Modeling thermophysiological comfort properties of ladies’ scarves using least squares approximation

Abstract

A scarf is a social requirement in feminine clothing, and contributes to a sober appearance. It offers many thermophysiological comfort features. The aim in this work is to develop a mathematical model to predict air and water vapor permeability, thermal resistance, moisture management permeability, and pilling resistance in scarves, as a function of warp count, weft count ends per inch, picks per inch, and fabric weight in grams per square meter. Linear and quadratic mathematical models were fitted using the least squares approximation technique. Error analysis of both models showed that quadratic models behave better for air and water vapor permeability, thermal resistance, and moisture management. However, for pilling resistance, the linear model is found to be better.

Keywords

Least squares approximation water vapor permeability air permeability thermal resistance

Comfort is an agreeable condition of physiological, psychological, and physical harmony between a human being and the environment. Clothing comfort can be categorized as thermophysiological, sensory (or tactile), or psychological.¹ A fabric that offers thermophysiological comfort has the ability to allow heat, air, and perspiration to move through it.² Air and water vapor permeability, thermal resistance, and moisture management control the passage of heat, air, and perspiration through the fabric. All these properties are influenced by the fiber’s nature, the yarn, and the fabric structure.^3
–20

Air permeability is the quantitative measure of air moving through a fabric. The air permeability of fabric is significant in many industrial processes, including the manufacture of filters, tents, sailcloth, parachutes, raincoat material, shirting, waterproof fabrics, and airbags.²¹ Outdoor clothing requires fabric with a low air permeability, to act as a windbreaker.²² Water vapor permeability is the quantitative measure of water vapor transmitting through a fabric under given circumstances. The higher the permeability of the fabric, the more rapid the water vapor transmission. A lower water vapor permeability reduces the flow of vapor across the barrier.²³ Thermal resistance is a quantitative measure of an object or material to resist heat flow.²⁴ A fabric’s thermal resistance is strongly influenced by the enclosed air affected by the fabric structure.²⁵ Moisture management is the process of wicking heavy moisture or perspiration, followed by evaporation, to keep the wearer dry.²⁶ Thermophysiological comfort can be assessed by evaluating the movement of air, heat, and, in both liquid and vapor forms, through clothing for thermal equilibrium.^3,5 Comfort is a physical property of clothing, including scarves. A scarf is a piece of fabric usually worn about the shoulders, around the neck, or over the head. Head scarves are worn for various reasons, for example, to protect the head and hair from rain, wind, dirt, cold, or warmth,²⁷ or for religious purposes. Moreover, a scarf may be thought to contribute to a sober appearance.

Thermal comfort concerning fabric balances the needs of the body with the properties of the environment.^6
–8 The yarn structure and the fiber cross-sectional shape greatly influence the thermal comfort of different woven fabrics.²⁸ The thermal properties of 1 × 1 rib polyester and cotton fabrics have been examined.²⁹ Interlock and 1 × 1 rib fabrics have remarkably high thermal conductivity and thermal resistance. Moreover, single jersey fabrics have a higher relative water vapor permeability than 1 × 1 rib and interlock fabrics.³⁰ Textured polyester knitted fabric has greater air permeability than moisture management polyester, for the same yarn count and knit structure.³¹

The fabric construction and the constituent fiber properties affect the thermal comfort properties of woven fabrics used to make clothing. Cellular weave, which is a derivative of satin and dice weaves, has the highest thermal resistance. Moreover, 2/2 twill and matte twill weaves exhibit the smallest water vapor thermal resistance.³² Cotton fabric of a specific areal density produced from coarser yarns with fewer ends per inch (EPI) and picks per inch (PPI) is found to admit better air permeability and tear strength, as compared with that made from finer yarns with greater EPI and PPI.³³ Cotton fabric admits higher air permeability and thermal resistance, compared with other cellulosic fabrics, whereas the moisture management properties of Tencel fabric are superior to those of other cellulosic fabrics.³⁴

Textile manufacturing processes can be mathematically modeled to predict the physical qualities of the fabrics. The function’s behavior depends on the input variables. Different numerical methods are used for modeling purposes.³⁵ Least squares approximation (LSA) is a polynomial fitting method to fit a given data set.³⁶ Data fitting involves using a parametric model with one or more coefficients that link the response data to the predictor data.³⁷ LSA minimizes the sum of squares of residuals to estimate coefficients of terms.

LSA is always in fashion for use in predictive models.^{5,6,13
–20,38
–46} The least squares method is convenient in formulation and error evaluation, generally in mixed and local (finite-element) versions, and its performance is competitive with other methods.⁴⁵ Systematic regression and LSA have been used to estimate and quantify the properties of fiber materials.⁴⁷ LSA has been used to study the relationship between intermingled yarn properties and melange fabric properties.⁴⁵

The literature related to the clothing comfort of woven fabric indicates that significant work has already been done to investigate the thermal comfort properties of such fabrics, but there is, to our knowledge, no research explicitly based on scarf fabric in Pakistan. Moreover, there is a lack of thermophysiological comfort property analysis concerning scarves.

The aim in this study is to develop a mathematical model to predict the thermophysiological comfort properties of scarves from various parameters of thermal comfort. The comfort properties include air and water vapor permeability, moisture management, thermal resistance, and pilling resistance. These quantities are modeled based on warp count, weft count, EPI, PPI, and grams per square meter (GSM). Linear and quadratic LSA models are fitted. An error analysis is presented, to investigate the construction of a better predictive model.

This manuscript is organized in the following manner. The next section details the methods used to collect the experimentation data. After this, the linear and quadratic mathematical modeling of the thermophysiological properties of ladies’ scarves is presented. The following section concerns the development of prediction models for thermophysiological properties, including air and water permeability, moisture management, and thermal resistance. The last section deals with the error analysis; finally, conclusions are drawn.

Materials and methods

The thermophysiological comfort properties of scarves can be predicted based on warp count (unit, Ne), weft count (unit, Ne), EPI, PPI, and GSM (a standard measure of fabric weight). To model the thermophysiological comfort properties, including air permeability, water vapor permeability, moisture management permeability (MMP), thermal resistance, and pilling resistance, we want the experimental data regarding these properties. This section is divided into two subsections, the first detailing experimentation to collect data and the second giving details of the mathematical technique, namely, LSA, used for modeling.

