Prediction of spunbonded nonwoven filtration performance from structural parameter reducts using rough set theory and support vector machine

Abstract

A novel approach to predicting the filtration performance of spunbonded nonwoven using a rough set theory- and support vector machine-based model is presented. The meso-structure of spunbonded nonwoven was characterized using a structural parameter set (O_s) containing nine parameters. Four reducts were extracted from O_s using rough set theory. Twenty models, each based on either a support vector machine (SVM) or a back-propagation artificial neural network (BP-ANN), were established to predict the filtration performance (under varying filtration velocity and particle size) of spunbonded nonwoven by taking the parameters of each reduct and O_s as inputs. The results show that the prediction accuracy of the model that takes thickness, fiber diameter, and pore size as its input parameters is higher than that of any other model, regardless of the model type. Moreover, the predictive power of the SVM-based model was found to exceed that of the BP-ANN-based model.

Keywords

spunbonded nonwoven rough set support vector machine filtration performance fiber web structure parameter

Nonwoven materials have excellent filtration properties given that they have a three-dimensional network structure and contain multiple micropores. Studies have shown that the filtration performance of a nonwoven material is closely related to its fiber web structure.^1–6 However, several parameters can be used to characterize the fiber web structure of spunbonded nonwoven. Establishing an equation system that includes all the parameters used in researching the influence of the fiber web structure on the filtration performance of spunbonded nonwoven would be a computationally intensive and inconvenient to apply. In addition, not every structural parameter has the same degree of influence on filtration performance; some parameters are redundant. Therefore, we should select as few parameters as possible for modeling—including only those parameters that have the greatest influence on filtration performance. The classical rough set (RS) theory developed by Pawlak in the early 1980’s,⁷ based on the conventional indiscernibility relation, can be used as a tool to discover data dependencies and to reduce the number of attributes, which are contained in a dataset, using the data alone without requiring any additional information. There is a complex nonlinear relationship between the parameters of the fiber web structure and the filtration performance of nonwoven, which is difficult to analyze using traditional methods such as mathematical statistics. A support vector machine (SVM) is a machine-learning algorithm based on statistical learning theory that has found applications in regression analysis and pattern recognition since it was first introduced in 1995. SVMs have also been applied, and found to work well, in the textile field.^8–14

Rough set theory

For a given dataset with discretized attribute values, it is possible to identify the most informative subsets (termed reducts) of the original attributes by applying RS theory.¹⁵ Let $X, Y \in U$ , where U is a nonempty set of finite objects (the domain). Assuming E is the equivalence relation defined on U, we define the lower approximation of X about E as $E_{-} X = {Y \in U / E : Y \subseteq X}$ . Moreover, the upper approximation of X about E is defined as $E^{-} (X) = {Y \in U / E : Y \cap X \neq φ}$ , where φ denotes an empty set. The boundary region of X is defined as $Bnd (X) = E^{-} (X) - E_{-} (X)$ . Let us now define rough sets. If $Bnd (X)$ is empty, set X is crisp. If $Bnd (X)$ is nonempty, set X is rough. Let S be a knowledge representation system, expressed as $s = á U, A, V, f ñ$ . Here, A is a nonempty finite set of attributes, V is a set of attribute values, and $f : U \times A \to V$ is an information function, i.e., for any $u \in U, a \in A$ , there is $f (u, a) = V$ . Let us assume $B \subseteq A$ ; then the indiscernibility relation $IND (B)$ is defined as
$IND (B) = {(x, y) | (x, y) \in U^{2}, \forall β \in B (β (x) = β (y))}$
(1)
If $IND (B) = IND (B - {β})$ , β is considered to be redundant in B.

Support vector machines

An SVM maps the input vectors into a high-dimensional feature space using suitable kernel function, and thus can be applied to solve the nonlinear case. SVM models are closely related to neural networks. The output is a linear combination of the intermediate nodes. Each intermediate node corresponds to one support vector. Based on the structural risk minimization principle, SVMs have been found to be more suitable than artificial neural networks (ANNs) because of their improved generalization capability and higher predictive power for smaller samples.¹⁶ Figure 1 shows the basic structure of an SVM model.
Figure 1.
Support vector machine model.

Materials and methods

Meso-structure and filtration performance of spunbonded nonwoven samples

Thirty samples of polypropylene spunbonded nonwoven, acquired from the Key Laboratory of Advanced Textile Material and Manufacturing Technology, Ministry of Education, Zhejiang Sci-Tech University, were selected. We used nine parameters to characterize the meso-structure of these spunbonded nonwoven samples: basis weight μ (g/m²), thickness T (mm), feature length of the elemental fiber deposition plane (elemental plane in short) σ (km/m²), number of elemental planes n, fiber diameter d (µm), orientation factor O_f, porosity ϕ (%), pore size P_s (µm), and variation coefficient of pore size V_P (%).

The test of μ was performed in the AL204-IC electronic scale. Ten different places were tested on each sample. The test of T was performed in the YG (B) 141D fabric thickness tester at a pressure of 0.5 kPa, 10 different places were tested on each sample.

The parameter d was measured on the images of the sample. Scanning electron microscopy (SEM) images of the samples were collected using a JSM-5610LV scanning electron microscope (JEOL Company, Ltd., Tokyo, Japan) with an amplifying multiple of 200. Ten different regions were scanned, and correspondingly 10 images were collected, for each sample. For example, Figure 2 shows SEM image No.1 of sample No.1 for an image size of 400 × 400 pixels. Image Pro-Plus (IPP) was applied to measure the fiber diameter. A total of 100 fibers in different SEM images were measured for each sample.
Figure 2.
SEM image No.1 of sample No.1.

The orientation factor O_f was employed to characterize the fiber orientation degree of the samples, and it is defined by equation (2)
$O_{f} = \cos 2 θ$
(2)
where θ is the mean value of the fiber orientation angle, which is defined as the angle between the fiber and the longitudinal direction of the nonwoven sample. However, there are two angles that are supplementary between the fiber and the longitudinal direction. Among these, the angle with a value less than or equal to 90° was defined as the fiber orientation angle. IPP was applied to measure the fiber orientation angles of all fibers in each image. Thus, the value of θ for each image can be obtained.

Tests of pore size P_s and its standard deviation were performed in the PSM165 pore size tester (Topas GmbH, Frankfurt, Germany). Five different places were tested on each sample.

Table 1 lists the test results of the above fiber web structure parameters of 30 samples, where the notation CV stands for the coefficient of variation. It can be seen from the table that besides P_s, the measured data show a small variation from the mean value since their CVs are all below 10%.
Table 1.
Test results of fiber web structure parameters of 30 spunbonded nonwoven samples

Sample No. μ
T
d
O_f
P_s

Mean (g/m²) CV (%) Mean (mm) CV (%) Mean (µm) CV (%) Mean CV (%) Mean (µm) CV (%)

1 81.7 3.25 0.448 4.36 22.34 8.55 0.0256 6.71 19.9 80.90

2 74.1 4.79 0.430 3.23 22.26 6.87 0.0630 3.45 27.2 64.34

3 66.4 3.40 0.416 2.25 21.96 8.11 0.1152 5.09 29.4 57.48

4 58.0 4.92 0.407 3.29 22.31 9.91 0.1781 4.48 34.1 48.09

5 52.1 3.77 0.386 5.14 21.82 7.88 0.2306 3.92 41.3 44.07

6 89.3 2.05 0.482 4.92 23.01 8.26 0.0305 5.51 17.3 93.64

7 81.4 3.61 0.456 4.70 22.87 7.56 0.0597 5.18 20.5 80.98

8 71.2 2.88 0.434 3.55 22.91 9.30 0.1125 3.94 28.2 67.02

9 62.8 4.24 0.421 2.93 23.13 5.53 0.1674 2.75 32.7 57.49

10 56.2 3.75 0.408 4.58 22.97 6.31 0.2320 4.90 37.6 49.20

11 98.2 2.62 0.519 3.64 23.76 9.51 0.0278 3.07 16.7 105.99

12 86.4 3.49 0.477 5.51 23.70 7.81 0.0589 5.38 18..0 90.56

13 74.6 5.33 0.449 2.60 23.87 8.09 0.1097 6.12 24.0 72.08

14 66.3 4.36 0.436 3.59 23.53 7.10 0.1766 3.67 30.8 62.01

15 59.7 3.71 0.426 2.82 23.62 8.13 0.2258 4.26 33.5 54.63

16 107.2 3.90 0.548 4.46 24.15 6.79 0.0283 5.30 13.3 127.07

17 91.6 2.83 0.497 4.71 24.26 6.43 0.0665 2.99 17.2 102.33

18 80.6 5.22 0.472 1.76 24.04 4.62 0.1217 6.03 20.8 84.62

19 71.1 3.15 0.454 4.63 24.31 7.28 0.1713 4.74 28.6 74.48

20 64.8 3.48 0.441 3.90 24.37 7.84 0.2247 5.52 32.0 67.50

21 117.8 2.32 0.569 1.94 24.83 5.72 0.0229 4.01 11.0 148.18

22 99.6 4.68 0.533 5.44 24.77 6.90 0.0632 2.78 16.3 136.81

23 89.1 5.17 0.496 4.61 24.67 9.32 0.1144 5.75 17.5 113.14

24 78.4 2.26 0.475 5.84 24.51 7.18 0.1660 3.67 23.8 99.58

25 69.5 4.73 0.457 4.49 24.90 7.51 0.2268 6.36 29.2 79.11

26 127.7 1.89 0.604 1.73 25.22 8.33 0.0287 3.81 10.3 175.73

27 109.8 3.21 0.579 2.77 25.38 7.37 0.0626 4.92 12.2 145.90

28 96.3 4.67 0.528 4.32 25.41 6.77 0.1111 2.83 16.9 130.77

29 82.8 3.98 0.490 3.17 25.29 7.20 0.1743 6.56 18.9 119.58

30 74.4 3.25 0.473 3.30 25.34 8.64 0.2351 3.10 26.3 92.02

Nonwoven can be considered as a fiber assembly that is composed of several layers of superimposed elemental planes. These elemental planes comprise several fibers in a crossover arrangement with a thickness that is twice the fiber diameter. The feature length of an elemental plane σ can be calculated as follows
$σ = \frac{8 \times μ}{π \times ρ \times d \times T}$
(3)
where ρ is the bulk density of the fiber (g/cm³).

