PREDICTING RAILROAD BALLAST FOULING CONDITIONS BASED ON BALLAST IMAGE

Abstract

Evaluating railway ballast fouling condition is critical to assessing track conditions and arranging proper ballast maintenance. Because fouled ballast materials with different fouling conditions have different material properties, these properties can be used to evaluate the fouling severity. Various previously developed approaches to estimating fouling conditions often require special sensors or equipment, and well-trained technicians. Recently, convolutional neural network (CNN) based computer vision approaches have performed particle segmentation to obtain ballast grain size distribution. While the coarse aggregate fraction can be evaluated, many such approaches do not segment fine particles. This disclosure is an image analysis approach to directly estimate the ballast fouling conditions. First, fouled ballast images with different fouling conditions are taken as the reference. Then, the RGB color distributions of the fouled ballast images are processed through statistical analysis. A strong linear correlation between Fouling Index (FI) and Variance is found and used to establish an FI prediction model which has been tested and validated by additional fouled ballast samples.

Claims

1. A method for evaluating railway ballast fouling conditions for assessing track conditions for determining proper ballast maintenance, the method comprising: training a machine-learned computer vision-based convolutional neural network (CNN) model to directly estimate ballast fouling conditions using an image analysis approach based on overall image characteristics; obtaining an overall image associated with a target section of railway ballast to be evaluated; inputting the overall image associated with the target section of railway ballast into the machine-learned computer vision-based convolutional neural network (CNN) model; and receiving, as output of the CNN model, estimation of the ballast fouling conditions of the target section of railway ballast.

2. The method according to claim 1, wherein the image analysis approach comprises evaluating fine particles in the overall image of the target section of railway ballast.

3. The method according to claim 2, wherein fine particles comprise particles finer than 1 mm.

4. The method according to claim 1, wherein the overall image associated with the target section of railway ballast comprises the combination of ballast particles, fines, and voids therebetween.

5. The method according to claim 4, wherein the image analysis approach comprises focusing on all the pixels of the entire overall image.

6. The method according to claim 4, wherein the image analysis approach comprises quantifying the overall image appearance based on the frequency distributions of a plurality of color channels.

7. The method according to claim 6, wherein the plurality of color channels comprise red, green, and blue, respectively.

8. The method according to claim 1, wherein the training comprises: taking as reference fouled ballast images with different fouling conditions; processing red/green/blue (RGB) color distributions of the reference fouled ballast images through statistical analysis; and determining strong linear correlation between a Fouling Index (FI) and Variance of the statistical analysis to establish an FI prediction model.

9. The method according to claim 8, wherein Variance .sup.2 of the statistical analysis of a planar sample of a target section of railway ballast comprises ${}^2=\frac{1}{N}\underset{i=1}{\overset{N}{.Math.}}{\left(x_i-\right)}^2$ where N=(image count)width of sampleheight of sample.

10. The method according to claim 1, wherein training the machine-learned computer vision-based convolutional neural network (CNN) model to directly estimate ballast fouling conditions is established based on the correlation between fouling severity and Variance of a statistical analysis of a planar sample of a target section of railway ballast.

11. A system for evaluating railway ballast fouling conditions for assessing track conditions for determining proper ballast maintenance, comprising: a machine-learned computer vision-based convolutional neural network (CNN) model trained to directly estimate ballast fouling conditions using an image analysis approach based on overall image characteristics; one or more processors; and one or more non-transitory computer-readable media that store instructions that, when executed by the one or more processors, cause the one or more processors to perform operations, the operations comprising: obtaining an overall image associated with a target section of railway ballast to be evaluated; inputting the overall image associated with the target section of railway ballast into the machine-learned computer vision-based convolutional neural network (CNN) model; and receiving, as output of the CNN model, estimation of the ballast fouling conditions of the target section of railway ballast.

12. The system according to claim 11, wherein the operations further comprise evaluating fine particles in the overall image of the target section of railway ballast.

13. The system according to claim 12, wherein fine particles comprise particles finer than 1 mm.

14. The system according to claim 11, wherein the overall image associated with the target section of railway ballast comprises the combination of ballast particles, fines, and voids therebetween.

15. The system according to claim 14, wherein the operations further comprise focusing on all the pixels of the entire overall image.

