Research on prediction model of thermal and moisture comfort of underwear based on principal component analysis and Genetic Algorithm–Back Propagation neural network

2.1 Selection of testers

The participants were five young men, all of whom were healthy. Before the experiment, the participants were asked not to smoke, drink alcohol and take stimulating drugs. Tell them the process and danger of the test truthfully, but don’t tell the subjects about the test fabric, so as to prevent the physiological and psychological influences of the subjects. The body size of the five college students are in Table 1.

2.2 Experimental condition

1. All the experiments were carried out in an artificial climate chamber with constant temperature and humidity. The ambient temperature was (25 ± 2)°C, the relative humidity was (65 ± 5)% and the wind speed ≤0.1 m/s.

2. Select men’s underwear with XL size and the same style and different fabrics.

3. Before each experiment is carried out, ensure that all experimental underpants are restored to their original state and placed in the artificial climate room for 24 h.

4. The tester randomly selects and tries on each underwear in turn without being informed of the underwear fabric for the experiment.

5. During measurement, the upper body of the tester is exposed, and each link is measured 3 times. In the next measurement, it shall be taken off and put on again before measurement.

2.3 Experimental underwear

Fifty underwears of different brands were purchased randomly. Take 10 underwears as an example. Table 2 shows the fabric parameters of underwear.

2.4 Subjective comfort evaluation

Five testers entered the artificial climate room at the same time on different days to prepare according to the experimental requirements. The whole test process is as follows: preparation (20 min, aimed at adapting to the test environment) → sit quietly (15 min) → limb movement (10 min) → rest (5 min) → jogging on treadmill (5 min, speed controlled at 4.6 km/h) → rest (15 min). Each participant wore all experimental underwear in turn and conducted experiment according to the above procedure. At the same time, the staff should record the subjective comfort evaluation value of the participants in each experimental link, and finally calculate the average value as the final subjective evaluation.

According to ISO 10551-2001, "Ergonomics of Thermal Environment Evaluates Impact of Thermal Environment by Subjective Judgment Scale", subjective evaluation is carried out, as shown in Figure 1 and Table 3.

Figure 1:

Subjective judgement scale. Note: level 0 (comfortable) (C), level 1 (slightly uncomfortable (SU), level 2 (uncomfortable) (U), level 3 (very uncomfortable) (VU), and level 4 (extremely uncomfortable) (EU).

2.5 Kendall correlation coefficient (KCC) test of subjective evaluation results

In order to verify the consistency of the evaluation results among the five evaluators (i.e., five testers), Kendall is used to analyse whether the judgement criteria of the evaluators are consistent and fair. KCC, also known as harmony coefficient, is a method to express the correlation degree of multi-rank variables.

where α is the number of judges or testers; β is the number of observation objects or observation indicators and R _i is the sum of the ranks of the i observation object.

It is generally believed that Kendall coordination coefficient <0.2, it indicates poor consistency. Between 0.2 and 0.4, the consistency degree is general. The consistency between 0.4 and 0.6 is moderate. Between 0.6 and 0.8, the consistency degree is strong. Between 0.8 and 1.0, the consistency is very strong.

The original hypothesis Kendall coefficient is 0, i.e., completely inconsistent. As shown by the above-mentioned test, asymptotics significance value = 0.000 < 0.05. The original hypothesis is not valid (obviously not equal to zero), whereas it shows Kendall consistency.

Kendall correlation coefficient (Kendall W^a) = 0.924 (see Table 4), which is greater than 0.8, indicating that the comfort evaluation of underwear by five professionals has a high consistency level and the data are reliable.

3.1 PCA optimization of input parameters

The initial input parameters of GA–BP are those in Tables 1 and 2, which may lead to network redundancy due to too many input parameters and complicated correlation. Multiple collinearities between input variables will lead to strange changes in network parameters, thus reducing the generalization performance of the network. Therefore, PCA is used to reduce the dimension of parameters, eliminate some irrelevant factors, and at the same time, eliminate the multi-collinearity among variables to improve the accuracy of GA–BP model.

1. Input optimization of underwear parameters

Principal component analysis was carried out on Table 1 by SPSS. Before principal component analysis, KMO and Bartlett tests were carried out on 12 items of data such as thickness, gram weight and longitudinal density. KMO value is an indicator used to check whether the data can be used for principal component analysis, as shown in Table 5.

As can be seen from Table 6, KMO value = 0.835, indicating that parameter data of underwear can be factor analysed. Then, the input parameters of underwear are analysed by principal component analysis, as shown in Tables 7 and 8.