The number of elemental planes n is calculated by
$n = \frac{T}{2 \times d}$
(4)

The parameter ϕ is calculated by
$ϕ = (1 - \frac{μ}{ρ \times T}) \times 100 %$
(5)

Table 2 presents the values of all nine parameters characterizing the meso-structure of these spunbonded nonwoven samples.
Table 2.
Values of all nine parameters characterizing the meso-structure of 30 spunbonded nonwoven samples

Sample No. μ (g/m²) T (mm) σ (km/m²) n d (µm) O_f ϕ (%) P_s (µm) V_P (%)

1 81.7 0.448 22.843 10.03 22.34 0.0256 79.96 19.9 80.90

2 74.0 0.430 21.634 9.66 22.26 0.0630 81.09 27.2 64.34

3 66.4 0.416 20.340 9.47 21.96 0.1152 82.46 29.4 57.48

4 58.0 0.407 17.874 9.12 22.31 0.1781 84.34 34.1 48.09

5 52.1 0.386 17.310 8.85 21.82 0.2306 85.17 41.3 44.07

6 89.3 0.482 22.531 10.47 23.01 0.0305 79.64 17.3 93.64

7 81.4 0.456 21.842 9.97 22.87 0.0597 80.38 20.5 80.98

8 71.2 0.434 20.038 9.47 22.91 0.1125 81.97 28.2 67.02

9 62.8 0.421 18.047 9.10 23.13 0.1674 83.61 32.7 57.49

10 56.2 0.408 16.781 8.88 22.97 0.2320 84.86 37.6 49.20

11 98.2 0.519 22.284 10.92 23.76 0.0278 79.21 16.7 105.99

12 86.4 0.477 21.387 10.06 23.70 0.0589 80.10 18.0 90.56

13 74.6 0.449 19.478 9.41 23.87 0.1097 81.74 24.0 72.08

14 66.3 0.436 18.084 9.26 23.53 0.1766 83.29 30.8 62.01

15 59.7 0.426 16.603 9.02 23.62 0.2258 84.60 33.5 54.63

16 107.2 0.548 22.667 11.35 24.15 0.0283 78.50 13.3 127.07

17 91.6 0.497 21.259 10.24 24.26 0.0665 79.75 17.2 102.33

18 80.6 0.472 19.877 9.82 24.04 0.1217 81.23 20.8 84.62

19 71.1 0.454 18.027 9.34 24.31 0.1713 82.79 28.6 74.48

20 64.8 0.441 16.873 9.05 24.37 0.2247 83.85 32.0 67.50

21 117.8 0.569 23.332 11.46 24.83 0.0229 77.25 11.0 148.18

22 99.6 0.533 21.111 10.76 24.77 0.0632 79.47 16.3 136.81

23 89.1 0.496 20.376 10.05 24.67 0.1144 80.26 17.5 113.14

24 78.4 0.475 18.844 9.69 24.51 0.1660 81.86 23.8 99.58

25 69.5 0.457 17.091 9.18 24.90 0.2268 83.29 29.2 79.11

26 127.7 0.604 23.459 11.97 25.22 0.0287 76.77 10.3 175.73

27 109.8 0.579 20.909 11.41 25.38 0.0626 79.16 12.2 145.90

28 96.3 0.528 20.086 10.39 25.41 0.1111 79.96 16.9 130.77

29 82.8 0.490 18.698 9.69 25.29 0.1743 81.43 18.9 119.58

30 74.4 0.473 17.370 9.33 25.34 0.2351 82.72 26.3 92.02

The filtration efficiency and pressure drop were tested using an TSI-3160 filter tester (TSI Inc., USA). Using different filtration velocities, the values of filtration efficiency and pressure drop of each sample were obtained under different particle sizes (Paraffin oil-based aerosol was used in this work). Table 3 describes the test scheme. Ten different regions on each sample were tested. Table 4 lists the test results. It can be seen from Table 4 that the measured data show a small variation from the mean value because all their CVs are below 10%.
Table 3.
Test scheme for filtration performance

Test No. Test parameters

Filtration velocity (cm/s) Particle size (µm)

1 3.5 0.3

2 5.3 0.1

3 5.3 0.3

4 5.3 0.5

5 7.3 0.3

Table 4.
Test results of filtration performance

Sample No. Filtering performance Test No.

1
2
3
4
5

Mean CV (%) Mean CV (%) Mean CV (%) Mean CV (%) Mean CV (%)

1 FE 28.93 4.93 11.12 6.16 25.11 4.78 37.61 4.86 20.89 7.12

ΔP 3.34 5.29 4.84 5.23 4.84 6.89 4.83 7.03 6.80 4.53

2 FE 24.06 7.10 9.24 4.55 21.85 7.04 30.54 5.46 16.95 5.87

ΔP 2.03 4.56 2.73 5.47 2.70 3.46 2.71 5.90 3.91 6.30

3 FE 22.70 5.54 8.87 6.80 20.55 6.55 28.15 4.85 16.06 5.11

ΔP 1.65 7.85 2.27 4.43 2.26 6.13 2.24 6.14 3.09 3.88

4 FE 20.89 3.49 7.11 5.62 17.27 3.27 26.32 5.15 15.34 7.48

ΔP 1.24 6.44 1.72 6.89 1.70 5.44 1.73 7.41 2.41 6.39

5 FE 19.16 8.61 6.93 7.35 15.50 8.21 23.24 7.70 13.55 4.16

ΔP 0.74 5.25 1.04 4.29 1.04 4.62 1.03 5.18 1.51 6.85

6 FE 29.54 5.72 11.92 6.77 25.79 6.67 39.73 6.45 21.78 6.20

ΔP 4.31 6.70 5.97 8.08 6.02 7.05 5.89 5.56 8.49 5.41

7 FE 26.01 4.88 10.40 5.20 23.17 5.30 36.83 6.53 19.40 3.55

ΔP 3.00 6.35 4.44 5.39 4.41 4.19 4.44 5.07 6.01 7.78

8 FE 23.80 6.06 9.58 6.17 20.74 6.70 30.07 6.72 17.88 5.92

ΔP 1.89 4.92 2.70 5.82 2.73 5.54 2.73 5.44 3.88 5.15

9 FE 22.85 5.75 7.92 4.44 18.84 4.39 28.45 7.19 16.48 8.25

ΔP 1.46 5.51 2.04 5.90 2.01 7.81 2.01 5.67 2.95 5.42

10 FE 19.98 3.99 7.33 9.18 16.30 7.97 24.50 7.24 14.10 4.79

ΔP 0.89 8.38 1.24 6.52 1.27 5.92 1.24 6.51 1.69 6.11

11 FE 30.19 4.62 12.22 6.78 27.13 6.36 41.24 3.89 22.15 3.76

ΔP 4.58 7.24 6.64 5.37 6.59 5.16 6.72 6.29 9.07 7.55

12 FE 28.94 6.57 11.13 4.21 25.15 5.42 37.55 4.75 20.86 6.09

ΔP 3.90 4.23 5.78 4.79 5.83 3.38 5.70 6.16 8.07 4.99

13 FE 26.31 4.80 9.90 6.85 22.44 5.74 32.71 4.49 19.45 5.78

ΔP 2.92 6.84 4.02 7.22 3.98 7.85 3.99 7.04 5.66 5.05

14 FE 23.37 6.11 8.92 5.84 19.97 4.49 30.25 5.85 17.48 6.13

ΔP 1.69 4.04 2.47 6.10 2.48 6.20 2.51 4.79 3.54 4.57

15 FE 20.71 4.38 7.58 6.59 17.11 6.19 26.08 6.33 15.29 5.60

ΔP 1.21 6.35 1.58 7.46 1.62 8.33 1.63 4.70 2.14 7.91

16 FE 34.64 5.27 13.07 5.51 28.53 5.25 43.04 8.18 24.58 4.96

ΔP 5.90 6.63 8.27 6.73 8.28 4.45 8.20 6.41 11.33 6.77

17 FE 29.41 4.12 11.79 4.66 25.42 7.03 39.64 5.55 21.79 7.40

ΔP 4.69 5.13 6.41 6.17 6.34 3.43 6.41 3.96 9.11 5.56

18 FE 26.80 6.03 10.50 6.79 23.24 7.47 36.78 7.42 19.62 6.31

ΔP 3.55 4.79 5.03 4.92 4.95 5.62 4.98 6.36 6.97 6.29

19 FE 25.72 6.49 9.48 5.54 21.01 6.03 30.91 4.50 17.60 6.98

ΔP 2.17 6.67 2.98 5.89 3.03 5.95 3.03 6.17 4.14 4.84

20 FE 23.91 4.54 8.71 6.23 19.64 4.40 29.07 5.39 16.83 3.93

ΔP 1.79 6.18 2.47 4.85 2.47 6.23 2.50 4.22 3.48 6.23

21 FE 36.82 4.73 13.98 6.47 30.80 4.88 44.80 7.53 24.83 9.09

ΔP 6.75 3.85 9.46 4.94 9.53 5.58 9.47 4.66 13.24 5.52

22 FE 31.35 2.96 12.32 6.28 26.24 3.71 41.55 3.85 22.45 3.17

ΔP 4.99 5.93 7.08 3.77 7.09 5.94 7.03 5.99 10.58 4.66

23 FE 29.93 5.21 11.91 5.30 25.16 5.64 37.71 5.58 21.66 5.04

ΔP 4.67 4.49 6.47 4.87 6.46 7.50 6.51 6.76 9.03 6.26

24 FE 27.18 4.08 10.02 5.95 22.65 5.85 34.32 4.14 19.16 4.95

ΔP 2.99 6.62 4.11 6.29 4.12 6.09 4.15 5.28 6.11 6.47

25 FE 25.97 6.55 9.73 4.11 20.31 3.55 31.07 6.80 17.66 4.49

ΔP 2.09 5.35 3.08 7.34 3.08 7.67 3.06 6.34 4.21 6.50

26 FE 39.12 5.86 14.51 6.50 32.55 3.42 48.72 5.11 28.06 3.82

ΔP 7.83 4.84 11.04 4.64 11.04 4.91 11.05 4.94 15.47 4.89

27 FE 36.53 4.30 13.37 3.70 29.08 6.22 43.63 3.76 23.94 6.62

ΔP 6.65 5.77 9.16 5.96 9.14 5.15 9.15 4.10 13.10 7.17

28 FE 32.28 6.57 11.93 6.76 27.47 5.76 41.17 7.16 23.71 5.05

ΔP 5.59 5.46 7.75 7.27 7.70 4.10 7.75 5.22 11.13 6.56

29 FE 30.01 4.96 11.20 6.89 25.21 6.12 38.56 4.24 21.26 3.64

ΔP 4.09 6.42 5.88 5.09 5.88 4.99 5.94 6.81 8.36 6.13

30 FE 27.47 6.18 9.77 5.97 22.83 6.54 32.91 5.97 19.36 6.82

ΔP 2.55 4.09 3.70 4.30 3.72 5.33 3.70 6.23 5.34 5.70

Notes: FE—filtration efficiency (%)

ΔP—pressure drop (Pa)