16. The system according to claim 14, wherein the operations further comprise quantifying the overall image appearance based on the frequency distributions of a plurality of color channels.

17. The system according to claim 16, wherein the plurality of color channels comprise red, green, and blue, respectively.

18. The system according to claim 11, wherein training the machine-learned computer vision-based convolutional neural network (CNN) model comprises: taking as reference fouled ballast images with different fouling conditions; processing red/green/blue (RGB) color distributions of the reference fouled ballast images through statistical analysis; and determining strong linear correlation between a Fouling Index (FI) and Variance of the statistical analysis to establish an FI prediction model.

19. The system according to claim 18, wherein Variance .sup.2 of the statistical analysis of a planar sample of a target section of railway ballast comprises ${}^2=\frac{1}{N}\underset{i=1}{\overset{N}{.Math.}}{\left(x_i-\right)}^2$ where N=(image count)width of sampleheight of sample.

20. The system according to claim 11, wherein training the machine-learned computer vision-based convolutional neural network (CNN) model to directly estimate ballast fouling conditions is established based on the correlation between fouling severity and Variance of a statistical analysis of a planar sample of a target section of railway ballast.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0025] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0026] A full and enabling disclosure of the presently disclosed subject matter, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended Figures, in which:

[0027] FIG. 1 is a graphical representation of the gradation of exemplary sample ballast materials as referenced in the presently disclosed subject matter;

[0028] FIGS. 2(a) through 2(f) illustrate six respective images of six different fouled ballast samples having different FI values used in accordance with the disclosure herewith;

[0029] FIG. 3(a) is an image of a presently disclosed test setup for image analysis;

[0030] FIG. 3(b) is a raw image example for a box test, and illustrating exemplary test box dimensions in accordance with presently disclosed subject matter;

[0031] FIG. 4 is a diagrammatical flowchart of the presently disclosed image analysis methodology;

[0032] FIGS. 5(a) through 5(c) respectively graphically illustrate cumulative relative frequency distributions of reference boards, regarding respective different color channels, all related to the presently disclosed subject matter;

[0033] FIGS. 6(a) through 6(f) represent images showing all the extracted sample images, representing extracted box images under different fouling conditions;

[0034] FIGS. 7(a) through 7(c) respectively graphically display all twenty-four cumulative relative-to-frequency curves generated from different fouling conditions (FIGS. 6(a) through 6(f)) for three different color channels;

[0035] FIGS. 8(a) through 8(c) respectively graphically illustrate cumulative probability distributions under different fouling conditions of different color channels;

[0036] FIGS. 9(a) through 9(e) graphically represented calculated statistical quantities following the definitions in Equations (1) through (5) as stated herein, respecting FI for three color channels;

[0037] FIGS. 10(a) through 10(c) respectively graphically illustrate cumulative probability distributions with validation fouling conditions of different color channels; and

[0038] FIG. 11 graphically represents Variance values of two validation fouling conditions when calculated and plotted.

[0039] Repeat use of reference characters in the present specification and drawings is intended to represent the same or analogous features or elements or steps of the presently disclosed subject matter.

DETAILED DESCRIPTION OF THE PRESENTLY DISCLOSED SUBJECT MATTER

[0040] It is to be understood by one of ordinary skill in the art that the present disclosure is a description of exemplary embodiments only, and is not intended as limiting the broader aspects of the disclosed subject matter. Each example is provided by way of explanation of the presently disclosed subject matter, not limitation of the presently disclosed subject matter. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the presently disclosed subject matter without departing from the scope or spirit of the presently disclosed subject matter. For instance, features illustrated or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the presently disclosed subject matter covers such modifications and variations as come within the scope of the appended claims and their equivalents.

[0041] The present disclosure is generally directed to image processing methodology to predict the Fouling Index (FI) of the fouled ballast based on the overall image characteristics instead of individual particles.

Ballast Image Acquisition

[0042] Ballast Material

[0043] The ballast material used as discussed herein was provided by MV Rail (formerly Transportation Technology Center, Inc.) from the Rainy Section test track at TTC. According to the Fouling Index (FI) definition, those particles smaller than No. 4 sieve can be considered fine particles. The fine particles of the Rainy Section material are mostly non-plastic materials from ballast aggregate degradation and a small portion of subgrade materials, and the specific gravity is 2.75. A clean ballast gradation, which meets AREMA No. 4 gradation requirements, is given in FIG. 1, and this clean ballast gradation is the same as the coarse aggregate fraction of all the fouled ballast shown in FIG. 1. The only difference between the different ballast samples is the content of the fine particles (particles passing No. 4 sieve). FIG. 1 is a graphical representation of the gradation of sample Rainy Section ballast materials.

