Characterizing the total within-sample variation in cotton fiber length using the High Volume Instrument fibrogram

Abstract

Within-sample variation in cotton fiber length is important when explaining variation in yarn quality. However, typical High Volume Instrument (HVI) length parameters, the Upper Half Mean Length (UHML) and Uniformity Index (UI), do not characterize the total within-sample variation in fiber length. HVI fiber length measurements are based on the fibrogram principle where the HVI generates a curve called a fibrogram and reports the UHML and UI. Our results, based on 19,628 commercial bales, reveal that the typical HVI length measurements do not characterize unique types of length variation. Fibrograms from a subset of 538 commercial samples suggest that the fibrograms capture additional within-sample variation in fiber length that is not being currently reported. Two additional sets of samples were then used to evaluate the importance of this additional length variation. Partial Least Square Regression models and leave-one-out cross-validation reveal that the HVI fibrogram explains yarn quality better than current HVI length parameters and is comparable with the Advanced Fiber Information System (AFIS) length distribution by number. The validation results show that the models built with the HVI fibrogram are better than models with the current HVI length parameters and at least as good as the AFIS length distribution by number when predicting yarn quality. Fiber length variation captured by the whole fibrogram could provide a new tool to breeders for selecting breeding lines and spinners for purchasing cotton bales.

Keywords

fiber length distribution High Volume Instrument Advanced Fiber Information System fibrogram fiber quality yarn quality

Cotton fiber is a naturally produced industrial raw material that exhibits within-sample variation in length and other fiber quality attributes. Longer fibers in a bale are important because, everything else being equal, samples with a longer average fiber length allow spinners to produce finer and stronger yarns.^1–3 The average fiber length is not the only important length parameter.^4–6 Samples with high levels of length variation among fibers result in an increased number of imperfections in the yarn, slower processing speeds, and increased waste.^3,7–10

High Volume Instrument (HVI) testing is widely used for cotton classification and research. Breeders often use HVI cotton fiber length measurements along with other fiber properties to select their breeding lines and ultimately release cultivars that fulfill the demand of the textile industry.^11,12 HVI length parameters, the Upper Half Mean Length (UHML) and Uniformity Index (UI), are often the only fiber length measurements available to spinners purchasing US cotton bales.¹³

Processes from harvesting to ginning and cleaning break fibers alter the within-sample distribution of fiber length.^14–16 Even spinning processes can degrade fiber quality by breaking fibers and, as a result, the quality of fiber in the yarn is not the same as the quality of the raw fiber.^17,18

HVI fiber length measurements are based on the fibrogram principle originally proposed by Hertel.¹⁹ In order to measure fiber length using this principle, a comb collects a sample of fibers by catching them randomly along their lengths (Figure 1).²⁰ These fibers form a fiber beard that is not end aligned. Before measurement, the beard is brushed to remove loose fibers and trash particles. The beard is then scanned over a light source starting 3.81 mm away from the base of the comb to the end of the fiber sample,^21,22 and a receiver on the opposing side of the beard is used to measure the amount of light attenuated by the beard. The starting point of the scanning of the beard is the maximum point of light attenuation and is used to standardize the measurement to 100%. As the beard is scanned over the light toward its tips, where fewer fibers are present to block the light, the scan eventually reaches a point where no fibers are long enough to attenuate the light. This results in a 0% point on the curve. The change in attenuation from 100% to 0% builds a curve called a fibrogram (Figure 2).^19,20

Figure 1.

A fiber beard prepared with a fibrosampler shows how fibers are scanned for the fiber length measurements with the High Volume Instrument.

Figure 2.

A typical fibrogram generated by the High Volume Instrument.

Two length measurements, the UHML and Mean Length (ML), are extracted from the HVI fibrogram. The UI is then obtained by calculating the ratio of the ML to the UHML, expressed as a percentage. Because many fibers are not measured by the HVI length module, that is, they are either trapped in the comb needles or they do not extend into the portion of the beard used to measure length, these two length parameters represent only the longer fibers in the sample.^21–23 After extracting these two length measurements, the fibrogram data are discarded by the instrument.

HVI fiber quality parameters, including fiber length measurements, are often used as indicators of potential yarn quality. One limitation of current HVI fiber length parameters is that they do not characterize the total within-sample variation in fiber length, a property that affects variation in yarn quality.^4,6,24 The current HVI system does not measure fiber length variation related to shorter fibers in the sample.^25,26 A higher short fiber content (SFC) in the raw cotton increases the rate of yarn breakage during manufacturing in high-speed modern spinning systems and also increases the hairiness level of the yarn.^3,25 SFC negatively affects the manufacturing process and ultimately the end product quality.^3,7 The negative impact of short fibers on yarn quality creates a need for the cotton industry to have a better measurement of SFC in raw cotton.^25–28

Within-sample variation in cotton fiber length can be measured with an Advanced Fiber Information System (AFIS).⁶ The AFIS measures the length of individual fibers by number and provides the complete fiber length distribution as a histogram (Figure 3).²⁹ Because they are based on the full within-sample variation in fiber quality, AFIS fiber length measurements hold important information needed for the development of germplasm with improved spinning performance.^5,6,12 While the AFIS fiber length measurement is faster than many other methods, it is too slow to be practical to meet the demands of the commercial cotton classification.