Attribute reduction

First, discrete normalization was applied to the attribute values, i.e., the values of the fiber web structure parameters in Table 2, using the equidistance method. Let step = (max − min) / 3, where max and min are the maximum and minimum in each column of the table, respectively. The attribute values of each column were classified into three grades. The original values between (min + 2 × step) and max were classified as the first level, labeled as “2”; those between (min + step) and (min + 2 × step) were classified as the second level, labeled as “1”; those between min and (min + step) were classified as the third level, labeled as “0”. The results are listed in Table 5. It can be seen that after discrete normalization, the data of samples 5, 7, 10, 15, 26, and 28 are repetitive, being the same as the data of samples 4, 1, 4, 9, 21, and 23, respectively. These repetitive data were deleted before attribute reduction, and therefore only the data of the remaining 24 samples in Table 5 were taken as the inputs to attribute reduction.
Table 5.
Discrete normalization result of the attribute values

Sample No. μ T σ n d O_f ϕ P_s V_P

1 1 0 2 1 0 0 1 0 0

2 0 0 2 0 0 0 1 1 0

3 0 0 1 0 0 1 2 1 0

4 0 0 0 0 0 2 2 2 0

5 0 0 0 0 0 2 2 2 0

6 1 1 2 1 0 0 1 0 1

7 1 0 2 1 0 0 1 0 0

8 0 0 1 0 0 1 1 1 0

9 0 0 0 0 1 2 2 2 0

10 0 0 0 0 0 2 2 2 0

11 1 1 2 1 1 0 0 0 1

12 1 1 2 1 1 0 1 0 1

13 0 0 1 0 1 1 1 1 0

14 0 0 0 0 1 2 2 1 0

15 0 0 0 0 1 2 2 2 0

16 2 2 2 2 1 0 0 0 1

17 1 1 2 1 2 0 1 0 1

18 1 1 1 0 1 1 1 1 0

19 0 0 0 0 2 2 2 1 0

20 0 0 0 0 2 2 2 2 0

21 2 2 2 2 2 0 0 0 2

22 1 2 1 1 2 0 0 0 2

23 1 1 1 1 2 1 1 0 1

24 1 1 0 0 2 2 1 1 1

25 0 0 0 0 2 2 2 1 0

26 2 2 2 2 2 0 0 0 2

27 2 2 1 2 2 0 0 0 2

28 1 1 1 1 2 1 1 0 1

29 1 1 0 0 2 2 1 0 1

30 0 1 0 0 2 2 2 1 1

In this study, attribute reduction was performed using a genetic algorithm by applying the software ROSETTA. Let O_s be the original structural parameter set of the fiber web, that is
$O_{s} = {μ, T, σ, n, d, O_{f}, ϕ, P_{s}, V_{p}}$
(6)

Four reducts of O_s were obtained after attribute reduction; let r_i represent the ith reduct (i = 1, 2, 3, 4). The reducts are given by
$r_{1} = {T, d, P_{s}}$
(7)

$r_{2} = {T, d, O_{f}}$
(8)

$r_{3} = {T, σ, d}$
(9)

$r_{4} = {T, n, d}$
(10)

From equations (6), (7), (8), (9), and (10), it can be seen that the parameters considered to be redundant in O_s are μ, ϕ, and V_p. This can be attributed to the fact that μ can be calculated using T, σ, ρ, and d according to equation (3), and ϕ can be calculated using σ and d according to equation (5) and equation (3). Moreover, the variation of V_p coincides well with that of P_s, which can be clearly inferred from the data in Table 2.

Prediction model

Selection of those structure parameters capable of most accurately predicting the filtration performance of spunbonded nonwovens was carried out by taking each reduct (r₁, r₂, r₃ and r₄) together with O_s as the inputs to the SVM- and BP-ANN-based models, respectively. Each model, irrespective of its type (SVM-based or BP-ANN-based), has two outputs (filtration efficiency and pressure drop). Therefore, 20 kinds of models were established. Table 6 presents the structures of the models. The k-fold cross validation technique was applied to train and test the models.
Table 6.
Structures of prediction models

Inputs Model Outputs

r₁ = {T, d, P_s} SVM Filtering efficiency

BP-ANN

SVM Pressure drop

BP-ANN

r₂ = {T, d, O_f} SVM Filtering efficiency

BP-ANN

SVM Pressure drop

BP-ANN

r₃ = {T, σ, d} SVM Filtering efficiency

BP-ANN

SVM Pressure drop

BP-ANN

r₄ = {T, n, d} SVM Filtering efficiency

BP-ANN

SVM Pressure drop

BP-ANN

O_s = {#x003BC;, T, σ, n, d, O_f, ϕ, P_s, V_P} SVM Filtering efficiency

BP-ANN

SVM Pressure drop

BP-ANN

BP-ANN: back-propagation artificial neural network; SVM: support vector machine.

Radial basis function (RBF) was taken as the kernel function of the SVM model. The parameters of each model, including the width of the RBF kernel (W), the penalty factor C, and the value of the precision parameter (η), were optimized using a trial and error method that utilized six-fold cross-validation on the training and testing subsets; the results are presented in Table 7. BP-ANN is a multilayer feed-forward network trained in terms of the error back-propagation algorithm. A BP-ANN model with a single hidden layer was applied in this investigation. A tangential S-shaped transfer function was used in the hidden layer. The number of nodes in the hidden layer was optimized using a trial and error method that utilized six-fold cross-validation on the training and testing subsets; the results are presented in Table 7.
Table 7.
Optimized SVM parameters and nodes in the hidden layer of BP-ANN models

Structural parameters Test No. Filtration efficiency
Pressure drop

SVM
BP-ANN (nodes in the hidden layer) SVM
BP-ANN (nodes in the hidden layer)

W C η W C η

r ₁ 1 14 1000 0.08 4 30 1500 0.04 5

2 18 900 0.10 5 30 1500 0.04 5

3 16 1100 0.06 7 28 1400 0.05 6

4 26 900 0.09 6 31 1600 0.03 7

5 23 1200 0.07 6 29 1700 0.05 4

r ₂ 1 2 9500 0.22 7 6 8800 0.24 7

2 2 9300 0.23 8 6 8900 0.25 7

3 1.5 8600 0.16 4 7 9400 0.29 6

4 3 8100 0.26 6 7 7900 0.33 6

5 2 6700 0.35 5 6 8400 0.25 7

r ₃ 1 90 5700 0.06 7 30 5700 0.06 6

2 15 1600 0.10 4 27 17000 0.08 5

3 11 17000 0.12 6 31 21000 0.04 7

4 22 6300 0.03 8 30 15000 0.05 5

5 38 4900 0.02 6 25 16000 0.10 5

r ₄ 1 33 1900 0.08 5 12 1100 0.07 4

2 34 1300 0.06 8 15 900 0.01 7

3 24 2000 0.12 7 9 1200 0.07 7

4 29 2200 0.13 5 13 800 0.11 6

5 28 2300 0.15 6 8 700 0.10 9

O_s 1 39 70 0.02 8 40 70 0.02 9

2 35 70 0.01 7 38 45 0.03 8

3 42 75 0.05 6 39 30 0.12 8

4 41 70 0.01 9 43 35 0.04 4

5 90 70 0.02 7 46 40 0.08 7

Prediction of filtration performance using SVM and BP-ANN based model

The filtration performance was predicted using SVM and BP-ANN-based models together with MATLAB programming. For example, the calculation processes to predict the filtration efficiency of the samples taking r₁ as the input of both SVM and BP-ANN-based models in the 2nd iteration of test No. 1 is described as follows. Given that samples 2, 11, 14, and 30 served as the test subset in this iteration, the values of structural parameters T, d, P_s of the remainder 20 samples were taken as the inputs, and at the same time the tested values of filtration efficiency and pressure drop of these 20 samples were taken as the outputs of the model (SVM or BP-ANN). Consequently, the model would be well trained. Therefore, the prediction values of filtration efficiency and pressure drop of samples 2, 11, 14 and 30 can be calculated by the model after the values of T, d, P_s of these samples are fed into the model. Table 8 shows the data obtained from the predicted values and tested values in the example.
Table 8.
Filtration efficiency data obtained from predicting and from testing in the example

Sample No. Predicted values
Tested values

SVM based model BP-ANN based model

2 23.75 24.69 24.06

11 30.50 29.62 30.19

14 24.01 24.12 23.37

30 27.26 28.20 27.47

Results and discussions

The mean value and variation coefficient of prediction accuracy (PA) was used to characterize the prediction accuracy of the models in this investigation. PA is defined as
$PA = (1 - \frac{| o - p |}{o}) \times 100 %$
(11)
where o is the measured value of the sample, p is the predicted value of the sample. Table 9 lists the prediction accuracy of models that take O_s and its 4 reducts as the inputs.
Table 9.
Prediction accuracy of models that take the original structural parameter set of the fiber web and its four reducts as the inputs

Structural parameters Test No. Filtration efficiency
Pressure drop

SVM
BP-ANN
SVM
BP-ANN

MPA (%) CV (%) MPA (%) CV (%) MPA (%) CV (%) MPA (%) CV (%)