[0044] FIGS. 2(a) through 2(f) illustrate six respective images of six different fouled ballast samples having different FI values used in accordance with the disclosure herewith. All the samples have identical large particles. The only difference between the samples is the additional amount of fines added to achieve different FI values. Of the six ballast samples prepared, one is completely clean and five are fouled samples (and collectively correspond with the six samples indicated per FIG. 1). Among the fouled samples, FI 13, FI 23, and FI 33 were used to explore potential correlations between FI and image parameters. The samples with FI 18 and FI 28 are reserved for testing and validation of possible correlations identified based on other samples. A star symbol (*) is used in FIG. 1 to indicate samples for validation only.

[0045] Test Setup

[0046] FIG. 3(a) is an image of a presently disclosed test setup for image analysis. FIG. 3(b) is a raw image example for a box test, and illustrating exemplary test box dimensions. After each of the six samples were prepared, the ballast material was transferred into an acrylic box (FIG. 3(a)), to take images. The size of the exemplary box was 26.7 cm (10.5 in.) in height, 30.5 cm (12 in.) in width, and 5.1 cm (2 in.) in depth, as shown in FIG. 3(b). All samples were lightly tamped with caution to the same volume to avoid scratching the acrylic glasses or damaging the box. Note the void ratio of the clean ballast was 1.0. The void ratios of other samples would decrease depending on FI.

[0047] While various digital imaging devices could be used, in this instance a smartphone was used to take images of the samples in the acrylic box and the reference boards together. For every fouling condition, the mixed materials shown in FIGS. 2(a)-2(f) were re-packed three times to prepare three samples with identical particles (both large particles and fines) but with different particle arrangements. For every sample in the box, one picture was taken from each side of the acrylic box. In other words, for every fouling condition, three samples were prepared; for each sample, two images were taken. In total, 24 images were collected for model development, and another 12 images were collected for model validation. Table 1 summarizes the image matrix.

TABLE-US-00001 TABLE 1 Ballast Sample and Image Matrix Type Model Validation Fouling Condition Clean/ FI FI FI FI FI FI 0 13 23 33 18* 28* Sample Count 3 3 3 3 3 3 Image Count 6 6 6 6 6 6

Ballast Image Analysis

[0048] FIG. 3(b) shows an example raw image taken by the camera. Each raw image from the camera is divided into four images, covering the Box, Reference Board 1 (RB1, red), Reference Board 2 (RB2, green), and Reference Board 3 (RB3, blue), respectively. The image size of the box is 25002800 pixels. The other three images of reference boards serve as the reference to ensure a consistent illumination condition.

[0049] FIG. 4 shows the image analysis procedures in this subject disclosure, mainly having two tasks. One is the RGB-based characterizing under different fouling conditions, and the other is the illumination consistency check from reference boards. Consistent illumination is critical for fair comparisons and exploring representative correlations. Thus, FIG. 4 is a diagrammatical flowchart of the presently disclosed image analysis methodology.

[0050] RGB values are obtained for each image of the ballast sample. For example, the box covers 2,5002,800 pixels. Each pixel has three values for each RGB channel, ranging from [0,1][0,1][0,1]. In other words, every box image has three data sets corresponding to the red, green, and blue channels, respectively. Each data set has 7106 data points. Every data point ranges from 0 to 1, representing the intensity of each color channel (red, green, or blue). Each data set is labeled with four parameters: 1) Fouling Index; 2) color channel; 3) sample number; and 4) image number. All in all, for model development, there are 4 (fouling conditions)3 (color channels)6(images)4(image content, sample or reference boards)=288 data sets. Each data set will be analyzed and grouped according to different categories.

[0051] By grouping the fouling condition and the color channel, data sets from different reference boards are checked to show the illumination consistency of the images. If the illumination is consistent, the data set from the sample box will be used to generate the cumulative relative frequency curves. These curves could show a certain pattern if there is a potential correlation between the fouling conditions and the images.