Figure 3.

Complete fiber length distribution by number measured with the Advanced Fiber Information System.

HVI length parameters based on current laboratory protocols measure only the longest fibers in the fiber beard, but the parameters are extracted from a curve that characterizes variation in the lengths of all fibers included in the measured beard. The first objective of this research is to characterize the relationship between the most common HVI length parameters, the UHML and UI, and the fibrogram. The second objective is to develop a method for defining new length parameters that characterize variation in the fibrogram that is not captured by the UHML and UI. Finally, we evaluate whether the information captured by these new length parameters is useful for explaining variation in yarn quality.

Material and methods

The first analysis, relating the UHML and UI to the variation in the fibrogram, is based on samples taken from a large subset of the commercial production in the USA. These samples are used to identify the portion of the fibrogram captured by current HVI length measurement protocols. A small subset of the commercial samples is then used to identify additional fiber length variation that is not currently captured by the UHML and UI, effectively defining new length parameters derived from the complete fibrogram curve. The investigation into the usefulness of the new length parameters requires samples large enough to produce yarn. Thus, the usefulness of the new length parameters is evaluated on two sample types, with one set representing the range of fiber quality that might be present in a breeding program and the other set representing the range of fiber quality expected in commercial bales.

Each of these experiments depends on evaluating the within-sample variation of fiber length using the fibrogram. Two operation modes of the HVI were needed to assess this variation in quality.

System testing – the system testing operating mode reports several important fiber quality parameters, such as the UHML, UI, Strength, Micronaire, Yellowness, and Reflectance. This mode does not provide a fibrogram curve. The fiber length measurements (UHML and UI) for this mode are calibrated with two US Department of Agriculture (USDA) standard samples.

Module testing – the HVI has three independent testing modules, that is, length and strength, micronaire, and color and trash. The length and strength module allows the operator to test using only the length and strength portion of the instrument. For the strength measurement, the micronaire needs to be entered manually as it is one of the variables used to estimate the mass of the sample being broken. This module provides a non-calibrated curve that is measured from a beard of fibers that is not end aligned. The portion of the fiber beard going from the edge of the comb to the scanning starting point is 3.81 mm (0.15 inch) long and is the same for all Uster HVIs.^21–23 Values are expressed as distances and not lengths because the starting offset distance is not included for analysis in this research. However, this is a constant offset and including it should not change the presented results.

The fibrogram curve is reported as a vectored image file and not a raw data file. Thus, a specialized procedure is required for extracting the fibrogram data and using the information present in the curve.

Extracting the fibrogram

The data points of the fibrogram represent the standardized attenuated light amount as a function of the distance traveled by the fiber beard through the light sensing apparatus inside the HVI. The HVI records the level of attenuated optical light with a 0.635 mm (0.025 inch) step from 0 to 50.8 mm, resulting in 81 data points when including the zero point. The HVI reports these data points when run in module testing as vectored plots embedded in an Excel file. A MATLAB (Math Works Inc., MATLAB R2018a) script was developed to automate the extraction of the 81 data points that characterize the fibrogram generated by the HVI for each sample.

The fibrogram is used to measure lengths, such as the UHML and UI, but the raw response values for the fibrograms are reported as standardized attenuated light in percentage for a given displacement (Figure 2). We transposed the fibrogram curves to a set of fixed light attenuation levels in order to have a curve measurement where distance is the response (Figure 4). All fibrogram analyses in this paper have been conducted on transposed fibrograms where distances are the response values. This conversion ensures the data extracted from the fibrogram curves during further statistical analysis is proportional to the fiber length and not attenuated light.

Figure 4.

An illustration of the transposed fibrogram where distance is the response value.

The transposition into a distance–response curve was conducted with the MATLAB script to export the data from the HVI report. The optimal number and location of the interpolation points depend on the sample set and type. Because this was an initial investigation into the fibrogram and three types of samples were used in the analysis, the script was set up to identify fixed 1% intervals between 0% to 100% standardized attenuated light. This resulted in a distance–response curve of span lengths for 101 light attenuation levels. The span length 100 is an origin point and is always zero, and the span length at 0% does not characterize fiber length data. Therefore, these two span lengths were excluded from the analysis. This set of 99 span lengths was used in the analysis of all datasets included in this paper.