r ₁ 1 98.04 1.86 97.33 2.12 97.07 2.17 96.44 2.69

2 97.69 1.82 97.03 2.45 98.24 1.25 97.50 1.52

3 98.03 1.44 96.64 1.88 98.82 1.06 98.01 1.75

4 98.55 1.58 98.13 1.96 98.39 1.28 97.83 1.90

5 97.99 1.55 97.26 1.94 97.71 1.80 97.12 2.55

r ₂ 1 96.38 3.04 95.49 3.90 88.96 14.00 89.39 13.91

2 95.44 5.73 94.51 5.34 88.68 14.48 86.26 15.84

3 96.79 2.93 94.70 4.22 89.02 14.15 87.95 17.03

4 96.39 3.58 94.66 4.71 89.72 14.31 88.48 16.17

5 96.02 2.97 95.15 4.09 89.32 12.59 87.67 14.68

r ₃ 1 96.68 3.06 95.39 3.68 87.72 10.73 87.09 12.35

2 96.44 2.78 95.26 4.13 89.36 11.89 88.19 13.46

3 97.41 2.09 96.17 2.88 89.87 12.25 88.83 13.59

4 95.58 3.87 94.43 5.67 89.77 12.66 88.78 12.12

5 96.22 3.17 95.24 4.37 89.29 11.49 88.06 13.50

r ₄ 1 97.40 2.59 96.43 3.16 88.98 6.62 87.25 7.81

2 94.83 4.32 95.11 5.98 90.23 6.83 88.40 8.03

3 95.56 3.27 94.04 4.62 88.44 6.98 89.49 8.92

4 95.83 3.17 93.87 4.73 90.55 6.62 88.26 8.16

5 95.34 2.78 94.25 3.99 89.13 7.08 88.17 8.74

O_s 1 96.89 3.01 95.77 3.32 94.27 5.63 93.83 6.89

2 96.61 2.69 95.72 3.25 95.14 5.96 94.21 7.34

3 97.10 2.84 96.03 3.86 94.90 5.96 93.28 7.94

4 97.37 2.57 96.19 3.42 94.38 5.44 93.13 7.32

5 97.09 1.88 95.96 2.44 94.43 3.03 93.37 3.90

The abbreviation MPA indicates the mean value of PA. It can be seen from the table that the prediction accuracy of the model that takes r₁ as input is higher than any other model except the one that takes O_s as input. This indicates that there exist fiber web structure parameters that have low impact on the filtration performance within O_s. Apart from the models that take r₃ and r₄ as inputs to predict the filtration efficiencies in Test No. 3 and Test No. 1, respectively, the prediction accuracy of the models that take r₂, r₃, and r₄ as inputs are all lower than that of the model that takes O_s as input, according to both MPA and CV. Therefore, it can be concluded that r₁ is the most representative reduct of O_s for predicting the filtration performance of spunbonded nonwoven. The ranking of the inputs as regards to predictive ability is r₁ > O_s > r₄ > r₃ > r₂. This ranking is based on the prediction accuracy for pressure drop because the results show that the differences in the prediction accuracy for pressure drop were far greater than those for filtration efficiency. In fact, all three elements in r₁, i.e., the thickness, fiber diameter, and pore size, influence the filtration performance of spunbonded nonwoven considerably. The filtration efficiency increases as the pore size decreases; however, the pressure drop increases correspondingly. This is because smaller pores allow fewer particles to pass through and generate higher resistance to air flow.^2,6,17 Increasing the thickness of a spunbonded nonwoven material can improve its filtration efficiency and increase its pressure drop. This is because the pores in nonwoven materials are interconnected and three-dimensional; hence, the thicker the material, the more tortuous its pore channels are. As a result, more particles can be intercepted with increasing resistance to air flow.^18,19 Decreasing the fineness of fibers can improve the filtration efficiency of nonwovens. The main reason is that the specific surface area of the fiber increases when the fiber diameter decreases, such that the fiber can intercept more particles.^4,5 The influence of fiber diameter on filtration efficiency can also be observed in the experimental results in this investigation. The values of basis weight and thickness of sample No.12 are larger than those of sample No.1, while the pore size of sample No.12 is smaller than that of sample No.1. However, the values of their respective filtration efficiencies are almost the same irrespective of the test No., as can be observed from Table 4, because the fiber diameter of sample No.1 is smaller than that of sample No.12. Similar situations can also be seen in other two sample pairs: sample No.4 and No.15; and sample No.6 and No.17. Further, the influence of parameters σ, n, and O_f on the filtration performance of spunbonded nonwoven is considered to be comparatively indirect. From among them, n can be calculated using T and d, according to equation (4). Besides, the influence of parameters σ and O_f on the filtration performance can be reflected indirectly by using parameter P_s. The reason is that the pore size can be considered to be determined by several elemental planes.²⁰ (For straight stiff fibers, the number of elemental planes Nep is 2; thus, for spunbonded nonwoven materials, Nep can be considered to be 2.) The elemental plane can be characterized using the three parameters σ, d, and O_f; therefore, the parameter P_s can reflect the information contained by parameters σ and O_f about the fiber web structure to a certain degree. Generally, the basis weight of a nonwoven plays an important role in influencing the filtration performance. The reason why the basis weight fails to be taken as the governing parameter for predicting the filtration performance according to rough set theory may be due to the fact that, according to the filtration mechanism, it is the fibers that intercept the particles. Therefore, it is the number of fibers per unit volume, the character of the fiber (including its diameter, cross-section shape, etc.) and the stacking morphology of fibers (namely the pore structure), as opposed to the weight of the fiber in a unit area that determine the filtration performance of a nonwoven. The basis weight can only influence the filtration performance of nonwovens indirectly.¹⁸

In order to ascertain whether r₁ is indeed the most representative reduct of O_s for predicting the filtration performance of spunbonded nonwoven, the structural parameter subsets obtained using the methods “r₁ − 1” (corresponding to two input parameters) or “r₁ + 1” (corresponding to four input parameters) were taken as the inputs for SVM and BP-ANN-based models. The notation “1” in “r₁ − 1” indicates one of the parameters in “r₁” and the notation “1” in “r₁ + 1” indicates one of the parameters in the subset “O_s − r₁” consisting of μ, σ, n, O_f, ϕ and V_p. The process of parameter optimization and prediction calculation is the same as those of the models taking r₁, r₂, r₃, r₄, and O_s as their inputs. Table 10 shows the parameter optimization and Table 11 shows the filtration performance prediction results.
Table 10.
Parameter optimizing results of models taking “r₁ − 1” and “r₁ + 1” as the inputs

Structural parameters Test No. Filtration efficiency
Pressure drop

SVM
BP-ANN (nodes in the hidden layer) SM
BP-ANN (nodes in the hidden layer)

W C η W C η

T, d 1 12 3000 0.13 7 3 3200 0.03 8

2 13 3500 0.11 4 2 2200 0.03 6

3 11 2800 0.14 5 2 2500 0.01 6

4 9 27000 0.10 4 2 2100 0.01 9

5 9 32000 0.11 6 2 3300 0.02 4

T, P_s 1 11 3300 0.09 8 120 1100 0.17 7

2 3 1100 0.12 7 125 1200 0.16 5

3 130 1000 0.13 7 140 900 0.11 7

4 3 800 0.15 9 150 700 0.14 6

5 3 1000 0.23 5 170 500 0.10 4

d, P_s 1 3 1800 0.26 7 160 800 0.11 8

2 3 2100 0.15 6 140 900 0.09 6

3 4 2300 0.21 8 180 600 0.12 5

4 4 2400 0.20 7 140 700 0.11 7

5 4 2600 0.24 4 110 900 0.18 9

μ, T, d, P_s 1 21 6300 0.22 8 34 2500 0.13 5

2 23 80 0.19 5 32 2200 0.11 5

3 19 80 0.21 7 30 2300 0.16 7

4 21 2500 0.22 6 31 2100 0.10 8

5 25 80 0.23 4 35 2700 0.14 8

T, σ, d, P_s 1 6 5200 0.31 7 11 2200 0.29 10

2 8 5500 0.32 8 11 2600 0.28 9

3 10 5800 0.30 6 11 2300 0.27 10

4 10 5900 0.31 4 11 2400 0.28 4

5 10 6200 0.30 9 11 2600 0.26 7

T, n, d, P _s 1 6 5400 0.31 9 10 2200 0.34 9

2 8 5500 0.31 11 10 2500 0.33 10

3 16 5400 0.35 8 10 2700 0.29 8

4 16 4900 0.34 7 10 2800 0.29 9

5 18 5300 0.33 9 10 2900 0.30 9

T, d, O_f , P_s 1 6 5800 0.33 6 10 2900 0.31 7

2 8 4800 0.32 4 10 2000 0.36 5

3 16 5600 0.37 5 10 2600 0.28 6

4 16 4700 0.35 4 10 2700 0.27 7

5 18 5100 0.36 7 10 2400 0.33 6

T, d, ϕ, P_s 1 6 5900 0.38 8 10 3400 0.35 6

2 10 5200 0.27 9 10 2300 0.34 8

3 16 6400 0.38 6 10 2400 0.36 4

4 16 4900 0.39 8 10 1900 0.29 5

5 18 5300 0.37 5 10 2200 0.32 6

T, d, P_s, v 1 24 70 0.33 10 40 2600 0.12 9

2 30 70 0.18 8 32 2300 0.11 8

3 45 80 0.22 7 30 2400 0.16 6

4 25 80 0.34 5 32 2300 0.11 4

5 70 80 0.24 9 34 2600 0.15 7

Table 11.
Filtration performance predicting results of models taking “r₁ − 1” and “r₁ + 1” as the inputs

Structural parameters Test No. Filtration efficiency
Pressure drop

SVM
BP-ANN
SVM
BP-ANN

MPA (%) CV (%) MPA (%) CV (%) MPA (%) CV (%) MPA (%) CV (%)

