Powder Flow Data

Five commercially available powders of different particle shapes and sizes and known flowability were considered as test powders in this study. These are Portland cement, cake flour, maize flour, quartz, and table salt. These powders were utilized as subjects to examine the applicability of the proposed approach to characterise the powder flow behaviour.

As shown in the experimental setup in Figure 6-15, the time series were obtained through real-time measurement of the mass of the powders in the digital balance. In particular, the time series data were gathered by allowing the powders to flow through an orifice onto a base plate, from which it overflowed onto a digital balance linked to a computer that logged the mass in grams instantaneously

A sum of 33,914 observations that spread across these powders were recorded. These were subsequently analysed using the recurrence texture analysis. For the segmentation of the time series, a window width of b = 1000 was estimated using the autocorrelation function where the sliding step was chosen to be m =50. The distribution of segments using the said parameters are tabulated in Table 6-7. A total of 580 segments are considered in this study using the estimated windowing dimensions. Each of these segments are

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transformed into distance matrices using Euclidean distances, from where the textural features are extracted.

Figure 6-15. Schematic diagram of the experimental setup showing the a vessel (A)

powders flow through an orifice (B) onto a base plate (C) and overflow is measured in digital balance (D) connected to computer (E)

Table 6-7. Mass data of the powders

Type of Powder (Acronym) No. of observations (n) No. of Segments (N) (using b=1000, m=50) Portland Cement (PC) 7,126 123 Cake Flour (CF) 6,733 115 Maize Flour (MF) 10,922 199 Quartz (Q) 6,144 103 Table Salt (TS) 2,989 40 TOTAL 33,914 580

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Figure 6-16. The raw time-series mass data of the five powders

Figure 6-17. The autocorrelation function of the powder time series data, showing

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6.4.2 Results and Discussion

The distance matrices of each powder is presented in Figure 6-18. Visually, in general, it seemed that the distance matrices of PC, CF and TS are quite identical with regards to its features. The distance matrices of Q and MF, on the other hand, appear unique with the latter has the coarsest distance matrix among all of them.

Figure 6-18. Euclidean distance matrices (with colour maps) of the Portland cement

(A), Cake flour (B), Maize flour (C), Quartz (D), and Table salt (E)

It is apparent that the distance matrix features of PC and CF are quite similar, with some resemblance to that of the TS. The textures are relatively finer. On the contrary, the textures of MF distance matrix are coarse, while the distance matrix of Q is a bit finer than MF but looks coarser than the other three. Coarse textures are related to a tendency to avalanche.

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Figure 6-19. Textural features of (A) GLCM and wavelet, (B) LBP, (C) texton, and

(D) combined GLCM, wavelet, LBP and texton, (E) AlexNet, and (F) VGG16 as projected onto 3-D principal component subspace

To further study these distance matrices, its textural features were extracted. Six texture matrices were obtained, coming from the considered textural extraction and CNN algorithms. In this paper, however, the GLCM and wavelet features were combined into a single feature matrix due to their lesser dimensionality relative to other features. In addition, the GLCM, wavelet, Texton and LBP feature matrices were combined to a single matrix for comparison. These were analysed thoroughly, by visualisation of data and

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by classification models. The features are visualised by projecting the features into first 3-D principal component subspace, as presented in Figure 6-19.

From Figure 6-19, although the clusters of portland cement, cake flour, and table salt are difficult to identify due to overlapping, it can still be inferred that distinct clusters are apparent to maize flour (green) and quartz (black). Remarkably, the maize flour are well separated from the other groups for all features. The cluster of quartz, on the other hand, is hard to localise in GLCM + Wavelet features but are distinct and quite separable to other clusters (with some overlapping) in other features. It is interesting to note that these observations supported the visual interpretation of the features of distance matrices, that the maize flour, has the coarsest distance matrix, followed by quartz, while the other three have finer textures and quite similar to one another.

