77; 57:26Þ for the data from Fig. 9(b). With the obtained parameters, the Weibull fitting curves were superimposed to illustrate the distribution of initial data as seen in Fig. 10. In practice, the distribution of particle is often divided into diameter sections; therefore, the initial individual data was categorized following some empirical rules. Considering a typical application of gearbox, a suggested category for wear particle characterization was adopted here [8]. As seen in Table 1, four dimension sections (0–10, 10–40, 40–100 and 4 100 μm) and corresponding four wear stages (i.e., normal wear, abnormal initiation, severe wear and faults) were defined. Test statistics were calculated for each dimension section using the obtained Weibull distribution function. The results of the morphological and the integrated methods are shown in Fig. 11. It is observed that the probability of the categorized data was close to that of the corresponding Weibull distribution of the initial data, which indicates that the results of the segmentation methods closely follow the Weibull distribution. To examine the fitting of the categorized data to the Weibull distribution, the fitness indicators, KN1 and KN2, were calculated using Eq. (12) (see [24]), and they are

Wear stages

Data from Fig. 10(a)

Data from Fig. 10(b)

K N1 ¼ ∑

Normal wear Abnormal initiation Severe wear Faults

1 19 31 11

2 34 46 7

and

and ^ ¼ hðAÞ

^

A ∑N i ¼ 1 ðdi  δÞ lnðdi  δÞ ^

1=A ∑N i ¼ 1 ðdi  δÞ

;

ð11Þ

where di is the obtained sample value. With a series of sample data, a function with two unknown parameters can be established using Eq. (7). By using Eqs. (9)–(11), the two unknown parameters, ^ BÞ, ^ can be calculated. Thus, the maximum likelihood function ðA; can be established for characterizing the particle distribution. 4.1.2. Decision criterion The decision criterion is formulated according to the Pearson principle [23]. Specifically, a series of sample data, denoted by di, is grouped into several sections, denoted as S1 ; S2 ; …; Sr . The overall probability is pi ¼ P F fdi A Si g, where i ¼ 1; …; r and the sample probability mi denotes the frequency of the sample di falling into the i-th section Si. A fitness indicator is employed as follows: 2 r ðm  Np Þ2 N mi i i pi ¼ ∑ Npi i ¼ 1 pi N i¼1 r

KN ¼ ∑

ð12Þ

In Eq. (12), KN denotes the fitness of N samples to a specific distribution function as K N  χ 2 ðr  k  1Þ and N-1. Furthermore, k is the number of unknown parameters in the function, and r is the number of groups that the samples are divided into. Finally, the decision criterion for hypothesis can be made as follows: Case 1: If K N o χ 2 ðr  k  1Þ, accept H0. Case 2: If K N 4 χ 2 ðr  k  1Þ, accept H1. Table 1 Category for gearbox and the corresponding grouping results for the preliminary data. Dimension sections (μm)

0–10 10–40 40–100 100–1

m2i N ¼ 1:72; i ¼ 1 Npi

N ¼ 62; r ¼ 4

ð13Þ

m2i N ¼ 1:66; Np i i¼1

N ¼ 89; r ¼ 4:

ð14Þ

r

r

K N2 ¼ ∑

Fig. 11. Comparison of the frequencies between estimated Weibull distribution and current obtained segmentation result. (a) The result of the binary segmentation. (b) The result of the integrated segmentation method.

T. Wu et al. / Wear 316 (2014) 19–29

With a significance level of 0.05, a comparison between the calculated and the standard fitness was obtained as χ 20:05 ð1Þ ¼ 3:841, and thus K N2 o K N1 o χ 20:05 ð1Þ. Therefore, the final decision about the hypothesis was made: H0 was not rejected indicating that the dimension of the separated wear debris satisfied the Weibull distribution. Moreover, the comparison between the fitness indicators of the two proposed segmentation methods had demonstrated that the integrated method has a higher accuracy.

5. Conclusion An imaged wear debris particle separation method had been proposed to improve the applicability of ferrography to on-line machine condition inference. Wear particles flowing through the machine lubrication return path were imaged from transmitted and reflected lights. A primary separation of particles was made based on their intensities and boundaries using the watershed algorithm. A secondary process using the multi-scale morphological corrosion and expansion operations was then undertaken to further segment the particle images and improved the separation accuracy. Comparisons to morphology only methods were carried out and the proposed integrated approach indicated an improved particle image extraction performance. Furthermore, particle features determined by the developed method were shown to follow closely the Weibull distribution.

Acknowledgments The financial support of the present research was provided by the National Science Foundation of China (Grant no. 51275381) and the Science and Technology Planning Project of Shaanxi Province, China (Grant no. 2012GY2-37). Special thanks for the financial support from the China Scholarship Council (Grant no. 201206285002) during the term of this project. The authors would also like to acknowledge all members of the Tribology research group in The University of New South Wales (UNSW Australia) for very helpful discussions. References [1] A.K. Jardine, D. Lin, D. Banjevic, A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mech. Syst. Signal Process. 20 (7) (2006) 1483–1510. [2] S. Raadnui, Wear particle analysis utilization of quantitative computer image analysis: a review, Tribol. Int. 38 (10) (2005) 871–878.

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