Materials and mechanical tests for data collection

Usually, scarves are made of polyester, viscose, cotton, and blends of these fibers. A sample of 10 scarves was collected from the market; fabrics were made of 100% polyester; 100% viscose; 100% cotton; 83% polyester and 17% viscose; and 64% polyester and 36% viscose. The EPI, PPI, and warp and weft counts (units, Ne) of each sample were determined using standard testing methods. The GSM of each sample was determined according to ISO 3801:1977.⁴⁸ The air permeability of fabric was determined using an air permeability tester (MO21A, SDL Atlas), following BS ISO 9237:1995,⁴⁹ and measured using a testing head of area 20 cm² and air pressure 100 Pa. The thermal resistance and water vapor permeability of woven fabrics were tested using a Permetest instrument, giving results equivalent to those produced by the BS EN ISO 11092:2014 standard test method.⁵⁰ The moisture management of fabrics was determined using the AATCC TM 195:2011 method.⁵¹ The experimental data led to the values given in Table 1 for air permeability, water vapor permeability, thermal resistance, and pilling resistance, as well as warp and weft counts (units, Ne), EPI, PPI, and GSM.

Table 1.

Data collection

Fabric type	Warp (x)	Weft (y)	Ends per inch (z)	Picks per inch (s)	Grams per square meter (t)	Air permeability (F₁)	Water vapor permeability (F₂)	Thermal resistance (F₃)	Moisture management permeability (F₄)	Pilling resistance (F₅)
100% polyester	28.36	29.64	65	47	90	2403	95.0	0.027	0.76	2
100% viscose	28.48	19.79	47	32	82	3331	96.7	0.026	0.73	2
83% polyester; 17% viscose	37.9	30.15	60	39	71	3118	95.1	0.02	0.66	1.5
100% polyester	46.42	41.1	90	56	80	1386	97.3	0.019	0.79	4.5
100% polyester	45.18	38.26	60	39	51	4888	90.1	0.024	0.64	1.5
100% cotton	45.1	45.45	61	51	66	1950	97.1	0.016	0.62	1.5
64% polyester; 36% viscose	75.2	35.17	172	56	98	761	99.0	0.019	0.67	4
100% polyester	51.3	49.9	71	67	64	5375	97.9	0.016	0.59	2.5
100% cotton	69.87	70.31	88	66	50	2239	98.7	0.015	0.77	3
100% polyester	28.83	27.98	57	38	81	2926	94.1	0.021	0.8	2

Mathematical modeling using LSA

The mathematical technique used for the mathematical modeling is the LSA. The LSA approximates the coefficients of the polynomial terms. For the coefficient approximation, a standard set of equations is formed and solved. The resulting expression is the required prediction model for the thermophysical property. Let the function F indicate a thermophysical property of the scarf. Let the variables x, y, z, s, and t, respectively, denote the warp count, weft count, EPI, PPI, and GSM. The LSA methods for the sake of linear and quadratic polynomials are given as follows.

Linear polynomial approximation

Let us consider a linear function F in five variables x, y, z, s, and t, expressed mathematically as

F (x, y, z, s, t) : F = a + b x + c y + d z + e s + f t

(1)

where a, b, c, d, e, and f are coefficients to be determined. According to LSA, the coefficients are determined using the following system of equations:

\sum F = r a + b \sum x + c \sum y + d \sum z + e \sum s + f \sum t

(2)

\sum x F = a \sum x + b \sum x^{2} + c \sum x y + d \sum x z + e \sum x s + f \sum x t

(3)

\sum y F = a \sum y + b \sum x y + c \sum y^{2} + d \sum y z + e \sum y s + f \sum y t

(4)

\sum z F = a \sum z + b \sum x z + c \sum y z + d \sum z^{2} + e \sum z s + f \sum z t

(5)

\sum s F = a \sum s + b \sum x s + c \sum y s + d \sum z s + e \sum s^{2} + f \sum s t

(6)

\sum t F = a \sum t + b \sum x t + c \sum y t + d \sum z t + e \sum s t + f \sum t^{2}

(7)

Quadratic polynomial approximation

Let us consider a quadratic function F in five variables x, y, z, s, and t, mathematically expressed as

\begin{array}{l} F (x, y, z, s, t) : F = a + b x + c x^{2} + dxy + exz + fxs \\ + gxt + h y + i y^{2} + jyz + kys + lyt \\ + m z + n z^{2} + ozs + pzt + q s + r s^{2} \\ + ust + v t + w t^{2} \end{array}

(8)

where a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, u, v, and w are coefficients to be determined. According to LSA, the coefficients are determined using the following system of equations:

\begin{array}{l} \sum F = r a + b \sum x + c \sum x^{2} + d \sum x y + e \sum x z + f \sum x s \\ + g \sum x t + h \sum y + i \sum y^{2} + j \sum y z + k \sum y s \\ + l \sum y t + m \sum z + n \sum z^{2} + o \sum z s + p \sum z t \\ + q \sum s + r \sum s^{2} + u \sum s t + v \sum t + w \sum t^{2} \end{array}

(9)

\begin{array}{l} \sum x F = a \sum x + b \sum x^{2} + c \sum x^{3} + d \sum x^{2} y + e \sum x^{2} z \\ + f \sum x^{2} s + g \sum x^{2} t + h \sum x y + i \sum x y^{2} \\ + j \sum xyz + k \sum xys + l \sum xyt + m \sum x z \\ + n \sum x z^{2} + o \sum xzs + p \sum xzt + q \sum x s \\ + r \sum x s^{2} + u \sum xst + v \sum x t + w \sum x^{2} t^{2} \end{array}

(10)

\begin{array}{l} \sum x^{2} F = a \sum x^{2} + b \sum x^{3} + c \sum x^{4} + d \sum x^{3} y \\ + e \sum x^{3} z + f \sum x^{3} s + g \sum x^{3} t + h \sum x^{2} y \\ + i \sum x^{2} y^{2} + j \sum x^{2} y z + k \sum x^{2} y s + l \sum x^{2} y t \\ + m \sum x^{2} z + n \sum x^{2} z^{2} + o \sum x^{2} z s + p \sum x^{2} z t \\ + q \sum x^{2} s + r \sum x^{2} s^{2} + u \sum x^{2} s t + v \sum x^{2} t \\ + w \sum x^{3} t^{2} \end{array}

(11)

\begin{array}{l} \sum xyF = a \sum x y + b \sum x^{2} y + c \sum x^{3} y + d \sum x^{2} y^{2} \\ + e \sum x^{2} y z + f \sum x^{2} y s + g \sum x^{2} y t + h \sum x y \\ + i \sum x y^{3} + j \sum x y^{2} z + k \sum x y^{2} s + l \sum x y^{2} t \\ + m \sum xyz + n \sum x y z^{2} + o \sum xyzs + p \sum xyzt \\ + q \sum xys + r \sum x y s^{2} + u \sum xyst + v \sum xyt \\ + w \sum x^{2} y t^{2} \end{array}