Current fiber length parameters

An evaluation of standard HVI length parameters, the UHML and UI, is needed before defining new length parameters. A set of 19,628 USDA Agricultural Marketing Service (AMS) samples covering a wide range of fiber length characteristics seen in commercial production were selected to meet this objective. A 4-4-10 (4 color and trash measurements; 4 micronaire measurements; 10 length and strength measurements) testing research protocol was used to obtain the typical HVI fiber quality parameters of the 19,628 USDA AMS samples. These samples were measured with a HVI (Uster HVI ™ 1000) at the Fiber and Biopolymer Research Institute (FBRI) from 2011 to 2016. While the HVI reports the UHML and UI, it measures the UHML and ML. The UI parameter is not measured directly but is calculated as the ratio of the ML to UHML, expressed as a percentage. In this part of the study, the raw values measured by the HVI were evaluated by calculating the ML from the UHML and UI. The linear correspondence of the UHML and ML was determined using simple linear regression.

Investigation of the fibrograms

The fibrogram is reported by the HVI when using the length and strength module testing mode. In order to obtain the full suite of typical HVI fiber quality characteristics along with the fibrogram data, the samples were first be run in the system test mode followed by a length and strength module test.

The FBRI cotton phenomics lab evaluated a random subset of the US cotton production on the AFIS. The subset of commercial production was separated into groups in order to facilitate processing through the lab. One of these groups, consisting of 538 samples from commercial bales produced in 2016, was selected for use in this objective. These samples were evaluated with HVI length and strength module testing with 10 replications to obtain the fibrogram curves. The distance–response fibrogram curves were generated and each sample was represented as the average of the 10 length and strength module replications.

The 99 points in the distance–response curves are multicollinear and do not characterize unique types of length variation. A principal component analysis (PCA) of the averaged fibrograms was used to summarize the total variation in fiber length captured by the fibrogram (Math Works Inc., MATLAB R2018a). The PCA characterizes each type of variation in the fibrogram curve, such as magnitude and shape, as independent variables called scores.

While these scores are commonly used to plot the original data in a PCA biplot, they can also be used as independent variables in a statistical analysis.³⁰ In this research, these scores were used to define independent variables that characterize the maximum amount of length variation captured by the fibrogram as linear combinations of the original 99 span lengths. The formula used to calculate the scores was saved and applied in other types of analysis described in this paper.

Explaining variation in yarn quality

Sample selection

Fiber length characteristics depend on genetics, environment, and fiber processing.^{15,16,31–34} Processes such as lint cleaning can break fibers and alter the within-sample distribution of fiber length. Breeder samples can have a wider range of genetic variation and are subjected to different processes than commercial samples. All of these factors have the potential to affect the within-sample distribution of fiber length and, as a result, the fibrogram curve. Therefore, it is important to determine whether the fiber length variation captured by the whole fibrogram can be useful to predict yarn quality for different types of samples. Two sets of samples with a sufficient amount of fiber for spinning trials, and that represent different sample types, were selected for this experiment (Tables 1 and 2).

Table 1.

Summary of High Volume Instrument fiber quality parameters for two sets of samples

Fiber quality	Set A				Set B
Fiber quality	Min	Ave	Max	CV%	Min	Ave	Max	CV%
Micronaire	3.17	4.32	5.23	12.3	3.26	4.55	5.61	9.9
Strength [g/tex]	25.4	28.7	31.9	5.00	24.4	31.2	38.9	9.0
Elongation (%)	6.10	8.57	10.90	13.0	3.10	5.09	7.30	17.9
UHML (mm)	26.7	29.0	31.8	3.5	25.7	29.7	35.1	7.7
UI (%)	77.6	81.3	84.1	1.5	77.9	82.2	85.8	1.8
Rd (%)	70.1	76.2	81.6	3.5	68.6	72.6	75.7	1.8
+b	6.7	8.4	9.6	7.4	6.5	7.7	9.2	6.2

UHML: Upper Half Mean Length; UI: Uniformity Index.

Table 2.

Summary of Advanced Fiber Information System fiber quality parameters for two sets of samples

Fiber quality	Set A				Set B
Fiber quality	Min	Ave	Max	CV%	Min	Ave	Max	CV%
Neps [count/g]	226	390	608	23.3	182	357	823	31.8
UQLw [mm]	27.4	29.7	33.0	3.8	26.2	31.2	37.9	8.5
Ln [mm]	16.8	18.8	22.4	5.8	17.3	20.6	24.9	7.7
SFCn [%]	20.3	30.0	39.0	11.6	14.8	24.7	37.0	16.3
Fineness [mtex]	142	163	184	5.3	136	166	201	7.5
Maturity Ratio	0.77	0.85	0.93	3.9	0.80	0.92	1.01	3.6