T, d 1 95.69 3.14 93.37 4.28 87.21 8.14 85.79 9.55

2 94.85 5.19 93.02 5.07 86.27 11.45 85.18 13.43

3 94.47 4.19 92.85 5.55 86.91 10.71 85.21 12.46

4 94.79 3.87 93.19 5.41 86.95 10.68 84.60 12.09

5 94.86 3.18 92.74 4.90 85.14 10.89 83.35 12.62

T, P_s 1 96.50 2.50 94.23 2.96 89.88 9.89 87.47 12.11

2 94.91 5.76 92.46 7.38 89.79 9.62 86.92 11.70

3 96.99 1.75 95.51 2.85 88.11 14.22 86.04 14.72

4 96.88 2.66 95.50 3.72 89.17 9.92 86.28 10.66

5 95.60 4.53 94.38 6.71 86.06 17.40 87.43 16.26

d, P_s 1 93.29 5.58 91.96 6.03 90.20 11.78 88.54 12.29

2 92.11 7.90 90.64 8.99 90.92 10.24 89.04 12.35

3 94.19 6.01 92.17 6.73 90.81 9.11 89.91 11.28

4 94.60 5.85 94.23 6.44 90.27 9.93 88.27 12.24

5 95.60 4.25 94.45 6.19 91.85 8.11 89.96 9.19

μ, T, d, P_s 1 97.51 2.16 96.02 2.75 96.04 3.50 95.57 4.82

2 97.27 2.58 96.68 3.03 97.85 1.57 96.15 1.98

3 97.66 2.49 96.24 3.74 96.76 3.19 95.77 4.04

4 97.86 1.71 96.88 2.56 97.30 1.87 96.40 2.73

5 97.21 2.12 96.13 2.67 97.14 2.06 95.49 2.92

T, σ, d, P_s 1 96.91 3.48 95.93 3.94 94.84 4.16 94.08 6.26

2 96.92 3.04 96.40 3.79 95.81 3.79 94.61 4.59

3 97.78 2.08 96.37 3.43 95.76 3.48 94.17 5.45

4 97.61 2.16 96.85 2.81 95.24 3.89 94.56 5.01

5 97.31 2.41 96.29 3.04 96.13 3.11 95.22 4.18

T, n, d, P_s 1 97.44 2.76 96.61 3.16 94.25 4.78 93.54 5.65

2 97.34 2.45 96.72 2.95 95.87 3.33 94.75 5.26

3 97.27 1.94 96.83 2.58 95.52 4.44 94.34 6.32

4 97.91 1.57 97.04 2.23 95.20 4.59 95.58 4.30

5 97.62 1.53 96.47 1.89 95.73 3.94 94.19 4.45

T, d, O_f , P_s 1 97.74 2.50 96.20 3.07 94.40 4.66 93.96 5.77

2 97.40 2.37 97.85 2.24 95.71 3.48 94.71 5.42

3 97.76 1.54 96.59 2.46 95.52 4.96 93.89 6.06

4 98.20 1.64 97.36 2.72 95.35 4.61 94.44 5.91

5 97.72 1.36 96.61 1.82 95.15 5.75 94.05 6.18

T, d, ϕ, P_s 1 97.82 2.92 96.48 3.14 93.92 5.31 92.88 5.85

2 97.42 2.14 97.67 2.69 95.20 3.61 94.50 5.39

3 97.72 1.58 96.52 2.70 95.18 4.61 94.12 6.24

4 98.00 1.59 97.23 2.81 95.02 4.41 93.76 5.92

5 97.51 1.67 96.84 1.58 96.20 3.45 94.83 4.14

T, d, P_s, v 1 96.80 3.38 95.90 3.65 95.34 3.96 94.07 5.05

2 97.43 1.51 96.35 2.47 96.39 3.40 95.66 4.73

3 97.38 1.85 96.71 1.81 95.31 6.53 94.29 7.81

4 97.66 1.71 97.13 2.25 96.16 5.03 95.25 5.87

5 97.11 1.91 96.44 2.78 96.46 3.34 94.91 4.26

It can be observed from Table 11 that irrespective of the type of model (SVM-based or BP-ANN-based) or the test parameters (filtration velocity and particle size), the prediction accuracy (MPA and CV) of all the models taking either “r₁ − 1” or “r₁ + 1” as their inputs are worse than that of the models taking r₁ as their input. In addition, apart from the models that take T, P_s as inputs to predict the filtration efficiencies in Test No.1 and Test No.3, the prediction accuracy of the models taking “r₁ − 1” as their input is worse than that of the models taking O_s as their input. Therefore, the absence of any one parameter in r₁ will deteriorate the prediction accuracy of the model. Moreover, all models taking “r₁ + 1” as their inputs demonstrate a relatively high predictive power because all the MPAs of the predicted values are higher than 92%, and all the CVs of the predicted values are lower than 8%. Furthermore, among all the 240 prediction accuracy values (MPA and CV) of these models, 88.33% of them, that is, 212 values are better than their counterparts in the model taking O_s as its input, indicating that a model whose input includes r₁ demonstrates good prediction ability. All the above results further prove the conclusion that r₁ is the most representative reduct of O_s for predicting the filtration performance of spunbonded nonwoven.

Besides, the results in Tables 9 and 11 indicate that the prediction accuracy of the SVM-based models exceeds that of the BP-ANN-based models, because among 280 prediction accuracy values (MPA and CV) predicted by SVM-based models, 94.29% of them, that is, 264 values were better than their counterparts predicted by BP-ANN-based models. This can be attributed to the improved generalization capacity and ability of the SVM-based models to handle noisy data as compared to the BP-ANN models. In summary, the SVM-based model that takes thickness, fiber diameter, and pore size as its input parameters is the best fit equation to predict the filtration efficiency or pressure drop of spunbonded nonwoven.

Conclusion

RS theory was applied to simplify the inputs of SVM- and BP-ANN-based models for predicting the filtration performance of spunbonded nonwoven. As a result, the number of input parameters decreased from nine to three after attribute reduction, greatly improving the working efficiency. The most informative reduct, r₁, consisted of thickness, fiber diameter, and pore size parameters. The accuracy of prediction models taking r₁ as their input was higher than that of the models taking the original structural parameter set of the fiber web as their input. In addition, the predictive power of the SVM model was found to be superior to that of the BP-ANN model. Therefore, it can be concluded that thickness, fiber diameter, and pore size are the key factors influencing the filtration performance of spunbonded nonwoven, and the RS–SVM-based model could be an effective method for predicting the filtration performance of these materials. However, the influence of the other six parameters (μ, σ, n, O_f, ϕ, v) on the filtration performance of spunbonded nonwoven should not be considered negligible. They are only of lesser importance in predicting the filtration efficiency and pressure drop of these materials compared with parameters T, d, and P_s.

Sample No.	μ	T	d	O_f	P_s
1	81.7	3.25	0.448	4.36	22.34	8.55	0.0256	6.71	19.9	80.90
2	74.1	4.79	0.430	3.23	22.26	6.87	0.0630	3.45	27.2	64.34
3	66.4	3.40	0.416	2.25	21.96	8.11	0.1152	5.09	29.4	57.48
4	58.0	4.92	0.407	3.29	22.31	9.91	0.1781	4.48	34.1	48.09
5	52.1	3.77	0.386	5.14	21.82	7.88	0.2306	3.92	41.3	44.07
6	89.3	2.05	0.482	4.92	23.01	8.26	0.0305	5.51	17.3	93.64
7	81.4	3.61	0.456	4.70	22.87	7.56	0.0597	5.18	20.5	80.98
8	71.2	2.88	0.434	3.55	22.91	9.30	0.1125	3.94	28.2	67.02
9	62.8	4.24	0.421	2.93	23.13	5.53	0.1674	2.75	32.7	57.49
10	56.2	3.75	0.408	4.58	22.97	6.31	0.2320	4.90	37.6	49.20
11	98.2	2.62	0.519	3.64	23.76	9.51	0.0278	3.07	16.7	105.99
12	86.4	3.49	0.477	5.51	23.70	7.81	0.0589	5.38	18..0	90.56
13	74.6	5.33	0.449	2.60	23.87	8.09	0.1097	6.12	24.0	72.08
14	66.3	4.36	0.436	3.59	23.53	7.10	0.1766	3.67	30.8	62.01
15	59.7	3.71	0.426	2.82	23.62	8.13	0.2258	4.26	33.5	54.63
16	107.2	3.90	0.548	4.46	24.15	6.79	0.0283	5.30	13.3	127.07
17	91.6	2.83	0.497	4.71	24.26	6.43	0.0665	2.99	17.2	102.33
18	80.6	5.22	0.472	1.76	24.04	4.62	0.1217	6.03	20.8	84.62
19	71.1	3.15	0.454	4.63	24.31	7.28	0.1713	4.74	28.6	74.48
20	64.8	3.48	0.441	3.90	24.37	7.84	0.2247	5.52	32.0	67.50
21	117.8	2.32	0.569	1.94	24.83	5.72	0.0229	4.01	11.0	148.18
22	99.6	4.68	0.533	5.44	24.77	6.90	0.0632	2.78	16.3	136.81
23	89.1	5.17	0.496	4.61	24.67	9.32	0.1144	5.75	17.5	113.14
24	78.4	2.26	0.475	5.84	24.51	7.18	0.1660	3.67	23.8	99.58
25	69.5	4.73	0.457	4.49	24.90	7.51	0.2268	6.36	29.2	79.11
26	127.7	1.89	0.604	1.73	25.22	8.33	0.0287	3.81	10.3	175.73
27	109.8	3.21	0.579	2.77	25.38	7.37	0.0626	4.92	12.2	145.90
28	96.3	4.67	0.528	4.32	25.41	6.77	0.1111	2.83	16.9	130.77
29	82.8	3.98	0.490	3.17	25.29	7.20	0.1743	6.56	18.9	119.58
30	74.4	3.25	0.473	3.30	25.34	8.64	0.2351	3.10	26.3	92.02

Sample No.	μ (g/m²)	T (mm)	σ (km/m²)	n	d (µm)	O_f	ϕ (%)	P_s (µm)	V_P (%)
1	81.7	0.448	22.843	10.03	22.34	0.0256	79.96	19.9	80.90
2	74.0	0.430	21.634	9.66	22.26	0.0630	81.09	27.2	64.34
3	66.4	0.416	20.340	9.47	21.96	0.1152	82.46	29.4	57.48
4	58.0	0.407	17.874	9.12	22.31	0.1781	84.34	34.1	48.09
5	52.1	0.386	17.310	8.85	21.82	0.2306	85.17	41.3	44.07
6	89.3	0.482	22.531	10.47	23.01	0.0305	79.64	17.3	93.64
7	81.4	0.456	21.842	9.97	22.87	0.0597	80.38	20.5	80.98
8	71.2	0.434	20.038	9.47	22.91	0.1125	81.97	28.2	67.02
9	62.8	0.421	18.047	9.10	23.13	0.1674	83.61	32.7	57.49
10	56.2	0.408	16.781	8.88	22.97	0.2320	84.86	37.6	49.20
11	98.2	0.519	22.284	10.92	23.76	0.0278	79.21	16.7	105.99
12	86.4	0.477	21.387	10.06	23.70	0.0589	80.10	18.0	90.56
13	74.6	0.449	19.478	9.41	23.87	0.1097	81.74	24.0	72.08
14	66.3	0.436	18.084	9.26	23.53	0.1766	83.29	30.8	62.01
15	59.7	0.426	16.603	9.02	23.62	0.2258	84.60	33.5	54.63
16	107.2	0.548	22.667	11.35	24.15	0.0283	78.50	13.3	127.07
17	91.6	0.497	21.259	10.24	24.26	0.0665	79.75	17.2	102.33
18	80.6	0.472	19.877	9.82	24.04	0.1217	81.23	20.8	84.62
19	71.1	0.454	18.027	9.34	24.31	0.1713	82.79	28.6	74.48
20	64.8	0.441	16.873	9.05	24.37	0.2247	83.85	32.0	67.50
21	117.8	0.569	23.332	11.46	24.83	0.0229	77.25	11.0	148.18
22	99.6	0.533	21.111	10.76	24.77	0.0632	79.47	16.3	136.81
23	89.1	0.496	20.376	10.05	24.67	0.1144	80.26	17.5	113.14
24	78.4	0.475	18.844	9.69	24.51	0.1660	81.86	23.8	99.58
25	69.5	0.457	17.091	9.18	24.90	0.2268	83.29	29.2	79.11
26	127.7	0.604	23.459	11.97	25.22	0.0287	76.77	10.3	175.73
27	109.8	0.579	20.909	11.41	25.38	0.0626	79.16	12.2	145.90
28	96.3	0.528	20.086	10.39	25.41	0.1111	79.96	16.9	130.77
29	82.8	0.490	18.698	9.69	25.29	0.1743	81.43	18.9	119.58
30	74.4	0.473	17.370	9.33	25.34	0.2351	82.72	26.3	92.02