(12)

\begin{array}{l} \sum xzF = a \sum x z + b \sum x^{2} z + c \sum x^{3} z + d \sum x^{2} y z \\ + e \sum x^{2} z^{2} + f \sum x^{2} z s + g \sum x^{2} z t + h \sum xyz \\ + i \sum x y^{2} z + j \sum x y z^{2} + k \sum xyzs + l \sum xyzt \\ + m \sum x z^{2} + n \sum x z^{3} + o \sum x z^{2} s + p \sum x z^{2} t \\ + q \sum xzs + r \sum x z s^{2} + u \sum xzst + v \sum xzt \\ + w \sum x^{2} z t^{2} \end{array}

(13)

\begin{array}{l} \sum xsF = a \sum x s + b \sum x^{2} s + c \sum x^{3} s + d \sum x^{2} y s \\ + e \sum x^{2} s z + f \sum x^{2} s^{2} + g \sum x^{2} s t + h \sum xys \\ + i \sum x y^{2} s + j \sum xyzs + k \sum x y s^{2} + l \sum xyst \\ + m \sum xzs + n \sum x z^{2} s + o \sum x z s^{2} + p \sum xzst \\ + q \sum x s^{2} + r \sum x s^{3} + u \sum x s^{2} t + v \sum xst \\ + w \sum x^{2} s t^{2} \end{array}

(14)

\begin{array}{l} \sum xtF = a \sum x t + b \sum x^{2} t + c \sum x^{3} t + d \sum x^{2} y t \\ + e \sum x^{2} z t + f \sum x^{2} s t + g \sum x^{2} t^{2} + h \sum xyt \\ + i \sum x y^{2} t + j \sum xyzt + k \sum xyst + l \sum x y t^{2} \\ + m \sum xzt + n \sum x z^{2} t + o \sum xzst + p \sum x z t^{2} \\ + q \sum xst + r \sum x s^{2} t + u \sum x s t^{2} + v \sum x t^{2} \\ + w \sum x^{2} t^{3} \end{array}

(15)

\begin{array}{l} \sum y F = a \sum y + b \sum x y + c \sum x^{2} y + d \sum x y^{2} + e \sum xyz \\ + f \sum xys + g \sum xyt + h \sum y^{2} + i \sum y^{3} + j \sum y^{2} z \\ + k \sum y^{2} s + l \sum y^{2} t + m \sum y z + n \sum y z^{2} \\ + o \sum yzs + p \sum yzt + q \sum y s + r \sum y s^{2} \\ + u \sum yst + v \sum y t + w \sum y t^{2} \end{array}

(16)

\begin{array}{l} \sum y^{2} F = a \sum y^{2} + b \sum x y^{2} + c \sum x^{2} y^{2} + d \sum x y^{3} \\ + e \sum x y^{2} z + f \sum x y^{2} s + g \sum x y^{2} t + h \sum y^{3} \\ + i \sum y^{4} + j \sum y^{3} z + k \sum y^{3} s + l \sum y^{3} t \\ + m \sum y^{2} z + n \sum y^{2} z^{2} + o \sum y^{2} z s + p \sum y^{2} z t \\ + q \sum y^{2} s + r \sum y^{2} s^{2} + u \sum y^{2} s t + v \sum y^{2} t \\ + w \sum y^{2} t^{2} \end{array}

(17)

\begin{array}{l} \sum yzF = a \sum y z + b \sum xyz + c \sum x^{2} y z + d \sum x y^{2} z \\ + e \sum x y z^{2} + f \sum xyzs + g \sum xyzt + h \sum y^{2} z \\ + i \sum y^{3} z + j \sum y^{2} z^{2} + k \sum y^{2} z s + l \sum y^{2} z t \\ + m \sum y z^{2} + n \sum y z^{3} + o \sum y z^{2} s + p \sum y z^{2} t \\ + q \sum yzs + r \sum y z s^{2} + u \sum yzst + v \sum yzt \\ + w \sum y z t^{2} \end{array}

(18)

\begin{array}{l} \sum ysF = a \sum y s + b \sum xys + c \sum x^{2} y s + d \sum x y^{2} s \\ + e \sum xyzs + f \sum x y s^{2} + g \sum xyst + h \sum y^{2} s \\ + i \sum y^{3} s + j \sum y^{2} z s + k \sum y^{2} s^{2} + l \sum y^{2} s t \\ + m \sum yzs + n \sum y z^{2} s + o \sum y z s^{2} + p \sum yzst \\ + q \sum y s^{2} + r \sum y s^{3} + u \sum y s^{2} t + v \sum yst \\ + w \sum y s t^{2} \end{array}

(19)

\begin{array}{l} \sum ytF = a \sum y t + b \sum xyt + c \sum x^{2} y t + d \sum x y^{2} t \\ + e \sum xyzt + f \sum xyst + g \sum x y t^{2} + h \sum y^{2} t \\ + i \sum y^{3} t + j \sum y^{2} z t + k \sum y^{2} s t + l \sum y^{2} t^{2} \\ + m \sum yzt + n \sum y z^{2} t + o \sum yzst + p \sum y z t^{2} \\ + q \sum yst + r \sum y s^{2} t + u \sum y s t^{2} \\ + v \sum y t^{2} + w \sum y t^{3} \end{array}

(20)

\begin{array}{l} \sum z F = a \sum z + b \sum x z + c \sum x^{2} z + d \sum xyz + e \sum x z^{2} \\ + f \sum xzs + g \sum xzt + h \sum z y + i \sum y^{2} z \\ + j \sum y z^{2} + k \sum yzs + l \sum yzt + m \sum z^{2} \\ + n \sum z^{3} + o \sum z^{2} s + p \sum z^{2} t + q \sum z s \\ + r \sum z s^{2} + u \sum zst + v \sum z t + w \sum z t^{2} \end{array}

(21)

\begin{array}{l} \sum z^{2} F = a \sum z^{2} + b \sum x z^{2} + c \sum x^{2} z^{2} + d \sum x y z^{2} \\ + e \sum x z^{3} + f \sum x z^{2} s + g \sum x z^{2} t + h \sum z^{2} y \\ + i \sum y^{2} z^{2} + j \sum y z^{3} + k \sum y z^{2} s + l \sum y z^{2} t \\ + m \sum z^{3} + n \sum z^{4} + o \sum z^{3} s + p \sum z^{3} t \\ + q \sum z^{2} s + r \sum z^{2} s^{2} + u \sum z^{2} s t \\ + v \sum z^{2} t + w \sum z^{2} t^{2} \end{array}