[0052] By grouping the fouling condition and the color channel, all six data sets of different samples having the same fouling condition can be merged into one data set {x.sub.i} with size N. The cumulative relative frequency should represent the cumulative probability and vary following a certain pattern if there is any correlation between the fouling conditions and the image RGB value distributions. Otherwise, the fouling conditions and the image RGB value distribution are not correlated. For every merged data set of a ballast mixture, five statistical parameters are calculated as the following: [0053] Mean, :

[00001]$\begin{array}{cc}=\frac{1}{N}\underset{i=1}{\overset{N}{.Math.}}{x}_i& \left(1\right)\end{array}$ [0054] Median, m:

[00002]$\begin{array}{cc}m=\mathrm{sort}\left(x_i\right)\text{?}& \left(2\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$ [0055] Variance, .sup.2:

[00003]$\begin{array}{cc}{}^2=\frac{1}{N}\underset{i=1}{\overset{N}{.Math.}}{\left(x_i-\right)}^2& \left(3\right)\end{array}$ [0056] Skewness, s:

[00004]$\begin{array}{cc}s=\frac{\frac{1}{N}\text{?}(x_i-\text{?}}{[\frac{1}{N}\text{?}{\left(x_i-\right)}^3\text{?}}& \left(4\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$ [0057] Kurtosis, k:

[00005]$\begin{array}{cc}k=\frac{\frac{1}{N}\text{?}{\left(x_i-\right)}^4}{{\left[\frac{1}{N}\text{?}{\left(x_i-\right)}^3\right]}^2}& \left(5\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$ [0058] where N=6(image count)2500 (width of sample)2800 (height of sample)=4.210.sup.7.

[0059] The foregoing five quantities quantify the probability distribution statistically. Mean, and Median indicate the location of every distribution. Variance measures how far the data spread away from Mean. Skewness is a measure of the asymmetry of the data set and is related to the difference between Mean and Median. Kurtosis shows the size of the tails of a distribution. The distribution of a higher peak value has larger tails. This disclosure investigates whether these statistical quantities reflect the change in fouling conditions and quantifies the fouling index statistically.

Results and Discussion

[0060] FIGS. 5(a) through 5(c) respectively graphically illustrate cumulative relative frequency distributions of reference boards, regarding respective different color channels. The content represented by FIGS. 5(a) through 5(c) relate to illumination consistency check. As illustrated, curves from different color channels are plotted with different line types. Note the FI in the legend indicates with which fouling condition it is associated. As a methodology, first, three reference boards are painted with different (respective) colors. From FIGS. 5(a) through (c), the color channel with the largest value indicates the strongest color intensity, which matches the paint color very well. Second, four curves with different fouling conditions for each color channel show a consistent distribution. There is no significant varying trend relating to FI. Therefore, FIGS. 5(a) through 5(c) confirm that the illumination condition for all the images is consistent regardless of which sample is put in the acrylic box. Thus, the illumination condition would not introduce significant variation in the sample images.

[0061] After confirming the consistent illumination condition, the sample images can be analyzed and fairly compared. FIGS. 6(a) through 6(f) represent images showing all the extracted sample images, representing extracted box images under different fouling conditions. For every big particle, its position and size can be distinguished by the color difference with those voids and particles adjacent to it. However, it is harder to distinguish individual particles once the particle size gets smaller. The challenge exists in not only particle segmentation but also the pixel values of the voids, and the fines may get closer with higher fine contents. This is exactly why particle segmentation-based approaches cannot work with fine particles. Moreover, particle segregation issues often handicap particle segmentation-based approaches as well.

[0062] Because gravity is inevitable, the fine particles tend to accumulate at the bottom, leaving fouling conditions not spatially consistent for lightly and moderately fouled samples. For example, although FI 13 and FI 18 samples are light to moderately fouled, the bottom is similar to FI 28 and FI 33 samples, but the top is close to the Clean sample. It is possible for particle segmentation-based approaches to only read the relatively clean top area but cannot output meaningful results for the relatively heavily fouled bottom area.

[0063] Different from particle segmentation-based approaches, this presently disclosed subject matter focuses on the entire image of each sample. From FIGS. 6(a) through 6(f), it is easy to observe that more voids are occupied by fines with samples having higher FI. The ratio between the clean area and fouled area could intuitively suggest the fouling condition, regardless of where the fines accumulate. Hence, particle segregation or the heterogenous distribution of the fines would not be an issue if the image analysis focuses on all the pixels of the entire image instead of big particles only.

