Establishing a Genetic Algorithm-Back Propagation model to predict the pressure of girdles and to determine the model function

Abstract

A Genetic Algorithm-Back Propagation (GA-BP) neural network method has been proposed to predict the clothing pressure of girdles in different postures. Firstly, a Back Propagation (BP) neural network model was used to predict the clothing pressure based on seven parameters, and three optimal functions of the model were derived. However, the prediction error 0.85411 of the network was more than the forecast requirement of 0.5 and the optimal initial weights and thresholds for the network could not be calculated. Therefore, a GA model and the BP neural network model were combined into a new GA-BP neural network model, which was used to predict the clothing pressure based on the three optimal functions. The results showed that the prediction error for this GA-BP neural network model was 0.41652, which was less than the forecast requirement of 0.5. Hence, the model was shown to predict the girdle pressure with acceptable accuracy. Finally, the internal calculation function equation for the GA-BP neural network was derived.

Keywords

clothing pressure girdle postures Genetic Algorithm-Back Propagation neural network

The function of girdles is to impart shaping effects on the hips and waist of women. However, the pressure that they exert can make women feel uncomfortable. Medical research has shown that wearing tight girdles for a long time is harmful to women's health.^1–4 In 1972, Denton found that the range of comfortable clothing pressures ranged from 1.96 to 3.92 kPa.⁵ The critical value of uncomfortable clothing pressure is between 5.88 and 9.81 kPa, which is close to the average blood pressure on the human skin surface of 7.85 kPa.⁶ If the clothing pressure exceeds this value, blood flow is restricted and can be stopped. The prediction of clothing pressure enables a way to prevent this problem.⁷ However, the surface of the human body is irregular, and the pressure is related to many factors. Therefore, the relationships between these factors and the pressure are very complicated, making it difficult to predict an accurate pressure.

The pressure prediction of body shaping underwear has been investigated by some scholars.^8–12 Ishimaru et al. placed sensors on the surface of the human body and a technical method of numerical analysis was proposed to simulate the clothing pressure;⁸ Sun and Deng used Abaqus finite element software to generate a high quality mesh mode for analyzing the pressure distribution of electrocardiogram monitoring clothing;⁹ Zhang et al. established a geometric nonlinear mathematical model for human motion and the clothing pressure changes during the movement of the human body were simulated;¹⁰ Wang et al. designed a hexahedral mesh model to simulate the human body. Then, an iterative method was used to predict the relationship between the human body and the clothing pressure based on the human body deformation.¹¹ Mirjalili et al. used the Ansys software to build a finite element model to predict the distribution of clothing pressure.¹² The current research on the comfort of clothing pressure is mainly focused on the simulation of the distribution of three-dimensional dynamic clothing pressure. However, under the premise of many boundary conditions, it is very difficult to predict the clothing pressure accurately. The physical and predictive models of their systems have yet to be studied in depth.

The clothing pressure of girdles has also been investigated.^13,14 Fan and Chan proposed an improved mathematical programming method for the numerical simulation of fabric wrinkling. The clothing pressure was effectively predicted by this method for a standard human body model.¹³ You et al. established a correlation matrix based on the subjective feelings of clothing pressure comfort based on factor analysis, and the subjective feelings of the clothing pressure were predicted.¹⁴ The clothing pressure distribution of the girdles has been well predicted by these models, but many factors need to be determined and the estimation is complicated.

In the case of large data processing or complex relationships, the Back Propagation (BP) neural network can be used to simplify the estimation process and accurately find the complex internal relationships among the data.^15–18 However, its initial weights and thresholds are set randomly, if the pressure of the girdles is predicted by the model, which causes the model to easily fall into the local optimal solution and, therefore, fails to achieve the ideal prediction result.¹⁹ Therefore, the BP neural network model has not been well applied to predict the clothing pressure distribution so far.

Genetic algorithms (GA) have a strong global searching ability.²⁰ The BP neural network generates a set of optimal initial weights and thresholds after being searched over a large range by GA. GA can solve the problem of premature convergence of the BP neural network model.²¹ At present, some prediction models have combined GA and BP neural network to improve the prediction accuracy.^22–24

In order to investigate the clothing pressure of girdles, a new GA-BP neural network model was established. Firstly, the seven parameters affecting the girdle's pressure were identified by using a stepwise regression model. Secondly, a BP neural network prediction model was established using the seven parameters and the girdle's pressure. Then, a new GA-BP neural network model was established by using the GA algorithm to optimize the BP neural network. It was used to predict the girdle pressure. Finally, the prediction results of the model were compared with the prediction results of the grey BP neural network model and General Regression Neural Network (GRNN) neural network model.

