Discrimination of fabric frictional sounds based on Haar features

Fabric preparation

In total, 32 pieces of fabric are involved in this study. They are manufactured with a sample loom and prewashed before testing, covering common configurations concerning material, weave structure, and fabric count, as listed in Table 1.

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Table 1.

Fabric configurations

Material	Structure	Count
Wool		1. 72 × 30
	1. Plain	2. 72 × 50
	2. Twill	3. 96 × 50
		4. 96 × 70
Cotton		1. 68 × 30
	1. Plain	2. 68 × 50
	2. Twill	3. 92 × 50
		4. 92 × 70
Silk		1. 115 × 50
	1. Plain	2. 115 × 70
	2. Satin	3. 165 × 70
		4. 165 × 90
Flax		1. 75 × 50
	1. Plain	2. 75 × 60
	2. Twill	3. 95 × 60
		4. 95 × 70

For each type of material, there are eight fabric samples with two kinds of weave structures and four kinds of warp/weft count. The initial letter of the material, the number of the structure, and the count are combined to designate a specific sample. For example, W11 refers to the wool fabric sample of plain structure and weave count 72 × 30, whereas C24 refers to the cotton fabric sample of twill and count 92 × 70.

Wave acquisition

A simple apparatus is made to capture the frictional signals, as demonstrated in Figure 1. A strip of sample fabric is fixed at one end and hooked by a tensiometer at the other. The fabric sample is protected from being creased by a pair of flat clamps at the two ends. A microphone is installed on the moving rod and connected to the computer. The microphone is horizontally 40 cm away from the fixed end of the fabric, and its height from the surface of the fabric can be adjusted by gears on the moving rod. Before acquisition, the microphone was wrapped with the same kind of fabric then and lowered to touch it to produce 5 N on the tensiometer and guarantee close contact between the microphone and the fabric. Next, the power was turned on and the starter motor allowed to drive the rod moving to the right, reaching the fixed end of fabric in 1 second. The friction wave generated in this short period is collected by the microphone with the sampling rate 8 KHZ and recorded as a waveform audio (WAV file) into the computer. Wave acquisition with this apparatus is conducted under a constant environment of 20 degrees Celsius and air humidity of 65%. OPEN IN VIEWER

Typical sound signals acquired by the apparatus are exhibited in Figure 2. As shown in the figure, these signals are non-stationary and declining, in which situation the frequency domain analysis cannot work well. Therefore, instead of FFT, the Haar feature is employed to explore the signals in this study. OPEN IN VIEWER

Haar feature space

The Haar feature is a basic tool for pattern recognition. The Haar feature (denoted as F) of a signal (denoted as V) is defined as a product of two vectors as follows:

F ( s , p ) = V ( s , p ) × H ( s )

In this equation, s , p are the scale parameter and positional parameter respectively, V ( s , p ) represents the intercepted part of the signal with position p as the central and scale s as its range, and H ( s ) represents an instance of Haar wavelet fitting in scale s. If s and p are deemed as variables, F ( s , p ) establishes a three-dimensional space, which is the so-called Haar feature space of the signal V . Considering the sampling rate in this study, the acquired wave signal contains 8000 data points, which determines the two variables s and p falling into the scope [18,000]. The Haar feature space of a signal is therefore composed of 64 million feature points.

This feature space can be visualized with grayscale mapping techniques. Taking s and p as vertical and horizontal coordinates separately, mapping values of all feature points into grayscale scope 0 ∼ 1, the visual representation of Haar feature space is illustrated in Figure 3. OPEN IN VIEWER

In Figure 3, bright spots represent the large values in the feature space whereas dark spots represent the small values. The Haar feature spaces for all signals in Figure 2 are provided in Figure 4. OPEN IN VIEWER

Building of discriminators

The Haar feature space defined by F ( s , p ) presents features at all scales and positions of the signal. On each feature point provided by a pair of coordinates (s,p), a discriminator (denoted as D ) can be established as follows:

D ( s , p ) = { 1 F ( s , p ) ≥ t s , p 0 ( o t h e r w i s e ) or { 1 F ( s , p ) ≤ t s , p 0 ( o t h e r w i s e )

Here, t s , p serves as the threshold of D (s,p). D (s,p) tells positive samples from negatives with t s , p . Namely, a sample is considered positive by D ( s , p ) when its feature value F ( s , p ) falls into a specific side of t s , p , or negative otherwise.

Thus, the key to a discriminator is ascertaining its threshold. In this study, t s , p for D ( s , p ) is required to satisfy the following criteria:

t s , p must be capable of identifying all positive specimens.