(22)

\begin{array}{l} \sum zsF = a \sum z s + b \sum xzs + c \sum x^{2} z s + d \sum xyzs \\ + e \sum x z^{2} s + f \sum x z s^{2} + g \sum xzst + h \sum zsy \\ + i \sum y^{2} z s + j \sum y z^{2} s + k \sum y z s^{2} + l \sum yzst \\ + m \sum z^{2} s + n \sum z^{3} s + o \sum z^{2} s^{2} + p \sum z^{2} s t \\ + q \sum z s^{2} + r \sum z s^{3} + u \sum z s^{2} t + v \sum zst \\ + w \sum z s t^{2} \end{array}

(23)

\begin{array}{l} \sum ztF = a \sum z t + b \sum xzt + c \sum x^{2} z t + d \sum xyzt \\ + e \sum x z^{2} t + f \sum xzst + g \sum x z t^{2} + h \sum zyt \\ + i \sum z y^{2} t + j \sum y z^{2} t + k \sum yzst + l \sum y z t^{2} \\ + m \sum z^{2} t + n \sum z^{3} t + o \sum z^{2} s t + p \sum z^{2} t^{2} \\ + q \sum zst + r \sum z s^{2} t + u \sum z s t^{2} + v \sum z t^{2} \\ + w \sum z t^{3} \end{array}

(24)

\begin{array}{l} \sum s F = a \sum s + b \sum x s + c \sum x^{2} s + d \sum xys + e \sum xzs \\ + f \sum x s^{2} + g \sum xst + h \sum y s + i \sum y^{2} s \\ + j \sum yzs + k \sum y s^{2} + l \sum yst + m \sum s z \\ + n \sum s z^{2} + o \sum z s^{2} + p \sum zst + q \sum s^{2} \\ + r \sum s^{3} + u \sum s^{2} t + v \sum s t + w \sum s t^{2} \end{array}

(25)

\begin{array}{l} \sum s^{2} F = a \sum s^{2} + b \sum x s^{2} + c \sum x^{2} s^{2} + d \sum x y s^{2} \\ + e \sum x z s^{2} + f \sum x s^{3} + g \sum x s^{2} t + h \sum y s^{2} \\ + i \sum y^{2} s^{2} + j \sum y z s^{2} + k \sum y s^{3} + l \sum y s^{2} t \\ + m \sum s^{2} z + n \sum s^{2} z^{2} + o \sum z s^{3} + p \sum z s^{2} t \\ + q \sum s^{3} + r \sum s^{4} + u \sum s^{3} t \\ + v \sum s^{2} t + w \sum s t^{2} \end{array}

(26)

\begin{array}{l} \sum stF = a \sum s t + b \sum xst + c \sum x^{2} s t + d \sum xyst \\ + e \sum xzst + f \sum x s^{2} t + g \sum x s t^{2} + h \sum yst \\ + i \sum y^{2} s t + j \sum yzst + k \sum y s^{2} t + l \sum y s t^{2} \\ + m \sum szt + n \sum s z^{2} t + o \sum z s^{2} t + p \sum z s t^{2} \\ + q \sum s^{2} t + r \sum s^{3} t + u \sum s^{2} t^{2} + v \sum s t^{2} \\ + w \sum s t^{3} \end{array}

(27)

\begin{array}{l} \sum t F = a \sum t + b \sum x t + c \sum x^{2} t + d \sum xyt + e \sum xzt \\ + f \sum xst + g \sum x t^{2} + h \sum y t + i \sum y^{2} t + j \sum yzt \\ + k \sum yst + l \sum y t^{2} + m \sum z t + n \sum z^{2} t + o \sum zst \\ + p \sum z t^{2} + q \sum s t + r \sum s^{2} t + u \sum s t^{2} + v \sum t^{2} \\ + w \sum t^{3} \end{array}

(28)

\begin{array}{l} \sum t^{2} F = a \sum t^{2} + b \sum x t^{2} + c \sum x^{2} t^{2} + d \sum x y t^{2} \\ + e \sum x z t^{2} + f \sum x s t^{2} + g \sum x t^{3} + h \sum y t^{2} \\ + i \sum y^{2} t^{2} + j \sum y z t^{2} + k \sum y s t^{2} + l \sum y t^{3} \\ + m \sum z t^{2} + n \sum z^{2} t^{2} o \sum z s t^{2} + p \sum z t^{3} \\ + q \sum s t^{2} + r \sum s^{2} t^{2} + u \sum s t^{3} \\ + v \sum t^{3} + w \sum t^{4} \end{array}

(29)

Both the linear and the quadratic models lead to predictive functions. The error analysis of both models helps to check their validity.

Results and discussion

This section describes the construction of linear and quadratic mathematical models from the experimental data collected from the sample of 10 scarves. LSA (with Mathematica) is used to predict the thermophysiological comfort properties of scarves, depending on warp count, weft count, EPI, PPI, and fabric weight in GSM.

Modeling air permeability of scarves using LSA

The fabric air permeability is the air flow rate across a portion of fabric in a given period, as measured by the pressure difference across the fabric within the fabric test area. This property is mainly dependent on fabric weight, thickness, and porosity.

Linear model

For the data given in Table 1, an LSA linear model for the air permeability of a scarf in terms of warp (x), weft (y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = 15228.4 + 13.5369 x - 255.303 y \\ - 9.97842 z + 187.104 s - 157.257 t \end{array}

(30)

Quadratic model

For the data given in Table 1, an LSA quadratic model for the air permeability of a scarf in terms of warp (x), weft (y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = 9169.5 - 55 .0 467 x + 0. 372543 x^{2} \\ - 1 .0 8187 x y + 0. 43717 x z + 0. 579405 x s \\ - 2.4311 x t + 55.7658 y - 1.33377 y^{2} \\ - 1.12336 y z + 1 .0 2432 y s - 1.8905 y t \\ + 44 .0 709 z + 0. 386293 z^{2} - 0. 358853 z s \\ - 0.0 583972 z t + 75.716 s + 2.283 s^{2} \\ - 1.70184 s t + 42.2168 t - 0. 361811 t^{2} \end{array}

(31)

Modeling water permeability of scarves using LSA

Water vapor transmission is necessary for clothing comfort. A decrease in water permeability leads to an increase in relative humidity, causing discomfort to the human body. Thus, water vapor transmission is essential.