Although the clothing pressure of girdles could be accurately predicted by the new GA-BP neural network model, the computational process and specific function of the network were not revealed. The new GA-BP model is like a black box model that can only predict output through input. The degree of influence of human parameters on clothing pressure and the specific relationship between them could not be revealed. Therefore, the prediction equation for the model was derived by using the weights and thresholds of the GA-BP neural network. The prediction process is shown in Figure 1.

Figure 1.

Process for deriving prediction formula for girdle pressure. BP: Back Propagation; GA-BP: Genetic Algorithm-Back Propagation; GRNN: General Regression Neural Network.

Experimental

Subjects and sample

A total of 80 female college staff aged between 20 and 40, with BMI between 17 and 25 kg/m² participated in this experiment. A commercial girdle style was selected as the experimental samples with waist sizes 66, 72, 80 and 88 cm. These sizes were suitable for most women in China. The fabric for these girdles was made from 60% nylon and 40% spandex. The lining was made from 84% nylon and 16% spandex. The lace was made of nylon.

Pressure measurement

An airbag contact pressure tester (AMI3037-10, air pack type contact pressure tester, AMI TECHNO, CO.LTD, Japan) was used to measure the clothing pressure of girdles under different postures. The accuracy of the pressure tester was ±0.1 kPa and its range of sensitivity and reliability were 0–70 kPa and 0–34 kPa. The experiment was carried out in a quiet laboratory at a temperature of 25 ± 1 ℃, a relative humidity of 65 ± 2% and wind speed of less than 0.1 m/s. Ten pressure points (P₁–P₁₀) under six common postures were measured. The 10 pressure points are shown in Figure 2. Figure 3 shows six common postures (a) standing posture, (b) deep breathing when standing, (c) leaning forward, (d) sitting posture, (e) sitting deep breathing and (f) sitting leaning forward.

Figure 2.

Ten pressure points: (a) front view (b) back view.

Figure 3.

Six common postures: (a) standing posture, (b) deep breathing when standing, (c) leaning forward, (d) sitting posture, (e) sitting deep breathing and (f) sitting leaning forward.

The pressure sensor was calibrated before the experiments. The 10 pressure airbags were fixed on the 10 positions under the girdles, and the subjects were asked to adopt the six common postures. Once it was ensured that the pressure sensor was in the correct position and operating properly, the girdle pressure was recorded for at least 1 minute for each posture. The subjects were asked to rest for 5 minutes between each experiment. The girdle pressure of each subject was measured three times at each of the 10 positions in the six postures respectively and the average pressure was derived. Therefore, a total of 180 pressure values (3 × 10 × 6) were averaged as the general girdle pressure (y) for each subject. Then, the mean and SD of the 10 points' pressure values for all the subjects under the six common postures were calculated as shown in Table 1.

Table 1.

The mean and SD of the 10 pressure points (unit: kPa)

Postures		P ₁	P ₂	P ₃	P ₄	P ₅	P ₆	P ₇	P ₈	P ₉	P ₁₀
Standing postures	Mean	2.69	1.58	3.97	1.11	2.30	2.63	2.32	2.08	2.29	2.43
Standing postures	SD	1.08	1.05	1.15	1.03	1.02	1.02	1.03	1.04	1.12	1.06
Deep breathing when standing	Mean	2.72	1.62	4.23	1.09	2.28	2.63	2.38	2.13	2.33	2.51
Deep breathing when standing	SD	1.07	1.03	1.12	1.01	1.01	1.02	1.03	1.06	1.27	1.22
Leaning forward	Mean	2.02	2.55	2.90	1.30	2.48	2.96	1.84	3.15	4.12	2.61
Leaning forward	SD	1.06	1.14	1.03	1.01	1.01	1.01	1.01	1.02	1.10	1.09
Sitting posture	Mean	1.88	1.94	2.21	3.30	2.66	3.22	9.93	5.18	2.88	3.00
Sitting posture	SD	1.03	1.04	1.02	1.03	1.01	1.01	1.07	1.09	1.08	1.10
Sitting deep breathing	Mean	1.85	1.89	2.24	3.14	2.63	3.19	9.94	5.62	2.81	3.01
Sitting deep breathing	SD	1.03	1.06	1.03	1.04	1.01	1.01	1.03	1.09	1.13	1.14
Sitting leaning forward	Mean	2.55	3.40	2.48	4.58	3.01	3.61	4.23	5.13	5.65	3.55
Sitting leaning forward	SD	1.03	1.07	1.01	1.05	1.03	1.03	1.17	1.05	1.14	1.10