Set A: a set of 60 commercial-like samples representing a wide range of fiber lengths was selected for this experiment. This set consists of 12 commercial varieties grown in five different locations across the Texas High Plains in 2016: locations in Cochran, Terry, Mitchell, Bailey, and Gaines County. The 12 varieties grown in each location were FM 1830 GLT, FM 1911 GLT, CP 3475 B2XF, DP 1522 B2XF, DP 1612 B2XF, NG 3517 B2XF, NG 4545 B2XF, NG 3406 B2XF, NG 3405 B2XF, PHY 333 WRF, PHY 243 WRF, and PHY 308 WRF. A John Deere 7460 stripper harvester was used to harvest all locations except Mitchell. The Mitchell county location was harvested using a producer JD 7460 stripper harvester. The samples were ginned at the USDA Agricultural Research Service (ARS) Cotton Production and Processing Research Unit in Lubbock, Texas, with a Continental 93-saw gin – Double Eagle (1575 mm wide). This commercial type gin has a saw-type lint cleaner (one), a condenser, and a bale press. The processing speed of the seed cotton cleaner was 1427 kg per meter per hour, while the ginning speed was conducted at a constant speed of 1070 kg per meter per hour. The average moisture content of seed cotton across all the samples was 6.8%.

Set B: a set of 127 diverse samples was selected to have a wide range of fiber quality. Some of these samples are obsolete varieties developed without HVI screening, some are breeder germplasm, and some are commercially grown modern varieties. These samples were grown in an irrigated field at Weslaco Research and Extension Center with one field rep. The samples were harvested with a single-row mechanical spindle type cotton picker (1957 IH) modified for the research plot harvest. The samples were then ginned with a laboratory 10-saw gin without lint cleaner.

Fiber quality measurements

The typical HVI fiber quality parameters were measured with a system testing protocol (4 color and trash, 4 micronaire, 10 length and strength). The fibrograms were measured with the length and strength module testing mode with 10 replications. The fibrograms were converted to distance–response curves and a PCA was performed on each set to summarize the total within-sample variation in fiber length captured by the fibrogram in the presence of multicollinearity. Principal component (PC) scores were used to represent the variation in fiber length captured by the fibrogram curve.

Fiber length was also evaluated with the AFIS (USTER® AFIS Pro 2) for five replications of 3000 fibers. The first cumulative distribution of AFIS length distribution by number was calculated in order to summarize the total within-sample variation. The PCA was not performed on raw AFIS length distributions by number because it is a frequency distribution. Therefore, the PCA was performed on the first cumulative distribution of fiber length of each set to summarize the total within-sample variation in fiber length captured by the AFIS length distribution by number. PC scores were used to represent the within-sample variation in fiber length captured by AFIS length distribution by number.

Yarn production

At least 10 lbs of cotton fibers from each sample were used to produce carded ring spun yarn. A yarn count of 30 Ne was identified as a target count for this project. The goal was to produce yarn with a count as close to 30 Ne as possible without excluding samples from the spinning trial. A coarser yarn count was used for Set B because some samples did not exhibit a fiber quality profile well-suited for the production of 30 Ne yarn. Samples from Set B were spun into 24Ne carded ring spun yarn.

Set A: cottons from sample set A were carded (Truetzschler, DK 903) with a production rate of 54 kg/h to produce card slivers. The carded sliver was then drawn twice with the speeds of 548 and 365 meters/minute, respectively, to minimize within-sliver variation in mass. After the reduction of the linear density of these slivers by roving (SACO-LOWELL maremont, FC-1B), samples were processed to 30 Ne yarns on a ring spinning frame (Suessen, Fiomax1000) with a speed of 14,588 rpm and a twist multiplier (TM) of 3.62. Ten bobbins per sample were produced.

Set B: cottons from sample set B were carded (Rieter, C4) with a production rate of 9 kg/h to produce card slivers. The carded sliver was then drawn twice with a speed of 275 meters/minute to minimize within-sliver variation in mass. After the reduction of the linear density of these slivers by roving (SACO-LOWELL Maremont, FC-1B), samples were processed to 24 Ne on a ring spinning frame (Suessen, Fiomax1000) with a speed of 13,588 rpm and a TM of 3.75. Ten bobbins of yarn per sample were produced. Samples were processed for a coarser yarn count than set A, with a lower production rate.

The yarns were then evaluated for tensile properties and imperfections on 10 bobbins. For each bobbin, the yarn count was determined on 220 meters, and yarn tensile properties were measured on 20 single end breaks performed with the STATIMAT DS (Textechno STATIMAT, Textile Testing Technology, Germany). In addition to tensile property testing, 400 meters of yarn per bobbin was tested with the Uster Tester 5 (Uster® Technologies AG) for yarn evenness and imperfections.

Yarn quality

Genetic and agronomic effects, harvesting and ginning effects, and even the fiber quality measurement methodology can impart collinearity among fiber quality measurements. It is important to control for this multicollinearity when evaluating whether the full fibrogram curve relates to variation in yarn quality.³⁵ A Partial Least Square Regression (PLSR) was used to relate variation in fiber and yarn quality while controlling for multicollinearity.