As mentioned above, eight fabric samples of wool, cotton, silk, and polyester are separately involved in this research. Any category of the four contains eight positive samples, with 24 negative ones falling beyond it. For example, when determining the threshold for D(1,2) of the wool category, feature values of F(1,2) for all 40 samples are indicated in Figure 5. OPEN IN VIEWER

As seen, the ranges of feature values of the four types significantly overlap, making it impossible to carry out an effective division with one single threshold value. Given F(1,2) of wool samples covers 0.08–0.46, the threshold should be either 0.08 or 0.46 to identify all the positive samples (criterion 1). If 0.08 is adopted and samples with F(1,2) larger than or equal to 0.08 are regarded as positive, 20 negative samples will be misjudged. If 0.46 is adopted and samples with feature values smaller than or equal to 0.46 are regarded as positive, 15 negative specimens will be misjudged.

Therefore, the latter 0.46 should be chosen to meet criterion 2 and D (1,2) is thus determined as below:

D ( 1 , 2 ) = { 1 F ' ( 1 , 2 ) ≤ 0 . 46 0 ( otherwise )

Discriminators built this way are called “relaxed” or “weak”. They approve all positive samples and a certain number of negatives. Each of them has perfect accuracy on positives, but are extremely low on negatives. The role of a single discriminator is far from enough, but massive discriminators together can make a difference as each filters out certain negatives.

Overall, 64 million discriminators are built on the feature points in the Haar feature space. All positive samples could pass these discriminators, but the possibility of a negative sample passing all of them is tiny, as suggested in Figure 6. OPEN IN VIEWER

The number of discriminators that each negative sample of wool type passed are counted and marked in the figure. As shown, the passing numbers never exceed 64 million. Namely, no negative sample passes all discriminators, which means the 64 million discriminators together have a high precision on negatives.

Moreover, the passing numbers also indicate about 96% of wool negatives are declined by 80% of all discriminators, which implies there might be a large space for optimization.

Progressive discriminators

As mentioned, there are 64 million discriminators, which allow all positive samples and some negatives through. But these discriminators cannot be put into practice immediately as their huge numbers would lead to unacceptable heavy computation. So, a certain number of discriminators are selected to establish a discrimination queue in which positive samples pass along whereas negatives are declined as soon as possible.

A qualified discriminator in the queue must be capable of declining as many negatives as possible. Meanwhile, it must remedy some deficiency of the former discriminators, namely, fix some errors made by the last discriminator selection. To meet these requirements, a weight value is assigned to each negative sample of a certain type, and the value adjusted each time according to the results of discriminators to increase the weights of samples that have been falsely identified, making the selection process tendentious to the discriminators that can fill in the existing gaps. The main steps are below:

Step 1: Build all discriminators and assign an initial weight value 1.0 to each negative sample.

Step 2: For each discriminator, calculate a score for the sum of weights of negative samples that the discriminator declines.

Step 3: Select the discriminator with highest score (denoted as D(m)) and put it into the discrimination queue.

Step 4: Double the weights for the samples that have been misjudged by D(m), and go back to Step 2.

Steps 2–4 are repeated until a specific number of discriminators has been accumulated in the queue. These queued discriminators are called “progressive discriminators” as each of them improves the former in a progressive way.

By this means the discriminators of wool are filtered to build a queue of 40,000. The wool negatives handled in the queue are illustrated in Figure 7. OPEN IN VIEWER

As shown, there is no negative sample passing through the queue that is composed of 40,000 sequential discriminators. From Figure 6 to Figure 7, the number of discriminators has been sharply reduced, although a perfect accuracy remains.

Next, discriminators are built and the queue set up for each type of the frictional signal. Then the size of the queue is increased by 5000 each time to find out the relation between the identified negatives and the number of progressive discriminators (Figure 8). OPEN IN VIEWER

For wool, it takes 40,000 progressive discriminators to identify all the negatives. For silk, 20,000 progressive discriminators are capable of identifying all the negative samples. Overall, 45,000 progressive discriminators identify 23 cotton negatives and 50,000 progressive discriminators identify 22 flax negatives.

Separability of data

The original data of frictional sound signals is handled with K-Means clustering to find out their separability under conventional manipulation. It is as shown in Figure 9. OPEN IN VIEWER

As implied in the hierarchical diagram, the samples are easy to divide into two categories with high linkage distance, but they are unfit for dividing into four categories. If a four-category separation is imposed on these samples, the results are as in Table 2. The roman numeral i, ii, iii or iv below each sample ID denotes the category for the sample.

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Table 2.

Four-category separation under clustering

W11	W12	W13	W14	W21	W22	W23	W24
Iv	ii	i	iii	i	i	i	i
C11	C12	C13	C14	C21	C22	C23	C24
Ii	ii	ii	ii	ii	i	ii	ii
S11	S12	S13	S14	S21	S22	S23	S24
Iv	iv	Iv	iv	iv	iv	i	iv
F11	F12	F13	F14	F21	F22	F23	F24
Ii	ii	Ii	ii	ii	ii	ii	ii

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Table 3.