Another stimulating inference in these plots is the separability of the clusters in each plot. In particular, the texton and AlexNet are said to have provided better visualisation of data due to enhanced separations of clusters present in the plot. The clusters of maize flour are very distinct in this case. For cake flour, although some of the points overlapped to other clusters, its cluster is still identifiable. This observation is also the same to Portland cement. On the contrary, the cluster of table salt is difficult to identify. Thorough inspection revealed that a well-formed cluster for this powder is existed as well, but was found in the cluster of Portland cement, this it was hard to see in the plot. It could be, however, be seen in higher dimensional space (e.g. 4- D) but visualisation of data is then limited in this case. As an alternative, the use of feature selection that maximises inter-class discrimination can be performed such as Linear Discriminant Analysis (LDA). In this case, LDA was used here in visualising the data. It should be noted, however, that LDA or any techniques that accentuate maximising inter-class discrimination (e.g.

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Eigenvalue-based Mutual Information (EMI)) should be used with caution especially when dealing classification of high dimensional image data as it could result to overfitting of data (R. Liu & Gillies, 2016). Overfitting of data is normally occurred when the sample size is not large enough relative to its dimensionality. In this study, there are 580 segments that were analysed, big enough to minimise overfitting. Furthermore, the paper only used LDA as supplemental tool for visualisation of data. As presented in Figure 6-20, distinct clusters are observed, with a varying extent of separability among the clusters for each feature set.

Figure 6-20. Linear discriminant projection of RTA features namely (A) GLCM and

wavelet, (B) LBP, (C) textons, and (D) all features (GLCM, wavelet, LBP, textons), showing maximum separability between the powders.

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Table 6-8. Classification performance of the feature sets (highlighted the highest

classification accuracy in the test dataset) GLCM + Wavelet LBP Texton GLCM + Wavelet + LBP + Texton AlexNet VGG16 No. of dimensions 17 256 40 313 4096 4096 No. of segments, N 580 580 580 580 580 580 No. of classes 5 5 5 5 5 5 Classification Accuracy, % 81.6% 77.0% 94.8% 79.3% 93.3% 94.6%

To characterise the powder flow behaviour, a linear-SVM classification model is developed. The analysis is performed using five classes that correspond to the five powders, with the SVM as classifier. The classification accuracies are determined for each run using the sets of the features using holdout method. In this process, the datasets are randomly divided into training (70% of the datasets) and testing (remaining 30% of the datasets). Ten- fold cross validation is implemented in the validation stage to minimise overfitting. The trained models are then employed to predict the classes of the test data.

As presented in Table 7-5, it can be understood that, although all the features provided reliable results by getting more than 70% classification accuracy, the texton, and 2 CNN features have seen to outperform the other features including the combination of GLCM, wavelet, texton and LBP features. In other words, these three features gave the most discriminative features for each powder by obtaining more than 90% classification accuracy.

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To supplement the study, the RQA is also employed in this case and the results are compared to the RTA. As shown in Figure 6-21, the recurrence plots of Portland cement, cake flour and table salt are apparently comparable to each other. In contrast, the recurrence plot of maize flour can easily be differentiate to other recurrence plots. In the analysis, 10 RQA features were extracted from these recurrence plots. Figure 6-22 visualised these features in 3-D principal component subspace. As seen in the figure, the maize flour can be distinguished easily from other powders. The RQA features of quarts, on the other hand, are fairly scattered in the plot which were seen overlapping to most RQA features of other powders.

Figure 6-21. Exemplary samples of recurrence plots of (A) Portland cement, (B) cake

flour, (C) maize flour, (D) quartz, and (E) table salt.

These RQA features were treated as predictors in SVM classification model. Using the same procedure with RTA in the training and testing, the model successfully classified the classes of the powders using RQA features with accuracy of 81.1%. This result showed that RQA features could also be

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used to discriminate the classes of the powder which can be used in the development of the powder flowability.

Figure 6-22. 3-D plot of the RQA features using the first 3 principal component

scores.

In this comparative study, it has seen that the RTA-texton, RTA-AlexNet and RTA-VGG16 performed the best in classification with less than 7% error rate. Furthermore, the combined GLCM and wavelet also performed well, which has seen to be at par to the RQA features, which have both obtained 81% accuracy. More importantly, this comparative study displayed the robustness of RTA over RQA in characterising the dynamic behaviour of the process data.