Four different PLSR models were set up to investigate whether the full fibrogram contains the variation in fiber quality needed to explain some of the variations in yarn quality.

Model 1: Micronaire, Strength, Elongation, Reflectance (Rd) and Yellowness (+b).

Model 2: Model 1 + UHML and UI.

Model 3: Model 1 + Length parameters based on the major PCs of variation in the fibrogram.

Model 4: Model 1 + Major PCs of variation in the AFIS length distribution by number.

Model 1 characterizes variation in yarn quality without length parameters. The importance of fiber length in characterizing variation in yarn quality is well established in the literature.^3,4 The model without length parameters is included in this analysis as a point of comparison for the non-nested models and is not expected to be a suitable model.

Model 2 shows a more typical scenario, where the UHML and UI are added to Model 1. Model 3 then replaces the typical HVI length parameters, the UHML and UI, with the full variation in fiber length captured by the fibrogram. Finally, Model 4 replaces the HVI length parameters with components of variation extracted from the AFIS length distributions by number. Thus, Model 4 provides a model based on individual fiber measurement of the complete within-sample distribution of fiber length.

Each model was first evaluated by determining how much variation in yarn quality is explained by each set of fiber quality parameters based on the R² statistic. While PLSR was selected to prevent overfitting, there is always a risk of overfitting resulting in a reduction in the predictive power of a model. A second statistic was used to evaluate the predictive power of each model.

Leave-one-out cross-validation (LOOCV) is a method used to estimate the mean squared error (MSE) of prediction of PLSR models and is preferred to simple cross-validation when evaluating model fit.³⁶ In this procedure, one sample was withheld and the model was refit to the remaining set of samples. The model was then used to predict the value of the sample withheld from the model and the error in this prediction was recorded. This procedure was repeated until each sample was withheld one time and the error of each prediction was recorded. The average error generated during this prediction provides an estimate of the MSE of prediction.

Results and discussion

The HVI testing of commercial samples reveals a strong relationship between the UHML and ML (Figure 5). The R² value between the UHML and ML is 0.95, indicating that 95% of the variation in fiber length characterized by the UHML is also characterized by the ML. While the HVI reports another length parameter, the UI, it is calculated from these two variables, the UHML and ML (UI = (ML/UHML) * 100).

Figure 5.

Simple linear regression between the Upper Half Mean Length (UHML) and Mean Length (ML) of 19,628 US Department of Agriculture Agricultural Marketing Service samples shows high correlation between current High Volume Instrument length parameters.

The ASTM definition of the UHML is “the mean length by number, of the longer one half of the fiber by weight” and that of the ML is “the average length of all fibers in the test specimen based on mass-length.”³⁷ However, the HVI does not measure the fiber length by number or by weight; it measures the attenuated optical light along with the distance traveled by the fiber beard during scanning. According to Hertel's fibrogram theory, the ML and UHML should be calculated from a tangent to the curve from the 100% and 50% span lengths, respectively. The fibrogram measurements of 538 USDA AMS samples were used to determine how closely the current length parameters follow this theory.

The pairwise correlation between the UHML and each of the span lengths was plotted and used to determine the span lengths used to determine the measurement. This was repeated for the HVI UI. Variation in the region of the fibrogram corresponding to the tips of the longest fibers highly correlates with variation in the UHML and ML (Figure 6). The highest level of correlation with the UHML is with the span length of 1.8%, where the R² value is 0.999 (Figure 6). The highest level of correlation with the ML is with the span length of 7.8%, where the R² value is 0.999 (Figure 7). This suggests that the UHML is calculated from the 1.8% span length and the ML is calculated from the 7.8% span length.

Figure 6.

Linear regression of 538 US Department of Agriculture Agricultural Marketing Service sample Upper Half Mean Length (UHML) and Mean Length (ML) measurements with all the span lengths along with the fibrogram curve shows that the highest correlations of UHML and ML are with 1.8% span length and 7.8% span length, respectively.

Figure 7.

An illustration of the current fiber length measurement principles of the High Volume Instrument, which shows that two points from the curve are used for the measurement of the Upper Half Mean Length (UHML) and Mean Length (ML). UI: Uniformity Index.

Given that the HVI length parameters are calculated from the highly collinear variation at the 1.8% and 7.8% span lengths, they are unlikely to characterize the total length variation captured by the complete fibrogram curve. Much of the region of the fibrogram representing the shorter fibers is not captured by the UHML and UI (Figure 7). This region of the curve may be important, as fibrogram curves exhibit variation across the whole curve rather than only at the longest portion of the curve (Figure 8).

Figure 8.

Range of within-sample variation in fiber length captured by the fibrograms of 538 US Department of Agriculture Agricultural Marketing Service samples. The solid line shows the averaged fibrogram while the dashed lines show minimum and maximum values for each length group.