Linear model

For the data given in Table 1, an LSA linear model for the water permeability of a scarf in terms of warp (x), weft (y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = 15228.4 + 13.5369 x - 255.303 y \\ - 9.97842 z + 187.104 s - 157.257 t \end{array}

(32)

Quadratic model

For the data given in Table 1, an LSA quadratic model for the water permeability of a scarf in terms of warp (x), weft (y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = 9169.5 - 55 .0 467 x + 0. 372543 x^{2} \\ - 1 .0 8187 x y + 0. 43717 x z + 0. 579405 x s \\ - 2.4311 x t + 55.7658 y - 1.33377 y^{2} \\ - 1.12336 y z + 1 .0 2432 y s - 1.8905 y t \\ + 44 .0 709 z + 0. 386293 z^{2} - 0. 358853 z s \\ - 0.0 583972 z t + 75.716 s + 2.283 s^{2} \\ - 1.70184 s t + 42.2168 t - 0. 361811 t^{2} \end{array}

(33)

Modeling thermal resistance of scarves using LSA

The thermal resistance of the fabric is a function of the fabric thickness. Fabric with a high thermal conductivity will have a lower thermal resistance if it is thick enough. The thermal resistance is the time taken to transfer heat through the fabric in one direction at a speed determined by the heat conductivity.

Linear model

For the data given in Table 1, an LSA linear model for the thermal resistance of a scarf in terms of warp (x), weft (y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = 0.0 411882 - 0.000 343337 x \\ - 0.0000 248356 y + 0.000 131911 z \\ - 0.000 117701 s - 0.000 117848 t \end{array}

(34)

Quadratic model

For the data given in Table 1, an LSA quadratic model for the thermal resistance of a scarf in terms of warp (x), weft (y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = 0.0 231343 + 0.00 116112 x \\ - (2.98132 \times 1 0^{- 6}) x^{2} - (7.85462 \times 1 0^{- 7}) x y \\ - (1.61024 \times 1 0^{- 6}) x z - (9.75466 \times 1 0^{- 6}) x s \\ - (5 .0 3357 \times 1 0^{- 6}) x t + 0.000 784833 y \\ - (5.18899 \times 1 0^{- 7}) y^{2} + (5.69715 \times 1 0^{- 6}) y z \\ - 0.0000 106651 y s - 0.0000 172638 y t \\ - 0.000 461396 z + (1.97546 \times 1 0^{- 6}) z^{2} \\ + (8.22671 \times 1 0^{- 6}) z s - (5.34745 \times 1 0^{- 6}) t z \\ + 0.000 123107 s - (2.15726 \times 1 0^{- 6}) s^{2} \\ + 0.0000 107186 s t - 0.000 567994 t \\ + (7.71528 \times 1 0^{- 6}) t^{2} \end{array}

(35)

Modeling moisture management of scarves using LSA

Moisture management is an important criterion that determines the comfort level of that fabric. The consumer’s demand draws the attention of apparel manufacturers to the high-performance end, regarding the moisture management of fabric.

Linear model

For the data given in Table 1, an LSA linear model for the moisture management of a scarf in terms of warp (x), weft (y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = 0. 423675 - 0.00 998755 x - 0.0 167395 y \\ + 0.00 304431 z - 0.0 102781 s \\ + 0.00 486034 t \end{array}

(36)

Quadratic model

For the data given in Table 1, an LSA quadratic model for the moisture management of a scarf in terms of warp (x), weft (y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = 0. 83056 - 0.000 48401 x \\ - 0.000 291935 x^{2} - 0.0000 984435 x y \\ - (3.50773 \times 1 0^{- 6}) x z + 0.0000 522856 x s \\ - (4.81255 \times 1 0^{- 6}) x t + 0.00 487781 y \\ - 0.0000 118858 y^{2} + 0.000 213635 y z \\ + 0.000 103921 y s - 0.0000 362336 y t \\ - 0.00 124991 z + 0.0000 289056 z^{2} \\ + 0.000 111453 z s - 0.00 300543947 t z \\ - 0.00 822669 s + 0.0000 272888 s^{2} \\ - 0.000 234111 s t + 0.00 562085 t \\ + 0.0000 44884 t^{2} \end{array}

(37)

Modeling pilling resistance of scarves using LSA

Pilling is the tendency of fibers to come loose from a fabric surface and form balled particles of fiber. Pilling is caused by wear and abrasion, rubbing actions, the presence of softly twisted yarn, an excess of short fibers, and migration of fibers from the constituent yarn.

Linear model

For the data given in Table 1, an LSA linear model for the pilling resistance of a scarf in terms of warp (x), weft (y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = - 0. 511646 - 0.0 517001 x \\ + 0.0 308296 y + 0.0 336121 z \\ + 0.0 243579 s + 0.00 463296 t \end{array}

(38)

Quadratic model

For the data given in Table 1, an LSA quadratic model for the pilling resistance of a scarf in terms of warp (x), weft(y), EPI (z), PPI (s), and GSM (t) can be determined as

\begin{array}{l} F (x, y, z, s, t) = 6.84826 + 0. 174951 x - 0.00 524105 x^{2} \\ - 0.00 181568 x y - 0.000 347079 x z \\ + 0.000 493115 x s + 0.00 186555 x t \\ + 0.0 787211 y - 0.000 935822 y^{2} \\ + 0.00 421184 y z + 0.000 23328 y s \\ - 0.00 156671 y t - 0. 138736 z \\ + 0.000 527256 z^{2} + 0.00 321523 z s \\ - 0.00 167803 t z - 0. 167169 s \\ + 0.000 242464 s^{2} - 0.00 139305 s t \\ - 0.0 458221 t + 0.00 117326 t^{2} \end{array}

(39)

Validation of results

Error analysis is important, as it characterizes the validity of the predicted models. We have developed linear and quadratic relationships of the thermophysiological properties of scarves, for example, air and water permeability, thermal resistance, MMP, and pilling resistance, concerning the changes in warp (unit, Ne), weft (unit, Ne), EPI, PPI, and GSM. Based on error analysis, an effective and efficient model can be traced.

We took six samples for error analysis, the details of which are given in Table 2.

Table 2.

Data collection for model validation

Sample number	Fabric type	Warp (x)	Weft (y)	Ends per inch (z)	Picks per inch (s)	Grams per square meter (t)	Air permeability (F₁)	Water vapor permeability (F₂)	Thermal resistance (F₃)	Moisture management permeability (F₄)	Pilling resistance (F₅)
1	50% Micromodal; 50% cotton	60	60	80	70	63.6	1775	96.6	0.017	0.62	2.5
2	50% cotton; 50% modal	60	60	80	70	58.6	2616	94.8	0.015	0.78	2
3	50% micro polyester; 50% cotton	60	60	82	70	60	2545	92.5	0.013	0.63	2
4	50% Coolmax; 50% cotton	60	60	82	72	63.2	1887	94.8	0.016	0.80	2
5	50% viloft; 50% cotton	60	60	80	70	59.4	2248	98.3	94.6	0.67	2
6	100% cotton	60	60	80	70	61.6	3334	90.3	0.016	0.36	2.5

It is well known that errors are traced using a simple formula:

Error = Observed value - theoretical value

This leads to the errors in the samples, which can be used to show the validity of the model. We want to make a comparison between the linear and quadratic models for the same property, to find a reliable model for prediction purposes. Note that O represents the observed value in each sample, A₁ and A₂ denote the theoretical values determined by the linear and quadratic models, respectively, and E₁ and E₂ are the errors obtained from the linear and quadratic models, respectively.