Test No.	Test parameters
1	3.5	0.3
2	5.3	0.1
3	5.3	0.3
4	5.3	0.5
5	7.3	0.3

Sample No.	Filtering performance	Test No.
1	FE	28.93	4.93	11.12	6.16	25.11	4.78	37.61	4.86	20.89	7.12
ΔP	3.34	5.29	4.84	5.23	4.84	6.89	4.83	7.03	6.80	4.53
2	FE	24.06	7.10	9.24	4.55	21.85	7.04	30.54	5.46	16.95	5.87
ΔP	2.03	4.56	2.73	5.47	2.70	3.46	2.71	5.90	3.91	6.30
3	FE	22.70	5.54	8.87	6.80	20.55	6.55	28.15	4.85	16.06	5.11
ΔP	1.65	7.85	2.27	4.43	2.26	6.13	2.24	6.14	3.09	3.88
4	FE	20.89	3.49	7.11	5.62	17.27	3.27	26.32	5.15	15.34	7.48
ΔP	1.24	6.44	1.72	6.89	1.70	5.44	1.73	7.41	2.41	6.39
5	FE	19.16	8.61	6.93	7.35	15.50	8.21	23.24	7.70	13.55	4.16
ΔP	0.74	5.25	1.04	4.29	1.04	4.62	1.03	5.18	1.51	6.85
6	FE	29.54	5.72	11.92	6.77	25.79	6.67	39.73	6.45	21.78	6.20
ΔP	4.31	6.70	5.97	8.08	6.02	7.05	5.89	5.56	8.49	5.41
7	FE	26.01	4.88	10.40	5.20	23.17	5.30	36.83	6.53	19.40	3.55
ΔP	3.00	6.35	4.44	5.39	4.41	4.19	4.44	5.07	6.01	7.78
8	FE	23.80	6.06	9.58	6.17	20.74	6.70	30.07	6.72	17.88	5.92
ΔP	1.89	4.92	2.70	5.82	2.73	5.54	2.73	5.44	3.88	5.15
9	FE	22.85	5.75	7.92	4.44	18.84	4.39	28.45	7.19	16.48	8.25
ΔP	1.46	5.51	2.04	5.90	2.01	7.81	2.01	5.67	2.95	5.42
10	FE	19.98	3.99	7.33	9.18	16.30	7.97	24.50	7.24	14.10	4.79
ΔP	0.89	8.38	1.24	6.52	1.27	5.92	1.24	6.51	1.69	6.11
11	FE	30.19	4.62	12.22	6.78	27.13	6.36	41.24	3.89	22.15	3.76
ΔP	4.58	7.24	6.64	5.37	6.59	5.16	6.72	6.29	9.07	7.55
12	FE	28.94	6.57	11.13	4.21	25.15	5.42	37.55	4.75	20.86	6.09
ΔP	3.90	4.23	5.78	4.79	5.83	3.38	5.70	6.16	8.07	4.99
13	FE	26.31	4.80	9.90	6.85	22.44	5.74	32.71	4.49	19.45	5.78
ΔP	2.92	6.84	4.02	7.22	3.98	7.85	3.99	7.04	5.66	5.05
14	FE	23.37	6.11	8.92	5.84	19.97	4.49	30.25	5.85	17.48	6.13
ΔP	1.69	4.04	2.47	6.10	2.48	6.20	2.51	4.79	3.54	4.57
15	FE	20.71	4.38	7.58	6.59	17.11	6.19	26.08	6.33	15.29	5.60
ΔP	1.21	6.35	1.58	7.46	1.62	8.33	1.63	4.70	2.14	7.91
16	FE	34.64	5.27	13.07	5.51	28.53	5.25	43.04	8.18	24.58	4.96
ΔP	5.90	6.63	8.27	6.73	8.28	4.45	8.20	6.41	11.33	6.77
17	FE	29.41	4.12	11.79	4.66	25.42	7.03	39.64	5.55	21.79	7.40
ΔP	4.69	5.13	6.41	6.17	6.34	3.43	6.41	3.96	9.11	5.56
18	FE	26.80	6.03	10.50	6.79	23.24	7.47	36.78	7.42	19.62	6.31
ΔP	3.55	4.79	5.03	4.92	4.95	5.62	4.98	6.36	6.97	6.29
19	FE	25.72	6.49	9.48	5.54	21.01	6.03	30.91	4.50	17.60	6.98
ΔP	2.17	6.67	2.98	5.89	3.03	5.95	3.03	6.17	4.14	4.84
20	FE	23.91	4.54	8.71	6.23	19.64	4.40	29.07	5.39	16.83	3.93
ΔP	1.79	6.18	2.47	4.85	2.47	6.23	2.50	4.22	3.48	6.23
21	FE	36.82	4.73	13.98	6.47	30.80	4.88	44.80	7.53	24.83	9.09
ΔP	6.75	3.85	9.46	4.94	9.53	5.58	9.47	4.66	13.24	5.52
22	FE	31.35	2.96	12.32	6.28	26.24	3.71	41.55	3.85	22.45	3.17
ΔP	4.99	5.93	7.08	3.77	7.09	5.94	7.03	5.99	10.58	4.66
23	FE	29.93	5.21	11.91	5.30	25.16	5.64	37.71	5.58	21.66	5.04
ΔP	4.67	4.49	6.47	4.87	6.46	7.50	6.51	6.76	9.03	6.26
24	FE	27.18	4.08	10.02	5.95	22.65	5.85	34.32	4.14	19.16	4.95
ΔP	2.99	6.62	4.11	6.29	4.12	6.09	4.15	5.28	6.11	6.47
25	FE	25.97	6.55	9.73	4.11	20.31	3.55	31.07	6.80	17.66	4.49
ΔP	2.09	5.35	3.08	7.34	3.08	7.67	3.06	6.34	4.21	6.50
26	FE	39.12	5.86	14.51	6.50	32.55	3.42	48.72	5.11	28.06	3.82
ΔP	7.83	4.84	11.04	4.64	11.04	4.91	11.05	4.94	15.47	4.89
27	FE	36.53	4.30	13.37	3.70	29.08	6.22	43.63	3.76	23.94	6.62
ΔP	6.65	5.77	9.16	5.96	9.14	5.15	9.15	4.10	13.10	7.17
28	FE	32.28	6.57	11.93	6.76	27.47	5.76	41.17	7.16	23.71	5.05
ΔP	5.59	5.46	7.75	7.27	7.70	4.10	7.75	5.22	11.13	6.56
29	FE	30.01	4.96	11.20	6.89	25.21	6.12	38.56	4.24	21.26	3.64
ΔP	4.09	6.42	5.88	5.09	5.88	4.99	5.94	6.81	8.36	6.13
30	FE	27.47	6.18	9.77	5.97	22.83	6.54	32.91	5.97	19.36	6.82
ΔP	2.55	4.09	3.70	4.30	3.72	5.33	3.70	6.23	5.34	5.70

Sample No.	μ	T	σ	n	d	O_f	ϕ	P_s	V_P
1	1	0	2	1	0	0	1	0	0
2	0	0	2	0	0	0	1	1	0
3	0	0	1	0	0	1	2	1	0
4	0	0	0	0	0	2	2	2	0
5	0	0	0	0	0	2	2	2	0
6	1	1	2	1	0	0	1	0	1
7	1	0	2	1	0	0	1	0	0
8	0	0	1	0	0	1	1	1	0
9	0	0	0	0	1	2	2	2	0
10	0	0	0	0	0	2	2	2	0
11	1	1	2	1	1	0	0	0	1
12	1	1	2	1	1	0	1	0	1
13	0	0	1	0	1	1	1	1	0
14	0	0	0	0	1	2	2	1	0
15	0	0	0	0	1	2	2	2	0
16	2	2	2	2	1	0	0	0	1
17	1	1	2	1	2	0	1	0	1
18	1	1	1	0	1	1	1	1	0
19	0	0	0	0	2	2	2	1	0
20	0	0	0	0	2	2	2	2	0
21	2	2	2	2	2	0	0	0	2
22	1	2	1	1	2	0	0	0	2
23	1	1	1	1	2	1	1	0	1
24	1	1	0	0	2	2	1	1	1
25	0	0	0	0	2	2	2	1	0
26	2	2	2	2	2	0	0	0	2
27	2	2	1	2	2	0	0	0	2
28	1	1	1	1	2	1	1	0	1
29	1	1	0	0	2	2	1	0	1
30	0	1	0	0	2	2	2	1	1

Inputs	Model	Outputs
r₁ = {T, d, P_s}	SVM	Filtering efficiency
BP-ANN
SVM	Pressure drop
BP-ANN
r₂ = {T, d, O_f}	SVM	Filtering efficiency
BP-ANN
SVM	Pressure drop
BP-ANN
r₃ = {T, σ, d}	SVM	Filtering efficiency
BP-ANN
SVM	Pressure drop
BP-ANN
r₄ = {T, n, d}	SVM	Filtering efficiency
BP-ANN
SVM	Pressure drop
BP-ANN
O_s = {#x003BC;, T, σ, n, d, O_f, ϕ, P_s, V_P}	SVM	Filtering efficiency
BP-ANN
SVM	Pressure drop
BP-ANN

Structural parameters	Test No.	Filtration efficiency	Pressure drop
r ₁	1	14	1000	0.08	4	30	1500	0.04	5
2	18	900	0.10	5	30	1500	0.04	5
3	16	1100	0.06	7	28	1400	0.05	6
4	26	900	0.09	6	31	1600	0.03	7
5	23	1200	0.07	6	29	1700	0.05	4
r ₂	1	2	9500	0.22	7	6	8800	0.24	7
2	2	9300	0.23	8	6	8900	0.25	7
3	1.5	8600	0.16	4	7	9400	0.29	6
4	3	8100	0.26	6	7	7900	0.33	6
5	2	6700	0.35	5	6	8400	0.25	7
r ₃	1	90	5700	0.06	7	30	5700	0.06	6
2	15	1600	0.10	4	27	17000	0.08	5
3	11	17000	0.12	6	31	21000	0.04	7
4	22	6300	0.03	8	30	15000	0.05	5
5	38	4900	0.02	6	25	16000	0.10	5
r ₄	1	33	1900	0.08	5	12	1100	0.07	4
2	34	1300	0.06	8	15	900	0.01	7
3	24	2000	0.12	7	9	1200	0.07	7
4	29	2200	0.13	5	13	800	0.11	6
5	28	2300	0.15	6	8	700	0.10	9
O_s	1	39	70	0.02	8	40	70	0.02	9
2	35	70	0.01	7	38	45	0.03	8
3	42	75	0.05	6	39	30	0.12	8
4	41	70	0.01	9	43	35	0.04	4
5	90	70	0.02	7	46	40	0.08	7

Sample No.	Predicted values	Tested values
2	23.75	24.69	24.06
11	30.50	29.62	30.19
14	24.01	24.12	23.37
30	27.26	28.20	27.47