It can be seen from Table 7 that the cumulative contribution rate of principal components with eigenvalues greater than one is 84.306%, so five key feature size parameters of human body are obtained, which can be considered as sufficient to reflect the information of the original measurement data.

From Table 8, it can be seen that the input indexes of underwear parameters: the first main components are moisture regain, insulation rate, grammage and thermal resistance. The second principal component is air permeability, moisture permeability and heat transfer coefficient, and the third principal component is horizontal density and thickness. The fourth principal component is CLO value, longitudinal density. The fifth main component is wet resistance. Through principal component analysis, according to relevant articles [14], [15], [16], [17], [18] and professional knowledge, moisture regain, insulation rate, air permeability, horizontal density, CLO value and moisture permeability are selected as the input of underwear parameters. Therefore, the main fabric indexes that reflect the thermal and wet comfort of underwear are moisture regain, insulation rate, air permeability, horizontal density, CLO value and wet resistance.

1. Input optimization of body shape parameter

According to relevant documents and my previous research [19], [20], [21], [22], this paper mastered the key parts that affect the body shape or which parts have a greater correlation, so this paper finally selected abdominal and hip thickness, BMI, waist circumference, thigh circumference, waist-hip height as the input parameters of the body shape.

3.2 Pattern design of GA–BP algorithm

First, the BP algorithm is adopted to select initial values through a certain number of studies. Secondly, GAm is used to optimize the weights and thresholds of the BP network, to avoid the defect that the BP network falls into local optimization when optimizing the weights and thresholds, and completing the network learning with given precision [23]. When the GA has a slow convergence speed, BP algorithm is adopted to complete the network learning with a given precision. This network model has the advantages of strong generalization, good stability, strong memory, global convergence and fast speed. Figure 2 shows its prediction flow.

1. Parameter setting:base on BP neural network, GA is used to optimize the weight and threshold of BP algorithm to improve the accuracy of BP algorithm. Its flow chart is shown in Figure 2. Six characteristic variables (moisture regain, heat preservation rate, air permeability, horizontal density, Crohn’s value and wet resistance) and five variables (abdominal hip thickness, BMI, waist circumference, thigh circumference and waist hip height) of the fabric are taken as input layers of the artificial neural network. Since the subjective evaluation is consistent, the body shape data corresponding to each underwear fabric parameter can be randomly selected from five evaluators, and the subjective evaluation value of the thermal and moisture comfort of the underwear is the subjective evaluation value of the evaluator, so the output value is the average value of the subjective evaluation of each underwear.

Figure 2:

GA–BP prediction structure diagram.

The hidden layer is I + O + ∂ , where I is the number of input layer variables (i.e., the number of input layer nodes or neurons) and O is the number of output layer variables (i.e., the number of output layer nodes or neurons), which is a constant between 1 and 10. According to some studies [24], [25], [26], the hidden layer is usually 2–15, and this item is selected as 13. The output layer is subjective comfort value. Then, the network structure this time is 11–13–1. In addition, the maximum number of this training is set at 1000 and the learning rate is 0.1. The minimum learning error is 0.00001 and the additional momentum factor net.trainParam.mc = 0.95; minimum performance gradient net.trainParam.min_grad = 1e-6; Genetic neural parameter evolution algebra, i.e., iteration number maxgen = 30; sizepop = 50; cross probability pcross = 0.4; probability of mutation: pmutation = 0.2.

1. Normalization processing

Because the magnitude and dimension of these parameter values are different, there will be great differences between the data, so they should be standardized before establishing the model. In this paper, Formula (2) is directly adopted to normalize or normalize the data of X matrix.

where x _ij is the value before normalization of column j of the sample in row i; x _ij ^* is the normalized value of column j of the sample in row i; x _imax and x _imin are the maximum and minimum values before normalization, respectively.

1. Transfer function: Log-Sigmoid function is used for transfer function from input layer to hidden layer and transfer function from hidden layer to output layer.

1. Calculation of fitness function.

The coded chromosome is taken as the initial population of GA algorithm, and the weights and thresholds of BP training set are optimized according to fitness function (4).

where C i ′ (i = 1, 2, 3, 4, 5) is the fitting value of BP algorithm; C _i (i = 1, 2, 3, 4, 5) is the actual value of subjective evaluation of comprehensive comfort.

1. Test samples and training samples.

U1, U5, U9, U20, U37, U41 and U49 were randomly selected as test samples, and the remaining 43 groups of data were used as training samples.