Body measurements

Each subject's height (x₁), chest width (x₃), back width (x₄), upper bust (x₅), bust (x₆), lower bust (x₇), waist girth (x₈), hip girth (x₉), mid-hip girth (x₁₀), thigh root girth (x₁₁) and thigh girth (x₁₂) were measured, as shown in Figure 4. Their weight (x₂) was also measured.

Figure 4.

The body parameters.

The mean and SD of the 80 subjects' body parameters are shown in Table 2.

Table 2.

The mean and SD of the body parameters for all the subjects (unit: cm)

	x ₁	x ₃	x ₄	x ₅	x ₆	x ₇	x ₈	x ₉	x ₁₀	x ₁₁	x ₁₂
Mean	161.40	32.52	33.13	85.11	85.58	75.49	70.57	90.20	82.17	51.93	45.74
SD	4.62	2.71	2.05	4.02	4.61	3.21	3.89	4.50	4.86	3.48	2.94

Sample extraction

A stepwise regression model was established to determine which of the 12 body parameters (x₁–x₁₂) had the most significant effect on the overall or general pressure (y). The 12 parameters (x₁–x₁₂) and the general pressure (y) for each of the subjects are shown in Table 3. The stepwise regression model is a convenient regression model for establishing the relationship between the body parameters and the general girdle pressure (y).²⁵ The 12 parameters were treated as initial independent variables. The independent variable with the greatest impact on y was selected and tested. When no more independent variables which had an effect on y could be found, the model reached an optimal level.

Table 3.

Data of 12 body parameters(x₁–x₁₂) and the general pressure (y) of some subjects

Subjects information	1	2	3	4	5	6	7	…	79	80
x₁ (cm)	167	160	160	161	161	165	168		165	164
x₂ (kg)	53	49	55	50	50	54	60		55	54
x₃ (cm)	33.5	32.5	29.5	31	31.5	34.5	34.5		37	34
x₄ (cm)	37	31	31	28.5	35	31.5	32		36.5	34.5
x₅ (cm)	83	83.5	89	81	77	83	92		82	83
x₆ (cm)	81	82	87	81.5	79	84	92		84	87.5
x₇ (cm)	74	76	77.5	72	71	74	80		75.5	77
x₈ (cm)	70	69	76	66.5	66	69	73.5	…	70	74
x₉ (cm)	88	89.7	94	89	89	89	96		92	89.5
x₁₀ (cm)	83	82.7	88.5	81	76.5	81	87		80	83.5
x₁₁ (cm)	50	51	53.5	52	51	49	55		48	53.5
x₁₂ (cm)	47.5	45	48.5	46	48	45.5	49.5		43	45.5
y (kPa)	2.131	1.099	2.225	3.374	3.500	2.521	2.548		4.238	4.281

The result showed that six independent variables x₇, x₈, x₉, x₁₀, x₁₁ and x₁₂ had a significant effect on y. In order to study the effects of pressure points, the point numbers were also input as data as a new independent variable “pressure point.” Therefore, a total of seven parameters were selected as predictors in the models for building the predictive model.

Model

In the BP neural network model, the seven parameters were used to predict and analyze the clothing pressures of the girdles.