Table 3 and Figure 1 give the error analysis of the linear and quadratic models developed for air permeability (Equations (30) and (31), respectively).

Table 3.

Error analysis for air permeability

Sample number	O	A ₁	E ₁	\|E₁\|	A ₂	E ₂	\|E₂\|
1	1775	3020	−1245	1245	2631	−856	856
2	2616	3806	−1190	1190	4557	−1945	1945
3	2545	3566	−1021	1021	4093	−1548	1548
4	1887	3437	−1550	1550	3577	−1690	1690
5	2248	3680	−1432	1432	4250	−2002	2002
6	1764	3334	−1570	1570	3404	−1640	1640

Figure 1.

Error analysis of linear and quadratic models for air permeability.

Table 4 and Figure 2 give the error analysis of the linear and quadratic models developed for water permeability (Equations (32) and (33), respectively).

Table 4.

Error analysis for water permeability

Sample number	O	A ₁	E ₁	\|E₁\|	A ₂	E ₂	\|E₂\|
1	96.6	94.4	2.3	2.3	95.9	0.7	0.7
2	94.8	95.5	−0.7	0.7	97.1	−2.3	2.3
3	92.5	92.5	0.0	0.0	92.5	0.0	0.0
4	94.8	94.8	0.0	0.0	94.8	0.0	0.0
5	98.3	95.3	3.0	3.0	94.6	3.7	3.7
6	90.3	94.8	−4.5	4.5	92.4	−2.1	2.1

Figure 2.

Error analysis of linear and quadratic models for water permeability.

Table 5 and Figure 3 give the analysis of the linear and quadratic models developed for thermal resistance (Equations (34) and (35), respectively).

Table 5.

Error analysis for thermal resistance

Sample number	O	A ₁	E ₁	\|E₁\|	A ₂	E ₂	\|E₂\|
1	0.017	0.014	0.003	0.003	0.009	0.005	0.005
2	0.015	0.015	0.00	0.00	0.012	0.003	0.003
3	0.013	0.015	−0.002	0.002	0.012	0.003	0.003
4	0.016	0.014	0.002	0.002	0.009	0.005	0.005
5	0.015	0.014	0.001	0.001	0.011	0.003	0.003
6	0.016	0.014	0.002	0.002	0.009	0.005	0.005

Figure 3.

Error analysis of linear and quadratic models for thermal resistance.

Table 6 and Figure 4 give the error analysis of the linear and quadratic models developed for MMP (Equations (36) and (37), respectively).

Table 6.

Error analysis for moisture management permeability

Sample number	O	A ₁	E ₁	\|E₁\|	A ₂	E ₂	\|E₂\|
1	0.62	0.66	−0.04	0.04	0.64	−0.02	0.02
2	0.78	0.64	0.14	0.14	0.70	0.06	0.06
3	0.63	0.65	0.02	0.02	0.73	−0.08	0.08
4	0.8	0.65	0.15	0.15	0.69	0.04	0.04
5	0.67	0.64	0.03	0.03	0.69	−0.05	0.05
6	0.36	0.65	−0.29	0.29	0.67	−0.02	0.02

Figure 4.

Error analysis of linear and quadratic models for moisture management permeability.

Table 7 and Figure 5 give the error analysis of the linear and quadratic models developed for pilling resistance (Equations (38) and (39), respectively).

Table 7.

Error analysis for pilling resistance

Sample number	O	A ₁	E ₁	\|E₁\|	A ₂	E ₂	\|E₂\|
1	2.5	−2.6	0.1	0.1	2.5	0.0	0.0
2	2	2	0.0	0.0	1.9	0.1	0.1
3	2	2	0.0	0.0	2	0.0	0.0
4	2	2	0.0	0.0	2	0.0	0.0
5	2	2.1	−0.1	0.1	2	−0.1	0.1
6	2.5	2.3	0.2	0.2	2.4	0.1	0.1

Figure 5.

Error analysis of linear and quadratic models for pilling resistance.

Conclusion

The thermophysiological properties of ladies’ scarves are worth investigating, to increase the comfort of the consumer. These properties include air and water permeability, thermal and pilling resistance, and moisture management. We have determined a mathematical model for these properties, based on the minimum number of weaving parameters, including warp count, weft count, EPI, PPI, and GSM. The linear and quadratic mathematical models are fitted using the LSA technique. An error analysis of both models showed that the quadratic model is more accurate. Moreover, the model for pilling resistance is found to give the best approximation, as the least error is obtained for the linear and quadratic models.

Linear relationships for the prediction of air permeability, water vapor permeability, thermal resistance, MMP, and pilling resistance dependent on warp count (x), weft count (y), EPI (z), PPI (s), and GSM (t) have been developed. The results are summarized in Table 8.

Table 8.

Linear prediction models for air permeability, water vapor permeability, thermal resistance, moisture management permeability, and pilling resistance, dependent on warp count (x), weft count (y), ends per inch (z), picks per inch (s), and grams per square meter (t)

Comfort property	Function approximation
Air permeability (AP)	AP(x, y, z, s, t) = 15228.4 + 13.5369x − 255.303y − 9.97842z + 187.104s − 157.257t
Water permeability (WP)	WP(x, y, z, s, t) = 55.3297 + 0.618465x − 0.00119652y − 0.274997z + 0.0464624s + 0.429688t
Thermal resistance (TR)	TR(x, y, z, s, t) = 0.0411882 − 0.000343337x − 0.0000248356y + 0.000131911z −0.000117701s − 0.000117848t
Moisture management permeability (MMP)	MMP(x, y, z, s, t) = 0.423675 − 0.00998755x − 0.0167395y + 0.00304431z −0.0102781s + 0.00486034t
Pilling resistance (PR)	PR(x, y, z, s, t) = −0.511646 − 0.0517001x + 0.0308296y + 0.0336121z +0.0243579s + 0.00463296t

Quadratic relationships for the prediction of air permeability, water vapor permeability, thermal resistance, MMP, and pilling resistance dependent on warp count (x), weft count (y), EPI (z), PPI (s), and GSM (t) have been developed. The results are summarized in Table 9.

Table 9.