In order to extract additional independent types of length variation from the fibrogram curve, a PCA was performed to identify the largest sources of variation in fiber length characterized by the full fibrogram, revealing more than one independent type of length variation characterized by the fibrogram curve (Figure 9). The first three variables explain approximately 99% of the variation available in the fiber length.

Figure 9.

Relationship between scores of the first and second principal components shows that they are independent and characterize approximately 98% of the total within-sample variation.

The relationship between loadings of the first three components with the span lengths shows the types of fiber length variation captured by each component (Figure 10). These three components are independent and characterize different types of fiber length variation. The loadings of the first PC show a positive relationship with all of the span lengths, while the loadings for the second component show a negative relationship with the span length representing shorter fibers in the sample and positive relationship with the span length representing longer fibers in the sample. Finally, the loadings of the third PC show a positive relationship with the span lengths representing the shorter and longest region of the fibrogram, and negative relationship with the medium to longer region of the fibrogram. The two span lengths used for the current HVI length measurements (1.8% and 7.8% span length) do not capture the variation in fiber length that can be characterized by the second and third components.

Figure 10.

The relationship between loadings of each principal component (PC) with the span lengths.

The nature of length variation characterized by each of these PC axes can be elucidated by comparing them back to the original fibrogram curves. Doing so reveals that the first PC explains length variation due to differences in the average length of the fibers in the beard, or length magnitude (Figures 10 and 11). This type of length difference is common between samples and accounts for 91% of the total variation in this set. A larger value along this axis represents a sample that has longer fibers overall. While selecting cotton bales based on this variable could provide more desirable raw material for spinning than the current HVI length parameters, it cannot be used alone as it does not characterize differences in within-sample variation in fiber length.

Figure 11.

Fibrograms selected based on the difference in newly identified variable 1 show the magnitude difference. PC: principal component.

The second variable explains variation due to the shape differences in the fibrograms and it explains approximately 7% of the total fiber length variation among these samples (Figures 10 and 12). This type of variation is not captured by the standard HVI length parameters. Because this variable captures differences in within-sample variation, some span lengths have a positive correlation with this axis while others have a negative correlation. Thus, a larger value along this axis indicates distributional differences in fiber length that result in a crossover along the fibrogram curve. Excessive within-sample variation in fiber length increases the occurrence of mass imperfections in the yarn.^3,7,8,10 Selecting cotton bales based on this component should help reduce imperfection in the yarn structure.

Figure 12.

Fibrograms selected based on the difference in newly identified variable 2 show the shape difference. PC: principal component.

The third variable captures another type of within-sample variation in fiber length that causes the fibrogram curves to crossover twice (Figures 10 and 13). This type of variation among these samples is less common and accounts for 1% of the total variation in fiber length among the samples. While this does not account for a large portion of the total variation, variation in yarn mass is sensitive to within-sample variation in fiber length, and this parameter may hold important information about variation in yarn quality.

Figure 13.

Fibrograms selected based on the newly identified variable 3 show the shape difference caused by the double crossover. PC: principal component.

HVI length parameters, the UHML and UI, do not adequately characterize the total length variation captured by the fibrogram. The total variation in fiber length captured by the fibrogram can be summarized as linear combinations of span lengths using PCA. The scores from this analysis represent independent sources of variation that parameterize differences in within-sample variation in fiber length. The importance of this additional length information is investigated in the next section by manufacturing yarns and comparing them with more typical HVI and AFIS length parameters in their ability to explain variation in yarn quality.

Development of prediction models

The yarn spun from the samples chosen for this objective represents the range of yarn quality characteristics for tensile properties and yarn imperfections needed for characterizing the relationships between the model parameters (Tables 3 and 4). Yarn tenacity ranges from 9.52 to 15.08 [g/tex], while the coefficient of variation in yarn mass (CVm%) ranges from 15.08% to 18.88% among the commercial samples. The range in yarn tenacity for the breeder samples is 9.48–22.91 [g/tex], while the CVm% ranges from 12.52% to 18.57%. While a direct comparison cannot be made between these two sample sets due to sample preparation and yarn types, both sets exhibit the range in yarn quality characteristics needed for investigating the impact of variation in fiber quality on yarn quality.

Table 3.

Range of variation in yarn quality parameters for sample set A

Yarn quality	Minimum	Average	Maximum	CV%
Tenacity [g/tex]	9.52	11.89	15.08	10.08
CVm%	15.08	16.70	18.88	5.30
Thin places [count/km]	5.00	31.2	99.3	65.96
Thick places [count/km]	181	353	606	31.73
Neps 200% [count/km]	181	371	646	32.12
Hairiness [no unit]	5.58	6.63	9.00	10.26

Table 4.