Concept of BP neural network

A BP neural network is essentially a model that continuously debugs errors.²⁶ After the network is provided with inputs and targets, a set of initial weights and thresholds are set randomly. The network input is then passed to the output layer through its internal calculations automatically, which are compared with the target to continuously adjust the weights and thresholds until a set of optimal weights and thresholds are gained.²⁷

Research has shown that a three-layer BP neural network structure can be approximated to arbitrary nonlinear functions.^28,29 Figure 5 is a basic neural network structure topology diagram composed of four parts: input layer x, hidden layer y, output layer z and target layer t. The input layer has d neurons with x_i as its i-th neuron. The weights and thresholds of the input to the hidden layer are w_ji and w_j0. The values of w_ji and w_j0 are passed to the hidden layer in weighted sum with x_i. Then they are mapped by a transfer function f₁ to form the j-th output neuron y_j(x) in the hidden layer. The computational procedure for this is shown in equation (1)

y_{j} (x) = f_{1} (\sum_{i = 1}^{d} w_{ji} x_{i} + w_{j 0})

(1)

Figure 5.

BP neural network structure topology. BP: Back Propagation.

The weights and thresholds are w_kj and w_k0 in the hidden layer which are passed to the output layer. y_j (x) is the input, in the hidden layer. y_j (x) is weighted with the w_kj and w_k0 and is passed to the output layer. Then, the k-th output neuron z_k (x) is formed after the output layer is mapped by the transfer function f₂. The computational procedure for this is shown in equation (2)

z_{k} (x) = f_{2} (\sum_{j = 1}^{n_{H}} w_{ki} y_{j} (x) + w_{k 0})

(2)

To calculate the network minimum mean square error J(w), the output z_k(x) is compared with the real target output t_k, as shown in equation (3) where there are c neurons in the output layer, t_i is the i-th output neuron in the target layer, and z_i is the i-th output neuron in the output layer. The network continuously adjusts and updates the weights and the thresholds of each layer based on the mean square error J(w), until their optimal combination is obtained.

J (w) = \frac{1}{2} ‖ t - z ‖ 2 = \frac{1}{2} \sum_{i = 1}^{c} (t_{i} - z_{i}) 2

(3)

MATLAB neural network toolbox

MATLAB provides a large number of neural network toolbox functions, which can be directly and conveniently applied by users without custom programming.³⁰ Therefore, the MATLAB R2018a version was used as the working environment for the experimental operation.

Establishment of BP neural network prediction model

In this study, the seven parameters extracted from the stepwise regression model were treated as independent variables. The girdle pressures at each pressure point on each subject were regarded as the dependent variables. The independent variables were entered into the network, the dependent variables were output by the network and the clothing pressures prediction model was created.

The process for developing the prediction model in MATLAB followed the following five steps:

Step 1: Input matrix A and B in the workspace of MATLAB.

A is a matrix of 800 rows (80 subjects with 10 pressure points) and seven column parameters as input samples into the network. B is a matrix of the 800 rows and six columns (the pressure under six different postures) regarded as the target samples of the network, which are the pressure values corresponding to the input samples. A and B matrices are composed of 800 groups of samples.

Step 2: Establish the BP neural network by using the BP neural network toolbox function newff provided in MATLAB R2018a software.

Step 3: Initialize the weights and thresholds through the initial function.

Step 4: Train the network through the train function.

Step 5: After training, 80 groups of samples were randomly selected from 800 groups of samples, and then simulated using the sim function of MATLAB.

Adjustment of three network parameters

After the BP neural network was built using the newff function, three functions, which are the transfer function, the numbers of hidden layer nodes and the train function in the network, need to be adjusted to optimize the network.

Transfer function

In the established BP neural network, the transfer function from input to implicit layer is sigmoid function, and the sigmoid function contains two kinds of functions: tansig function and logsig function³¹ as shown in equations (4) and (5), respectively

tan sig (n) = \frac{2}{1 + e^{- 2 n}} - 1

(4)

log sig (n) = \frac{1}{1 + e^{- n}}

(5)

The range of n in equations (4) and (5) is any value between (−∞, + ∞). The logsig function maps n to the interval (0, 1), while the tansig function maps n to the interval (−1, 1).

Numbers of hidden layer nodes

The numbers of hidden layer nodes have a great impact on the network performance. Theoretically, the more neurons in the hidden layer, the better the network performances. However, excessive numbers of hidden layer nodes will also lead to the network over-fitting, but insufficient numbers of hidden layer nodes will make the network fault-tolerant.^32,33 Therefore, too many or too few numbers of the hidden layer nodes will result in insufficient prediction accuracy by the network.