Structural parameters	Test No.	Filtration efficiency	Pressure drop
r ₁	1	98.04	1.86	97.33	2.12	97.07	2.17	96.44	2.69
2	97.69	1.82	97.03	2.45	98.24	1.25	97.50	1.52
3	98.03	1.44	96.64	1.88	98.82	1.06	98.01	1.75
4	98.55	1.58	98.13	1.96	98.39	1.28	97.83	1.90
5	97.99	1.55	97.26	1.94	97.71	1.80	97.12	2.55
r ₂	1	96.38	3.04	95.49	3.90	88.96	14.00	89.39	13.91
2	95.44	5.73	94.51	5.34	88.68	14.48	86.26	15.84
3	96.79	2.93	94.70	4.22	89.02	14.15	87.95	17.03
4	96.39	3.58	94.66	4.71	89.72	14.31	88.48	16.17
5	96.02	2.97	95.15	4.09	89.32	12.59	87.67	14.68
r ₃	1	96.68	3.06	95.39	3.68	87.72	10.73	87.09	12.35
2	96.44	2.78	95.26	4.13	89.36	11.89	88.19	13.46
3	97.41	2.09	96.17	2.88	89.87	12.25	88.83	13.59
4	95.58	3.87	94.43	5.67	89.77	12.66	88.78	12.12
5	96.22	3.17	95.24	4.37	89.29	11.49	88.06	13.50
r ₄	1	97.40	2.59	96.43	3.16	88.98	6.62	87.25	7.81
2	94.83	4.32	95.11	5.98	90.23	6.83	88.40	8.03
3	95.56	3.27	94.04	4.62	88.44	6.98	89.49	8.92
4	95.83	3.17	93.87	4.73	90.55	6.62	88.26	8.16
5	95.34	2.78	94.25	3.99	89.13	7.08	88.17	8.74
O_s	1	96.89	3.01	95.77	3.32	94.27	5.63	93.83	6.89
2	96.61	2.69	95.72	3.25	95.14	5.96	94.21	7.34
3	97.10	2.84	96.03	3.86	94.90	5.96	93.28	7.94
4	97.37	2.57	96.19	3.42	94.38	5.44	93.13	7.32
5	97.09	1.88	95.96	2.44	94.43	3.03	93.37	3.90

Structural parameters	Test No.	Filtration efficiency	Pressure drop
T, d	1	12	3000	0.13	7	3	3200	0.03	8
2	13	3500	0.11	4	2	2200	0.03	6
3	11	2800	0.14	5	2	2500	0.01	6
4	9	27000	0.10	4	2	2100	0.01	9
5	9	32000	0.11	6	2	3300	0.02	4
T, P_s	1	11	3300	0.09	8	120	1100	0.17	7
2	3	1100	0.12	7	125	1200	0.16	5
3	130	1000	0.13	7	140	900	0.11	7
4	3	800	0.15	9	150	700	0.14	6
5	3	1000	0.23	5	170	500	0.10	4
d, P_s	1	3	1800	0.26	7	160	800	0.11	8
2	3	2100	0.15	6	140	900	0.09	6
3	4	2300	0.21	8	180	600	0.12	5
4	4	2400	0.20	7	140	700	0.11	7
5	4	2600	0.24	4	110	900	0.18	9
μ, T, d, P_s	1	21	6300	0.22	8	34	2500	0.13	5
2	23	80	0.19	5	32	2200	0.11	5
3	19	80	0.21	7	30	2300	0.16	7
4	21	2500	0.22	6	31	2100	0.10	8
5	25	80	0.23	4	35	2700	0.14	8
T, σ, d, P_s	1	6	5200	0.31	7	11	2200	0.29	10
2	8	5500	0.32	8	11	2600	0.28	9
3	10	5800	0.30	6	11	2300	0.27	10
4	10	5900	0.31	4	11	2400	0.28	4
5	10	6200	0.30	9	11	2600	0.26	7
T, n, d, P _s	1	6	5400	0.31	9	10	2200	0.34	9
2	8	5500	0.31	11	10	2500	0.33	10
3	16	5400	0.35	8	10	2700	0.29	8
4	16	4900	0.34	7	10	2800	0.29	9
5	18	5300	0.33	9	10	2900	0.30	9
T, d, O_f , P_s	1	6	5800	0.33	6	10	2900	0.31	7
2	8	4800	0.32	4	10	2000	0.36	5
3	16	5600	0.37	5	10	2600	0.28	6
4	16	4700	0.35	4	10	2700	0.27	7
5	18	5100	0.36	7	10	2400	0.33	6
T, d, ϕ, P_s	1	6	5900	0.38	8	10	3400	0.35	6
2	10	5200	0.27	9	10	2300	0.34	8
3	16	6400	0.38	6	10	2400	0.36	4
4	16	4900	0.39	8	10	1900	0.29	5
5	18	5300	0.37	5	10	2200	0.32	6
T, d, P_s, v	1	24	70	0.33	10	40	2600	0.12	9
2	30	70	0.18	8	32	2300	0.11	8
3	45	80	0.22	7	30	2400	0.16	6
4	25	80	0.34	5	32	2300	0.11	4
5	70	80	0.24	9	34	2600	0.15	7

Structural parameters	Test No.	Filtration efficiency	Pressure drop
T, d	1	95.69	3.14	93.37	4.28	87.21	8.14	85.79	9.55
2	94.85	5.19	93.02	5.07	86.27	11.45	85.18	13.43
3	94.47	4.19	92.85	5.55	86.91	10.71	85.21	12.46
4	94.79	3.87	93.19	5.41	86.95	10.68	84.60	12.09
5	94.86	3.18	92.74	4.90	85.14	10.89	83.35	12.62
T, P_s	1	96.50	2.50	94.23	2.96	89.88	9.89	87.47	12.11
2	94.91	5.76	92.46	7.38	89.79	9.62	86.92	11.70
3	96.99	1.75	95.51	2.85	88.11	14.22	86.04	14.72
4	96.88	2.66	95.50	3.72	89.17	9.92	86.28	10.66
5	95.60	4.53	94.38	6.71	86.06	17.40	87.43	16.26
d, P_s	1	93.29	5.58	91.96	6.03	90.20	11.78	88.54	12.29
2	92.11	7.90	90.64	8.99	90.92	10.24	89.04	12.35
3	94.19	6.01	92.17	6.73	90.81	9.11	89.91	11.28
4	94.60	5.85	94.23	6.44	90.27	9.93	88.27	12.24
5	95.60	4.25	94.45	6.19	91.85	8.11	89.96	9.19
μ, T, d, P_s	1	97.51	2.16	96.02	2.75	96.04	3.50	95.57	4.82
2	97.27	2.58	96.68	3.03	97.85	1.57	96.15	1.98
3	97.66	2.49	96.24	3.74	96.76	3.19	95.77	4.04
4	97.86	1.71	96.88	2.56	97.30	1.87	96.40	2.73
5	97.21	2.12	96.13	2.67	97.14	2.06	95.49	2.92
T, σ, d, P_s	1	96.91	3.48	95.93	3.94	94.84	4.16	94.08	6.26
2	96.92	3.04	96.40	3.79	95.81	3.79	94.61	4.59
3	97.78	2.08	96.37	3.43	95.76	3.48	94.17	5.45
4	97.61	2.16	96.85	2.81	95.24	3.89	94.56	5.01
5	97.31	2.41	96.29	3.04	96.13	3.11	95.22	4.18
T, n, d, P_s	1	97.44	2.76	96.61	3.16	94.25	4.78	93.54	5.65
2	97.34	2.45	96.72	2.95	95.87	3.33	94.75	5.26
3	97.27	1.94	96.83	2.58	95.52	4.44	94.34	6.32
4	97.91	1.57	97.04	2.23	95.20	4.59	95.58	4.30
5	97.62	1.53	96.47	1.89	95.73	3.94	94.19	4.45
T, d, O_f , P_s	1	97.74	2.50	96.20	3.07	94.40	4.66	93.96	5.77
2	97.40	2.37	97.85	2.24	95.71	3.48	94.71	5.42
3	97.76	1.54	96.59	2.46	95.52	4.96	93.89	6.06
4	98.20	1.64	97.36	2.72	95.35	4.61	94.44	5.91
5	97.72	1.36	96.61	1.82	95.15	5.75	94.05	6.18
T, d, ϕ, P_s	1	97.82	2.92	96.48	3.14	93.92	5.31	92.88	5.85
2	97.42	2.14	97.67	2.69	95.20	3.61	94.50	5.39
3	97.72	1.58	96.52	2.70	95.18	4.61	94.12	6.24
4	98.00	1.59	97.23	2.81	95.02	4.41	93.76	5.92
5	97.51	1.67	96.84	1.58	96.20	3.45	94.83	4.14
T, d, P_s, v	1	96.80	3.38	95.90	3.65	95.34	3.96	94.07	5.05
2	97.43	1.51	96.35	2.47	96.39	3.40	95.66	4.73
3	97.38	1.85	96.71	1.81	95.31	6.53	94.29	7.81
4	97.66	1.71	97.13	2.25	96.16	5.03	95.25	5.87
5	97.11	1.91	96.44	2.78	96.46	3.34	94.91	4.26

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The study was supported by the Key Laboratory of Zhejiang Industrial Textile Material and Preparation Technology Research (2012E10010).

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Sample No.	μ		T		d		O_f		P_s
Sample No.	Mean (g/m²)	CV (%)	Mean (mm)	CV (%)	Mean (µm)	CV (%)	Mean	CV (%)	Mean (µm)	CV (%)
1	81.7	3.25	0.448	4.36	22.34	8.55	0.0256	6.71	19.9	80.90
2	74.1	4.79	0.430	3.23	22.26	6.87	0.0630	3.45	27.2	64.34
3	66.4	3.40	0.416	2.25	21.96	8.11	0.1152	5.09	29.4	57.48
4	58.0	4.92	0.407	3.29	22.31	9.91	0.1781	4.48	34.1	48.09
5	52.1	3.77	0.386	5.14	21.82	7.88	0.2306	3.92	41.3	44.07
6	89.3	2.05	0.482	4.92	23.01	8.26	0.0305	5.51	17.3	93.64
7	81.4	3.61	0.456	4.70	22.87	7.56	0.0597	5.18	20.5	80.98
8	71.2	2.88	0.434	3.55	22.91	9.30	0.1125	3.94	28.2	67.02
9	62.8	4.24	0.421	2.93	23.13	5.53	0.1674	2.75	32.7	57.49
10	56.2	3.75	0.408	4.58	22.97	6.31	0.2320	4.90	37.6	49.20
11	98.2	2.62	0.519	3.64	23.76	9.51	0.0278	3.07	16.7	105.99
12	86.4	3.49	0.477	5.51	23.70	7.81	0.0589	5.38	18..0	90.56
13	74.6	5.33	0.449	2.60	23.87	8.09	0.1097	6.12	24.0	72.08
14	66.3	4.36	0.436	3.59	23.53	7.10	0.1766	3.67	30.8	62.01
15	59.7	3.71	0.426	2.82	23.62	8.13	0.2258	4.26	33.5	54.63
16	107.2	3.90	0.548	4.46	24.15	6.79	0.0283	5.30	13.3	127.07
17	91.6	2.83	0.497	4.71	24.26	6.43	0.0665	2.99	17.2	102.33
18	80.6	5.22	0.472	1.76	24.04	4.62	0.1217	6.03	20.8	84.62
19	71.1	3.15	0.454	4.63	24.31	7.28	0.1713	4.74	28.6	74.48
20	64.8	3.48	0.441	3.90	24.37	7.84	0.2247	5.52	32.0	67.50
21	117.8	2.32	0.569	1.94	24.83	5.72	0.0229	4.01	11.0	148.18
22	99.6	4.68	0.533	5.44	24.77	6.90	0.0632	2.78	16.3	136.81
23	89.1	5.17	0.496	4.61	24.67	9.32	0.1144	5.75	17.5	113.14
24	78.4	2.26	0.475	5.84	24.51	7.18	0.1660	3.67	23.8	99.58
25	69.5	4.73	0.457	4.49	24.90	7.51	0.2268	6.36	29.2	79.11
26	127.7	1.89	0.604	1.73	25.22	8.33	0.0287	3.81	10.3	175.73
27	109.8	3.21	0.579	2.77	25.38	7.37	0.0626	4.92	12.2	145.90
28	96.3	4.67	0.528	4.32	25.41	6.77	0.1111	2.83	16.9	130.77
29	82.8	3.98	0.490	3.17	25.29	7.20	0.1743	6.56	18.9	119.58
30	74.4	3.25	0.473	3.30	25.34	8.64	0.2351	3.10	26.3	92.02