Range of variation in yarn quality parameters for sample set B

Yarn quality	Minimum	Average	Maximum	CV%
Tenacity [g/tex]	9.48	15.01	22.91	19.10
CVm%	12.52	15.17	18.57	7.40
Thin places [count/km]	0.00	9.40	72.50	107.96
Thick places [count/km]	387	1027	2076	27.77
Neps 200% [count/km]	73	246	529	42.59
Hairiness [no unit]	4.77	5.99	7.08	8.61

PLSR yarn quality prediction models were chosen for minimizing the multicollinearity caused by the intercorrelation between fiber quality parameters. Regression between observed and predicted yarn quality for both sample sets shows a significant linear component in the relationship characterized by the models at the alpha level of 0.05 (Table 5).

Table 5.

Pairwise comparison between observed and predicted yarn quality shows a significant linear relationship

Yarn quality	Set A				Set B
Yarn quality	R ²	F	Slope	Offset	R ²	F	Slope	Offset
CVm%	0.86*	<0.001	0.86 ± 0.09	0.00 ± 0.09	0.77*	<0.001	0.77 ± 0.07	0.00 ± 0.07
Tenacity	0.89*	<0.001	0.89 ± 0.08	0.00 ± 0.08	0.93*	<0.001	0.93 ± 0.04	0.00 ± 0.04

*refers to the significant linear relationship.

Explaining variation in yarn quality

Fiber length is an important fiber quality characteristic to consider when explaining variation in yarn quality (Tables 6 and 7). Models of yarn quality that do not include fiber length information explain the lowest amount of variation in yarn quality.

Table 6.

Sample set A. The R² values show the amount of variation in yarn quality explained by different models. The mean squared errors (MSEs), analyzed by the leave-one-out cross-validation process, show the performance of each model while predicting yarn quality

Model	Tenacity [g/tex]		CVm%		Thin places [count/km]		Thick places [count/km]		Neps [count/km]		Hairiness [no unit]
Model	R ²	MSE	R ²	MSE	R ²	MSE	R ²	MSE	R ²	MSE	R ²	MSE
1	0.66	0.41	0.46	0.49	0.40	0.49	0.45	0.49	0.42	0.45	0.51	0.18
2	0.82	0.23	0.74	0.26	0.63	0.34	0.73	0.27	0.69	0.27	0.84	0.07
3	0.89	0.16	0.86	0.14	0.77	0.22	0.83	0.17	0.78	0.19	0.87	0.05
4	0.86	0.19	0.70	0.29	0.56	0.38	0.68	0.31	0.62	0.33	0.77	0.09

Table 7.

Sample set B. The R² values show the amount of variation in yarn quality explained by different models. The mean squared errors (MSEs), analyzed by the leave-one-out cross-validation process, show the performance of each model while predicting yarn quality

Model	Tenacity [g/tex]		CVm%		Thin places [count/km]		Thick places [count/km]		Neps [count/km]		Hairiness [no unit]
Model	R ²	MSE	R ²	MSE	R ²	MSE	R ²	MSE	R ²	MSE	R ²	MSE
1	0.86	0.15	0.66	0.38	0.43	0.63	0.24	0.83	0.35	0.72	0.75	0.27
2	0.89	0.13	0.69	0.36	0.47	0.60	0.32	0.78	0.43	0.65	0.83	0.19
3	0.93	0.09	0.78	0.26	0.49	0.61	0.48	0.62	0.46	0.64	0.89	0.13
4	0.89	0.13	0.73	0.31	0.47	0.61	0.43	0.66	0.46	0.65	0.81	0.23

The greatest amount of variation in an imperfection parameter explained by the model without a length parameter (Model 1) is hairiness, explaining 51% (Table 6) for the commercial-like samples and 75% (Table 7) for the diversity set. This stands in contrast with the amount of variation explained in yarn tenacity. When not using a length parameter, the standard HVI parameters explained 66% (Table 6) of the variation in yarn tenacity among the commercial-like samples and 86% (Table 7) of the variation in yarn tenacity among the diversity set.

The length parameters that hold the most important information for explaining yarn quality are those provided by the full fibrogram. Models including the full information extracted from the fibrogram (Model 3) have the greatest explanatory power of the models considered. The models including full fibrogram-based length parameters explained 89% of the variation in yarn tenacity for the commercial-like samples (Table 6) and 93% of the variation in yarn tenacity for the diversity set (Table 7), which is more than either the standard HVI length parameters or the AFIS length distribution-based length parameters (Model 4).

Information about fiber length provided by the full fibrogram provides a greater improvement when explaining the occurrence of yarn imperfections. The standard HVI parameters, including the UHML and UI, explained 74% of the CVm% among the commercial-like samples and 69% among the diversity set. Replacing the UHML and UI with the length parameters based on the full fibrogram increased this to 86% and 78%, respectively. Excessive within-sample variation in fiber length increases within-sample variation in yarn mass, as captured by the CVm% measurement.