[0064] RGB Value Distribution

[0065] By converting every image into RGB values, the cumulative relative frequency of each channel color can be calculated and plotted. FIGS. 7(a) through 7(c) respectively graphically display all twenty-four cumulative relative-to-frequency curves generated from different fouling conditions (FIGS. 6(a) through 6(f)) for three different color channels. Taking the Red channel as an example, such twenty-four curves in FIG. 7(a) show clear counterclockwise rotation with increased FI. For a large FI, the curves get slimmer, representing a less dispersed distribution. The intuitive reason is that the difference between the voids and big particles is more apparent when the content of fines is smaller. For heavier fouled ballast, the image appears to be more consistent with the appearance of fines, see FIGS. 6(a) through 6(f). Such trend holds not only for the Red channel but also for the Green and Blue channels. Therefore, a hypothesis can be made that six curves are the sampling results of a certain probability distribution for each fouling condition. Furthermore, the probability distribution of each color channel could be a function of the fouling condition.

[0066] Since a consistent trend is observed in FIGS. 7(a) through 7(c), it is reasonable to combine six image values for each fouling condition. Then, the approximated probability distributions can be obtained. As shown, FIGS. 8(a) through 8(c) respectively graphically illustrate cumulative probability distributions under different fouling conditions of different color channels. Apart from the changes in curve shape under different fouling conditions, the positions of curves of different color channels are also different. Obviously, the intensity of the Red channel is the largest, followed by the intensity of the Green channel, and the intensity of the Blue channel is the weakest. These are the conjugated results of the illumination and the mineralogy of ballast materials. During the tests, illumination conditions are controlled, and the ballast materials are all sample Rainy Section materials. Besides, the degree of distribution curve dispersion shrinks with the sequence of Red, Green, and Blue channels. It means that the Red channel's results can be the most dominant in this present disclosure.

[0067] Statistical Quantity Evaluation

[0068] Although the changes in distribution curves can be seen in FIGS. 8(a) through 8(c), the quantitative analysis should be performed to provide explicit correlations. Following the definition in Equations (1) through (5) as stated herein, calculated statistical quantities are presented respectively in graphical form in FIGS. 9(a) through 9(e), respecting FI for three color channels.

[0069] FIGS. 9(a) and 9(b) respectively illustrate that Mean or Median for each color channel remains stable when FI changes from 0 to 33. It means that Mean or Median is irrelevant to the fouling conditions. FIG. 9(c) graphically illustrates a strong linear correlation between FI and Variance for each color channel, and the Red channel has the most significant value change of Variance when FI changes from 0 to 33. Skewness graphically plotted in FIG. 9(d) indicates that the variation trend of Skewness with increasing FI is inconsistent for different color channels. Hence, Skewness will not be considered in the FI prediction model, and future investigation of such phenomenon will be needed. FIG. 9(e) graphically indicates that Kurtosis is a non-linear monotonic increasing function of FI. Given that only four FI values are prepared to build the FI prediction model, the non-linearity embedded in this Kurtosis-FI relationship cannot be well captured.

[0070] Fouling Index Prediction and Validation

[0071] Based on the results of FIGS. 9(a) through 9(e), Variance is a suitable statistical parameter to predict FI under controlled illumination conditions. FIG. 9(c) indicates Variance is linearly related to FI, meaning FI is linearly related to Variance. This linear function is adopted to predict FI based on Variance of color channel distribution:

FI.sub.c=a.sub.C.sup.2+b (6)

where the subscript C represents a color channel.

[0072] After performing the linear regression analysis, the values of Slope a, Intercept b, and R.sup.2, are listed in Table 2. The values of R.sup.2 show that these linear functions are good models to predict FI with Variance, and the Red channel is the best candidate with the largest R.sup.2 value.