Quadratic prediction models for air permeability, water vapor permeability, thermal resistance, moisture management permeability, and pilling resistance, dependent on warp count (x), weft count (y) , ends per inch (z), picks per inch (s), and grams per square meter (t)

Comfort property	Function approximation
Air permeability	F(x, y, z, s, t) = 9169.5 − 55.0467x + 0.372543x² − 1.08187xy +0.43717xz + 0.579405xs− 2.4311xt + 55.7658y −1.33377y² − 1.12336yz + 1.02432ys − 1.8905yt +44.0709z+ 0.386293z² − 0.358853zs − 0.0583972zt + 75.716s + 2.283s² − 1.70184st + 42.2168t− 0.361811t²
Water permeability	F(x, y, z, s, t) = 42.3449 + 0.406663x − 0.000946889x² − 0.000346543xy− 0.000364354xz + 0.00352523sx + 0.00426711tx + 0.224216y − 0.00285234y² + 0.0000333147yz + 0.000639188sy − 0.0000728566ty+ 0.0320306z − 0.000818532z² − 0.000749759sz − 0.00146693tz + 0.0776948s − 0.000033893s² − 0.00396243st + 0.379728t + 0.00168067t²
Thermal resistance	F(x, y, z, s, t) = 0.0231343 + 0.00116112x − (2.98132 × 10⁻⁶)x² − (7.85462 × 10 ⁻ ⁷)xy− (1.61024 × 10⁻⁶)xz − (9.75466 × 10⁻⁶)xs− (5.03357 × 10⁻⁶)xt + 0.000784833y− (5.18899 × 10⁻⁷)y² + (5.69715 × 10⁻⁶)yz − 0.0000106651ys − 0.0000172638yt− 0.000461396z + (1.97546 × 10⁻⁶)z² + (8.22671 × 10⁻⁶)zs− (5.34745 × 10⁻⁶)tz+ 0.000123107s − (2.15726 × 10⁻⁶)s²+0.0000107186st − 0.000567994t + (7.71528 × 10⁻⁶)t²
Moisture management permeability	F(x, y, z, s, t) = 0.83056 − 0.00048401x − 0.000291935x² − 0.0000984435xy − (3.50773 × 10 ⁻ ⁶)xz+ 0.0000522856xs− (4.81255 × 10 ⁻ ⁶)xt + 0.00487781y − 0.0000118858y² + 0.000213635yz+ 0.000103921ys − 0.0000362336yt − 0.00124991z + 0.0000289056z²+ 0.000111453zs − 0.00300543947tz − 0.00822669s + 0.0000272888s²− 0.000234111st + 0.00562085t + 0.000044884t²
Pilling resistance	F(x, y, z, s, t) = 6.84826 + 0.174951x − 0.00524105x² − 0.00181568xy − 0.000347079xz + 0.000493115xs + 0.00186555xt + 0.0787211y − 0.000935822y² + 0.00421184yz + 0.00023328ys − 0.00156671yt− 0.138736z + 0.000527256z² + 0.00321523zs − 0.00167803tz − 0.167169s + 0.000242464s²− 0.00139305st − 0.0458221t + 0.00117326t²

The key aim of this research is dependent on the error analysis of all the linear and quadratic models of the thermophysiological properties of scarves, such as air and water permeability, thermal resistance, MMP, and pilling resistance, with respect to the changes in warp (unit, Ne), weft (unit, Ne), EPI, PPI, and GSM. Tables (3) to (7) indicate that, for the same thermophysiological property, the error terms at each point in the quadratic model are smaller than the error terms of the linear model. Thus, the quadratic approximation leads to better results, compared with the linear approximation. Moreover, the model for pilling resistance is found to give the best approximation, as the smallest error is obtained for both the linear and the quadratic models.

This research can be extended to the mathematical prediction of other thermophysiological comfort properties of scarves. Moreover, this research can be extended to home textile products and other types of apparel, such as different wearables, hosiery, and sportswear.

Footnotes

Acknowledgment

We are grateful to the Higher Education Commission, Pakistan, and the National Textile University Faisalabad, Pakistan for their support.

Data and code availability

The data are available on request to the authors.

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Global Challenge Research Fund (GCRF), UK Research Innovation, and the Henry Royce Institute for Advanced Materials (EPSRC grant numbers EP/R00661X/1, EP/P025021/1, EP/P025498/1).

ORCID iDs

Muhammad Qamar Khan

Muhammad Salman Naeem

Muhammad Umar

References

Liu

Fung

, and Abida

Evaluation of perceived comfort and functional performance of activewear. In: Yip

(ed.) Latest material and technological developments for activewear. Duxford: Woodhead, 2020, pp. 89–118.

Islam

Golovin

, and Dolez

PI.

Clothing thermophysiological comfort: A textile science perspective. Textiles 2023; 3: 353–407.

Ayachi

Dorey

, and Guastavino

Identifying factors of bicycle comfort: An online survey with enthusiast cyclists. Appl Ergon 2015; 46: 124–136.

Choudhury

AKR

Majumdar

, and Datta

Factors affecting comfort human physiology and the role of clothing. In: Song

(ed.) Improving comfort in clothing. Cambridge: Woodhead Publishing, 2011; pp. 3–60.

Iftikhar

Hussain

Ali

, et al. Investigation of thermo-physiological comfort and mechanical properties of fine cotton fabrics for ladies’ summer apparel. J Nat Fibers 2020; 17: 1619–1629.

Ahmad

Afzal

, et al. Effect of weave structure on thermo-physiological properties of cotton fabrics. AUTEX Res J 2015; 15: 30–34.

Jahan

Effect of fabric structure on the mechanical properties of woven fabrics. Adv Res Text Eng 2017; 2: 1018.

Baghdadi

Alibi

Fayala

, et al. Investigation on air permeability of finished stretch plain knitted fabrics. I. Predicting air permeability using artificial neural networks. Fibers Polym 2016; 17: 2105–2115.

Abbey

How to use FEA for thermal analysis. DE247 Digital Engineering, https://www.digitalengineering247.com/ article/use-fea-thermal-analysis/ (2014, accessed 21 October 2024).

10.

Sfikas

Ingham

, and Baber

Simulating thermal behaviour of concrete by FEA: State-of-the-art review. Proc Inst Civ Eng Constr Mater 2018; 171: 59–71.

11.

Gulrajani

(ed.). Advances in the dyeing and finishing of technical textiles. Cambridge: Woodhead, 2013.

12.

Das

Alagirusamy

Science in clothing comfort. New Delhi: Woodhead, 2010, p. 54.

13.

Shachaf Schneider

Sisters, but not twin sisters: A comparison between the Union for Reform Judaism and the Israel Movement for Reform and Progressive Judaism. MA Thesis, Brandeis University, USA, 2017.

14.