Despite characterizing the complete within-sample variation in fiber length, the AFIS length distribution does not improve the explanatory power of the models over the variables extracted from the full fibrogram (Tables 6 and 7). The AFIS length parameters improved explanatory power over the standard HVI length parameters, the UHML and UI, but did not exceed the explanatory power of the length parameters based on the full fibrogram. The complete fibrogram explains yarn quality better than or at least as good as AFIS length distribution by number. One reason could be the number of fibers tested per sample. Samples were measured with the AFIS with five replications of 3000 fibers, totaling 15,000 fibers per sample. On the other hand, a fiber beard contains more than 20,000 fibers. If we assume the weight of a fiber beard is 80 mg, the ML is 20 mm by number, and the fineness is 170 mtex, then the number of fibers in that beard would be 23,530. For 10 replications the total number of fibers tested would be approximately 235,300, which is 26 times larger than AFIS fiber length measurements. Therefore, fibrograms may represent the original samples more accurately than the AFIS length distribution by number.

Evaluating goodness of fit

The fibrogram improves the estimated goodness of fit of the models captured by MSE, as models including length parameters derived from the full fibrogram provide the lowest MSE of prediction.

Models constructed with the base HVI parameters without including any length parameters have a poorer goodness of fit based on the MSE. The MSE for the models characterizing variation in yarn produced from the commercial-like bales ranges from 0.18 to 0.49 (Table 6), while the MSE for models based on the diversity set ranges from 0.15 to 0.83 (Table 7).

The estimated model MSE indicates an improved fit with the addition of the standard HVI length parameters, the UHML and UI. The model of thick places for the commercial-like bales based on HVI fiber quality parameters with the UHML and UI has a MSE of 0.27, compared with 0.49 with no length parameter (Table 6). Similarly, the model of thick places for the diversity set based on HVI fiber quality parameters with the UHML and UI has a MSE of 0.78, compared with 0.83 with no length parameter (Table 7).

Length parameters based on the complete fibrogram provide another improvement in the estimated model MSE. For the commercial-like bales, the model of thick places based on HVI fiber quality parameters, including the length parameters based on the full fibrogram in place of the UHML and UI, has a MSE of 0.17, compared with 0.49 with no length measurement and 0.27 with the UHML and UI (Table 6). Similarly, the model of thick places for the diversity set when using the length parameters based on the full fibrogram in place of the UHML and UI has a MSE of 0.62, compared with 0.83 with no length measurement and 0.78 with the UHML and UI (Table 7).

Improvements in the AFIS length distribution have been shown to result in an improved yarn quality.⁵ The results presented here are consistent with this literature, as the length distribution by number from the AFIS provides an improvement in MSE over the standard HVI length parameters, the UHML and UI. However, the models including the total variation captured by the AFIS length distribution do not have a better MSE than the model including the length variation captured from the complete fibrogram. The MSE for the yarn quality models with AFIS length distribution by number is not lower than the yarn quality model constructed with the complete fibrogram (Tables 6 and 7).

Conclusion

Fiber length parameters measured using current HVI protocols do not adequately characterize within-sample variation in fiber length. The two fiber length parameters (UHML and UI) reported by the HVI are based on the measurements of 1.8% span length and 7.8% span length, respectively, which are highly correlated and only characterize variation in the length of the longest fibers in the sample. The results presented in this paper demonstrate that more information is available in the fibrogram curve than is currently used.

When considering variation along the whole fibrogram curve, and not just two highly collinear points on the curve, it is possible to characterize more than one type of fiber length variation among samples. These can be used to define new length parameters that better capture within-sample variation in fiber length. Because these parameters are based on the HVI fibrogram, they can provide cotton breeders with valuable information from an instrument they are already using, the HVI.

Variations in fiber length based on the full fibrogram are also important for explaining variation in yarn quality. Using an independent statistic, our results showed that the new fiber length variables also improve the prediction of yarn quality over standard HVI length parameters, and they may be as good as the variation in fiber length captured by the AFIS length distribution by number. These new length parameters could provide spinning mills with important information needed to identify raw materials that is necessary to meet their production goals.

While these results are encouraging, more work needs to be done. Currently, the HVI UHML and UI measurements are calibrated based on a two-point calibration protocol. This calibration is performed after the 1.8% and 7.8% span lengths are extracted from the fibrogram curve, leaving the remaining curve uncalibrated and unused. If it is to be used, the calibration of the HVI with the whole fibrogram needs to be investigated.

While the approach presented here is an attempt to characterize the whole fibrogram curve, other strategies may exist. It may also be possible to identify a set of span lengths that adequately captures variation characterized by the fibrogram curve. Either approach would need to be automated and reported in a format familiar to the cotton research community. Once these new measurements are shown to be stable, and a calibration method is developed, these parameters will provide the cotton industry with a new method for assessing the within-sample distribution of fiber length without the need for additional testing.

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: This work was supported by the Cotton Incorporated (Grant No. 17-533).

ORCID iDs

Md Abu Sayeed

John Wanjura

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