Test No.	Test parameters
Test No.	Filtration velocity (cm/s)	Particle size (µm)
1	3.5	0.3
2	5.3	0.1
3	5.3	0.3
4	5.3	0.5
5	7.3	0.3

Sample No.	μ	T	σ	n	d	O_f	ϕ	P_s	V_P
1	1	0	2	1	0	0	1	0	0
2	0	0	2	0	0	0	1	1	0
3	0	0	1	0	0	1	2	1	0
4	0	0	0	0	0	2	2	2	0
5	0	0	0	0	0	2	2	2	0
6	1	1	2	1	0	0	1	0	1
7	1	0	2	1	0	0	1	0	0
8	0	0	1	0	0	1	1	1	0
9	0	0	0	0	1	2	2	2	0
10	0	0	0	0	0	2	2	2	0
11	1	1	2	1	1	0	0	0	1
12	1	1	2	1	1	0	1	0	1
13	0	0	1	0	1	1	1	1	0
14	0	0	0	0	1	2	2	1	0
15	0	0	0	0	1	2	2	2	0
16	2	2	2	2	1	0	0	0	1
17	1	1	2	1	2	0	1	0	1
18	1	1	1	0	1	1	1	1	0
19	0	0	0	0	2	2	2	1	0
20	0	0	0	0	2	2	2	2	0
21	2	2	2	2	2	0	0	0	2
22	1	2	1	1	2	0	0	0	2
23	1	1	1	1	2	1	1	0	1
24	1	1	0	0	2	2	1	1	1
25	0	0	0	0	2	2	2	1	0
26	2	2	2	2	2	0	0	0	2
27	2	2	1	2	2	0	0	0	2
28	1	1	1	1	2	1	1	0	1
29	1	1	0	0	2	2	1	0	1
30	0	1	0	0	2	2	2	1	1

Structural parameters	Test No.	Filtration efficiency				Pressure drop
		SVM			BP-ANN (nodes in the hidden layer)	SVM			BP-ANN (nodes in the hidden layer)
		W	C	η	BP-ANN (nodes in the hidden layer)	W	C	η	BP-ANN (nodes in the hidden layer)
r ₁	1	14	1000	0.08	4	30	1500	0.04	5
	2	18	900	0.10	5	30	1500	0.04	5
	3	16	1100	0.06	7	28	1400	0.05	6
	4	26	900	0.09	6	31	1600	0.03	7
	5	23	1200	0.07	6	29	1700	0.05	4
r ₂	1	2	9500	0.22	7	6	8800	0.24	7
	2	2	9300	0.23	8	6	8900	0.25	7
	3	1.5	8600	0.16	4	7	9400	0.29	6
	4	3	8100	0.26	6	7	7900	0.33	6
	5	2	6700	0.35	5	6	8400	0.25	7
r ₃	1	90	5700	0.06	7	30	5700	0.06	6
	2	15	1600	0.10	4	27	17000	0.08	5
	3	11	17000	0.12	6	31	21000	0.04	7
	4	22	6300	0.03	8	30	15000	0.05	5
	5	38	4900	0.02	6	25	16000	0.10	5
r ₄	1	33	1900	0.08	5	12	1100	0.07	4
	2	34	1300	0.06	8	15	900	0.01	7
	3	24	2000	0.12	7	9	1200	0.07	7
	4	29	2200	0.13	5	13	800	0.11	6
	5	28	2300	0.15	6	8	700	0.10	9
O_s	1	39	70	0.02	8	40	70	0.02	9
	2	35	70	0.01	7	38	45	0.03	8
	3	42	75	0.05	6	39	30	0.12	8
	4	41	70	0.01	9	43	35	0.04	4
	5	90	70	0.02	7	46	40	0.08	7

Sample No.	Predicted values		Tested values
Sample No.	SVM based model	BP-ANN based model	Tested values
2	23.75	24.69	24.06
11	30.50	29.62	30.19
14	24.01	24.12	23.37
30	27.26	28.20	27.47

Structural parameters	Test No.	Filtration efficiency				Pressure drop
		SVM		BP-ANN		SVM		BP-ANN
		MPA (%)	CV (%)	MPA (%)	CV (%)	MPA (%)	CV (%)	MPA (%)	CV (%)
r ₁	1	98.04	1.86	97.33	2.12	97.07	2.17	96.44	2.69
	2	97.69	1.82	97.03	2.45	98.24	1.25	97.50	1.52
	3	98.03	1.44	96.64	1.88	98.82	1.06	98.01	1.75
	4	98.55	1.58	98.13	1.96	98.39	1.28	97.83	1.90
	5	97.99	1.55	97.26	1.94	97.71	1.80	97.12	2.55
r ₂	1	96.38	3.04	95.49	3.90	88.96	14.00	89.39	13.91
	2	95.44	5.73	94.51	5.34	88.68	14.48	86.26	15.84
	3	96.79	2.93	94.70	4.22	89.02	14.15	87.95	17.03
	4	96.39	3.58	94.66	4.71	89.72	14.31	88.48	16.17
	5	96.02	2.97	95.15	4.09	89.32	12.59	87.67	14.68
r ₃	1	96.68	3.06	95.39	3.68	87.72	10.73	87.09	12.35
	2	96.44	2.78	95.26	4.13	89.36	11.89	88.19	13.46
	3	97.41	2.09	96.17	2.88	89.87	12.25	88.83	13.59
	4	95.58	3.87	94.43	5.67	89.77	12.66	88.78	12.12
	5	96.22	3.17	95.24	4.37	89.29	11.49	88.06	13.50
r ₄	1	97.40	2.59	96.43	3.16	88.98	6.62	87.25	7.81
	2	94.83	4.32	95.11	5.98	90.23	6.83	88.40	8.03
	3	95.56	3.27	94.04	4.62	88.44	6.98	89.49	8.92
	4	95.83	3.17	93.87	4.73	90.55	6.62	88.26	8.16
	5	95.34	2.78	94.25	3.99	89.13	7.08	88.17	8.74
O_s	1	96.89	3.01	95.77	3.32	94.27	5.63	93.83	6.89
	2	96.61	2.69	95.72	3.25	95.14	5.96	94.21	7.34
	3	97.10	2.84	96.03	3.86	94.90	5.96	93.28	7.94
	4	97.37	2.57	96.19	3.42	94.38	5.44	93.13	7.32
	5	97.09	1.88	95.96	2.44	94.43	3.03	93.37	3.90

Sample No.	μ	T	σ	n	d	O_f	ϕ	P_s	V_P
1	1	0	2	1	0	0	1	0	0
2	0	0	2	0	0	0	1	1	0
3	0	0	1	0	0	1	2	1	0
4	0	0	0	0	0	2	2	2	0
5	0	0	0	0	0	2	2	2	0
6	1	1	2	1	0	0	1	0	1
7	1	0	2	1	0	0	1	0	0
8	0	0	1	0	0	1	1	1	0
9	0	0	0	0	1	2	2	2	0
10	0	0	0	0	0	2	2	2	0
11	1	1	2	1	1	0	0	0	1
12	1	1	2	1	1	0	1	0	1
13	0	0	1	0	1	1	1	1	0
14	0	0	0	0	1	2	2	1	0
15	0	0	0	0	1	2	2	2	0
16	2	2	2	2	1	0	0	0	1
17	1	1	2	1	2	0	1	0	1
18	1	1	1	0	1	1	1	1	0
19	0	0	0	0	2	2	2	1	0
20	0	0	0	0	2	2	2	2	0
21	2	2	2	2	2	0	0	0	2
22	1	2	1	1	2	0	0	0	2
23	1	1	1	1	2	1	1	0	1
24	1	1	0	0	2	2	1	1	1
25	0	0	0	0	2	2	2	1	0
26	2	2	2	2	2	0	0	0	2
27	2	2	1	2	2	0	0	0	2
28	1	1	1	1	2	1	1	0	1
29	1	1	0	0	2	2	1	0	1
30	0	1	0	0	2	2	2	1	1

Sample No.	μ	T	σ	n	d	O_f	ϕ	P_s	V_P
1	1	0	2	1	0	0	1	0	0
2	0	0	2	0	0	0	1	1	0
3	0	0	1	0	0	1	2	1	0
4	0	0	0	0	0	2	2	2	0
5	0	0	0	0	0	2	2	2	0
6	1	1	2	1	0	0	1	0	1
7	1	0	2	1	0	0	1	0	0
8	0	0	1	0	0	1	1	1	0
9	0	0	0	0	1	2	2	2	0
10	0	0	0	0	0	2	2	2	0
11	1	1	2	1	1	0	0	0	1
12	1	1	2	1	1	0	1	0	1
13	0	0	1	0	1	1	1	1	0
14	0	0	0	0	1	2	2	1	0
15	0	0	0	0	1	2	2	2	0
16	2	2	2	2	1	0	0	0	1
17	1	1	2	1	2	0	1	0	1
18	1	1	1	0	1	1	1	1	0
19	0	0	0	0	2	2	2	1	0
20	0	0	0	0	2	2	2	2	0
21	2	2	2	2	2	0	0	0	2
22	1	2	1	1	2	0	0	0	2
23	1	1	1	1	2	1	1	0	1
24	1	1	0	0	2	2	1	1	1
25	0	0	0	0	2	2	2	1	0
26	2	2	2	2	2	0	0	0	2
27	2	2	1	2	2	0	0	0	2
28	1	1	1	1	2	1	1	0	1
29	1	1	0	0	2	2	1	0	1
30	0	1	0	0	2	2	2	1	1