DiNardo

Comparative study of comfort properties of five different common apparel textiles. Senior Hons. Thesis, Eastern Michigan University, USA, 2011.

15.

Hussain

Younis

Usman

, et al. Comfort and mechanical properties of polyester/bamboo and polyester/cotton blended knitted fabric. J Eng Fibers Fabr 2015; 10: 61–69.

16.

Özgen

Altaş

The investigation of thermal comfort, moisture management and handle properties of knitted fabrics made of various fibres. Tekstil ve Konfeksiyon 2014; 24: 272–278.

17.

Özkan

Meriç

Thermophysiological comfort properties of different knitted fabrics used in cycling clothes. Text Res J 2015; 85: 62–70.

18.

Kakvan

Shaikhzadeh Najar

, and Psikuta

Study on effect of blend ratio on thermal comfort properties of cotton/nylon-blended fabrics with high-performance Kermel fibre. J Text Inst 2015; 106: 674–682.

19.

Varshney

Kothari

, and Dhamija

A study on thermophysiological comfort properties of fabrics in relation to constituent fibre fineness and cross-sectional shapes. J Text Inst 2010; 101: 495–505.

20.

Demiryürek

Uysaltürk

Thermal comfort properties of Viloft/cotton and Viloft/polyester blended knitted fabrics. Tex Res J 2013; 83: 1740–1753.

21.

Aydin

Emon

Cheng

, et al. Performance of fabrics for home-made masks against the spread of COVID-19 through droplets: A quantitative mechanistic study. Extreme Mech Lett 2020; 40: 100924.

22.

Maduna

Patnaik

Heat, moisture and air transport through clothing textiles. Text Prog 2020; 52: 129–166.

23.

Tang

K-PM

Kan

C-W

, and Fan

J-T.

Evaluation of water absorption and transport property of fabrics. Text Prog 2014; 46: 1–132.

24.

Pezeshki

Soleimani

Darabi

, et al. Thermal transport in: Building materials. Constr Build Mater 2018; 181: 238–252.

25.

Limeneh

Ayele

Tesfaye

, et al. Effect of weave structure on comfort property of fabric. J Nat Fibers 2022; 19: 4148–4155.

26.

Bal

Das

Moisture management and wicking behavior of textiles. In: Maity

Singha

, and Pandit

(eds.) Functional and technical textiles. Cambridge, MA: Woodhead, 2023, pp. 453–498.

27.

Cochrane

Cao

Girouard

, et al. Breathing scarf: Using a first-person research method to design a wearable for emotional regulation. In: TEI ’22: Proceedings of the Sixteenth International Conference on Tangible, Embedded, and Embodied Interaction, Daejeon, Republic of Korea, 13–16 February 2022, paper no. 24, New York: ACM.

28.

Marmarali

Effects of fiber cross-section shape on thermal comfort properties of polyester interlock fabrics. Commun Dev Assemb Text Prod 2023; 4: 42–50.

29.

Jhanji

Gupta

, and Kothari

VK.

Thermal and mass transport properties of polyester–cotton plated fabrics about back layer fibre profiles and face layer yarn types. J Text Inst 2018; 109: 669–676.

30.

Asfand

Daukantienė

VJ.

Evaluation of the moisture management and air permeability of cotton/antistatic polyester knitted fabrics. J Ind Text 2023; 53: 15280837231194369.

31.

Nasrin

Characterizing the effects of fabric parameters on drying performance in active sportswear. M.Sc. Thesis, Oklahoma State University, USA, 2023.

32.

Begum

Milašius

Factors of weave estimation and the effect of weave structure on fabric properties: A review. Fibers 2022; 10: 74.

33.

Ullah

Fiaz

Abbas

, et al. Thermal comfort and mechanical analysis of vigorous diamond and diaper weaves; warp, weft and balanced float fabrics with equal thread densities. Int J Therm Sci 2024; 204: 109235.

34.

Nazir

Shaker

Nawab

, et al. Thermo-physiological comfort of woven fabrics made from different cellulosic yarns. J Nat Fibers 2022; 19: 4050–4062.

35.

Bullón Pérez

González Arrieta

Hernández Encinas

, et al. Manufacturing processes in the textile industry: Expert systems for fabrics production. ADCAIJ: Adv Distrib Comput Artif Intell J 2017; 6: 17–23.

36.

Suzuki

Yoshida

Penalized least squares approximation methods and their applications to stochastic processes. Jpn J Stat Data Sci 2020; 3: 513–541.

37.

Harrell

Jr.

General aspects of fitting regression models. In: Harrell

Jr (ed.) Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis. Cham: Springer, 2015; pp. 13–44.

38.

Özkan

Kaplangiray

BM.

Investigating thermophysiological comfort properties of polyester knitted fabrics. J Text Eng Fashion Technol 2019; 5: 50–56.

39.

Özdemir

Thermal comfort properties of clothing fabrics woven with polyester/cotton blend yarns. AUTEX Res J 2017; 17: 135–141.

40.

Miller

SJ.

The method of least squares. In: Miller

(ed.) The probability lifesaver: All the tools you need to understand chance. Princeton: Princeton University Press, 2017, pp. 625–635.

41.

Molugaram

Rao

GS.

Statistical techniques for transportation engineering. Oxford: Butterworth- Heinemann, 2017.

42.

Gao

Zhou

On the choice of design points for least square polynomial approximations with application to uncertainty quantification. Commun Comput Phys 2014; 16: 365–381.

43.

Chen

, and Tsay

TK.

Application of weighted-least-square local polynomial approximation to 2D shallow water equation problems. Eng Anal Boundary Elem 2016; 68: 124–134.

44.

Error estimates for the moving least-square approximation and the element-free Galerkin method in n-dimensional spaces. Appl Numer Math 2016; 99: 77–97.

45.

Chen

, and Wang

Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method. Appl Math Comput 2015; 262: 56–78.

46.

Wickramasinghe

GLD

Dolawatte

Thebuwana

, et al. Effect of air pressure on polyester/nylon air-intermingled yarn and melange fabric properties. J Text Inst 2021; 112: 526–537.

47.

Shaffie

Mohd Nasir

Putra Jaya

, et al. Statistical approach model to evaluate permanent deformation of steel fiber modified asphalt mixtures. Sustainability 2023; 15: 3476.

48.

ISO 3801:1977. Textiles—Woven fabrics—Determination of mass per unit length and mass per unit area.

49.

BS EN ISO 9237:1995. Textiles. Determination of the permeability of fabrics to air.

50.

ISO 11092:2014: Textiles—Physiological effects—Measurement of thermal and water-vapour resistance under steady-state conditions (sweating guarded-hotplate test).

51.

TM 195:2011. Liquid moisture management properties of textile fabrics.