Comparison of accuracy under clustering and progressive discriminators

	Clustering	Progressive discriminators
Wool	84.38%	100%
Cotton	68.75%	96.88%
Silk	93.75%	100%
Flax	71.88%	93.75%

As shown in Table 2, the four-category separation under clustering is far from acceptable considering the true categories of the samples. The resulting accuracy of separation under the clustering and the progressive discriminators is listed below.

It is evident that the mechanism of progressive discriminators is superior to conventional clustering.

The improved Haar feature

In this study, the Haar features provide primary data for the discrimination mechanism. Furthermore, a kind of improved Haar feature is found to be capable of delivering more detailed data, thus differentiating the signals more efficiently. This improved Haar feature (denoted as F′) is calculated as a correlation coefficient between the intercept of the signal and the instance of the Haar wavelet.

F ' ( s , p ) = corrcoef ( V ( s , p ) , H ( s ) )

Here, the function corrcoef represents the correlation coefficient. The improved Haar feature spaces corresponding to the conventional ones in Figure 4 are exhibited in Figure 10. OPEN IN VIEWER

In comparison, the improved Haar feature spaces seem better at enhancing the details. It was found that the improved Haar features participating in progressive discriminators led to a reduced size of the queue, as shown in Figure 11. OPEN IN VIEWER

Compared with Figure 8, it is implied that involving the improved Haar feature does not help in improving the performance of discrimination. This is because the improved Haar feature is built upon the conventional version and does not provide additional but a condensed feature of the data. However, it is also suggested that the numbers of discriminators can be reduced with the improved version to promote the efficiency of discrimination.

With the improved Haar feature, 35,000 progressive discriminators, decreasing by 12.5% compared to the 40,000 discriminators indicated in Figure 8, can identify all the wool negatives. Now 40,000 discriminators identify 23 cotton negatives and 35,000 discriminators identify 22 flax negatives. Even for silk, whose discriminators are necessary to identify all negatives, still keeps 20,000; the discrimination ability of each size less than 20,000 has been promoted.

The enhanced discrimination

A discriminator is built for each point in the feature space. The threshold for the discriminator is determined in the way that all positive samples are allowed through and as many negative samples are declined as possible. While approving all the positives, a single discriminator has poor precision on the negatives. But a great many discriminators together can make a difference as they can gradually eliminate the negatives. A negative sample passing over millions of discriminators is rare.

The huge number of discriminators is inefficient as they introduce a heavy load on computation. Progressive discrimination has been put forward as a solution to select effective discriminators. By constantly adjusting the weights of the negatives, making the discriminator good at handling the last missed samples inclined to be selected, the number of discriminators is sharply reduced whereas the discrimination capacity remains.

However, the discriminators, whether queued or not, are not necessarily perfect. As indicated in Figure 8 and Figure 11, the 50,000 queued discriminators for each of cotton and flax fail to achieve perfect accuracy. In fact, the 64 million discriminators together could not reach 100% accuracy for these two categories because the eight samples are not sufficient to cover the exclusive features that distinguish the categories from each other. This can be solved by introducing more samples, as shown in Figure 12. OPEN IN VIEWER

Eight more samples for cotton and flax are added separately; the two categories then can be clearly identified. In this situation, all cotton negatives can be denied by 45,000 progressive discriminators, and all flax negatives by 50,000 discriminators.

Effects of other factors

The main factors other than material involved are in the fabric count and the weave structure. It makes sense to reveal how these factors influence the discrimination performance. There are some clues to this issue suggested in Figure 7.

As observed, in all the negative wool samples, those with a low count are more likely to be declined at an early stage of the discrimination queue, whereas many of the high-count samples are declined at a later stage. In other words, the samples with a low count are easier to discriminate than those with a high count. Similarly, it is also suggested in Figure 7 that samples of plain weave are easier to examine than those of twill or satin weave.

To carry more conviction, the frequencies of low- and high-count samples distributed along the length of the queue are calculated respectively; the resulting histogram is shown in Figure 13. OPEN IN VIEWER

Here, the low-count samples refer to those of the first two count configurations in the material category, and the high-count ones refer to those of the last two. For each category there are 24 negatives: 12 low- and 12 high-count samples. Thus, there are 96 negatives of all four categories, including 48 low-count samples and 48 high.

As indicated in Figure 13, the low-count samples concentrate the distribution in 0.3, whereas the high-count ones are distributed mainly in 0.6. Thus, there is clear evidence that the fabrics of low count are easy to discriminate with this mechanism compared to those with a high count.

Likewise, the frequencies of different weave structures can also be calculated to uncover the effect of weave structure on discrimination, as illustrated in Figure 14. OPEN IN VIEWER

According to the figure, the plain weave samples concentrate in about 0.5, and the twill/satin samples are centered around 0.7. Therefore, the fabrics of plain weave are easier to discriminate than those of twill and satin weave.