TABLE-US-00002 TABLE 2 Linear Fitting Results Between FI and Variance for Different Color Channels Channel Slope a Intercept b R.sup.2 R 2597.51193 49.67336 0.990 G 3274.06369 49.53459 0.987 B 5392.95253 52.2989 0.965

[0073] As shown in FIGS. 6(a) through 6(f), validation cases, FI 18* and FI 28*, appear to follow the trend of color change with different fouling conditions. By assembling all the six images, the cumulative probability distribution curves of FI 18* and FI 28* can be plotted together with other cases to check if the trend is followed or not. FIGS. 10(a) through 10(c) respectively graphically illustrate all the probability curves of six different fouling conditions, including the two validation cases. In other words, FIGS. 10(a) through 10(c) respectively graphically illustrate cumulative probability distributions with validation fouling conditions of different color channels.

[0074] FIGS. 10(a) through 10(c) collectively confirm that the two validation cases well fit the pattern observed for all three color channels. The distribution curve of FI 18* falls between the curves of FI 13 and FI 23, and the curve of FI 28* falls between those of FI 23 and FI 33.

[0075] Based on the definition in Equation (3) otherwise listed herein, Variance values of two validation fouling conditions are calculated and plotted in FIG. 11. In FIG. 11, filled markers are the data points for modeling, three lines are the linear regression models, and star markers are the data points for model validation. The linear relationship between Variance and FI holds for validation cases, although the predicted values of FI are underestimated a bit. For predicted results from different channels, the Red channel shows the best prediction, followed by the Green channel, and the performance of the Blue channel is behind. Variance of the Red channel for Clean ballast is the largest among the three color channels, and Variance is non-negative. Hence, the Variance curve of the Red channel is the most sensitive to the change of FI, which results in Variance of the Red channel as a better prediction model. Besides, this ranking may not be universal because only one illumination condition and one ballast material are used in this present disclosure.

[0076] The predicted FI values according to the linear Variance-FI relationships are listed in Table 3. It can be noticed that all FI values are underestimated a bit for both fouling conditions. The error is acceptable considering the field practice.

TABLE-US-00003 TABLE 3 Performance of RGB-based FI Prediction Model Ground Truth: FI 18 Ground Truth: FI 28 Channel Predicted FI Error Predicted FI Error R 16.5 1.5 25.7 2.3 G 16.5 1.5 24.7 3.3 B 15.4 2.6 22.4 5.6

[0077] According to the fouling category proposed by Selig and Waters (1), ballast is Moderately Fouled with FI ranging from 10 to 19 and is Fouled with FI ranging from 20 to 39. The fouling status of FI 18 and FI 28 can be classified with the results shown in Table 3. Table 4 shows that this RGB-based model performs well in fouling status classification.

TABLE-US-00004 TABLE 4 Performance of RGB-based Fouling Category Prediction Model Ground Truth: FI 18 Ground Truth: FI 28 Predicted Predicted Channel True Category Category True Category Category R Moderately Moderately Fouled Fouled Fouled G Fouled Moderately Fouled Fouled B Moderately Fouled Fouled

Conclusions

[0078] This present disclosure acquires images of the same ballast materials having different fouling conditions. The images share a consistent illumination condition, and RGB-based analysis is performed. Based on the limited results, the following conclusions can be drawn: [0079] 1. Ballast with different fouling conditions shows different visual effects. Big particles are easier to be distinguished when the ballast is relatively less fouled. When the fine content increases, a higher portion of the fouled ballast image is occupied by fines, leading to a more consistent appearance. [0080] 2. Every color image has three color channels, Red, Green, and Blue. No matter which channel, the color frequency distribution changes with the increase of FI. The channel values of a heavier fouled ballast tend to have a less diverged frequency distribution. [0081] 3. Five statistical quantities, Mean, Median, Variance, Skewness, and Kurtosis, are calculated. Among these five quantities, Variance shows a strong linear relationship to FI, and Skewness or Kurtosis changes non-linearly. Mean and Median are stable. [0082] 4. An FI prediction model is established based on the Variance of color channels. The established FI prediction model is tested and validated by additional fouled ballast materials and shows promising performance. [0083] 5. The good prediction results of fouling conditions show the potential of this method for further development for prediction with different illumination conditions, ballast particle mineralogizes, and fouling materials.

[0084] This written description uses examples to disclose the presently disclosed subject matter, including the best mode, and also to enable any person skilled in the art to practice the presently disclosed subject matter, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the presently disclosed subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they include structural and/or step elements that do not differ from the literal language of the claims, or if they include equivalent structural and/or elements with insubstantial differences from the literal languages of the claims.

REFERENCES

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