So far, no good method has been found to calculate the numbers of hidden layer nodes.³⁴ Equation (6) is summed up by predecessors based on experience to determine a general range of the number of neurons in the hidden layer

n = \sqrt{n_{i} + n_{o}} + a

(6)

where n_i is the number of neurons in the input layer, n_o is the number of neurons in the target layer, n is the number of neurons in the hidden layer, and a is a constant in the range of (1, 10). In the model, 800 groups of samples were input, and six kinds of action girdle pressures were output. Therefore, n_i is 800, and n_o is 6, and n is calculated as a range near 28. By adjusting the number of neurons in the hidden layer continuously, it was found that the network had the best training effect when the hidden layer neurons were in the range between 20 and 30.

Train function

The essence of a BP neural network training function is the algorithmic approach to correct the weights and thresholds.³⁵ Different algorithmic methods correspond to different training functions. At present, the neural network algorithm is mainly based on the numerical optimization algorithm and heuristic algorithm. The numerical optimization algorithm mainly includes the quasi-Newton method, conjugate gradient method and Levenberg-Marquardt method. They correspond to three training functions respectively: trainbfg, traincgf and trainlm.

Heuristic algorithms mainly include the basic gradient descent method, the gradient descent method with a momentum term and the adaptive algorithm with mining term. They correspond to three training functions respectively: traingd, traingdm and traingdx. Since the training function of the numerical optimization algorithm is more efficient than the training function of the heuristic algorithm, this study only selected three training functions: trainbfg, traincgf and trainlm for the numerical optimization algorithm for prediction comparison.

Forecast results for different parameters

In order to find the best network parameters, the transfer functions of logsig and tansig were used as transfer functions in the input to the implicit layer; the trainbfg, traincgf and trainlm functions of the numerical optimization algorithm were selected as the training functions; the numbers of hidden layer nodes were set between 20 and 30. Therefore, a total of 60 network models with different parameters were combined, as shown in Table 4. Then each network model was trained and a set of unique weights and thresholds for each model were derived. Finally, each model after training was verified by the 80 groups of samples selected randomly.

Table 4.

Mean square error of 60 network models

60 network models	Mean square error
Transfer function	logsig			tansig
Training functions	trainbfg	traincgf	trainlm	trainbfg	traincgf	trainlm
21	0.9737	0.8195	0.8281	0.9251	0.8132	0.8054
22	0.9224	0.8529	0.7997	0.9211	0.8324	0.8675
23	0.9183	0.9699	0.7730	0.9737	0.7990	0.9636
24	0.9737	0.8063	0.7340	0.9729	0.8286	0.9928
25	0.9737	0.8576	0.7775	0.8913	0.8391	0.8188
26	0.9600	0.8596	0.7898	0.9648	0.8796	0.9497
27	0.9306	0.85411	0.7251	0.9120	0.8025	0.8139
28	0.9737	0.8200	0.7310	0.9737	0.8457	0.9907
29	0.8523	0.8915	0.7517	0.8743	0.7665	0.9967
30	0.9295	0.8262	0.8016	0.9172	0.8088	0.8592

Table 4 lists the verification results in terms of “mean square error” between the pressure predicted by the model and the actual pressure. The minimum error is 0.7251 when the network transfer function was logsig, the training function was trainlm, and the numbers of hidden layer nodes was 27.

Figure 6 shows that the mean square error of the network reduced to the lowest value of 0.7251 when the training step reached 200. The performance target value of the network was 0.5. After training the network, the mean square error of the network did not meet the performance target.

Figure 6.

Mean square error of BP neural network training process. BP: Back Propagation.

Train is the mean square error. An epoch is a training step. Goal is the desired performance value.

Error analysis

After the prediction process was analyzed, it was evident that the BP neural network model could predict the pressure of the girdles through the seven parameters. In the prediction process, this model needed to set the three optimal parameters. However, the overall prediction ability of the model did not reach the performance target. The initial weights and thresholds of the model were set randomly, without proper calculation. Therefore, it was necessary to calculate the optimal initial weights and thresholds in order to improve the model prediction level.

Improved model

In order to improve the model, a GA was used to calculate the optimal initial weights and thresholds of the BP neural network to predict the clothing pressure of the girdles.

Genetic algorithm principle

A GA is an intelligent algorithm developed in recent years by imitating the law of biological evolution in nature, which is mainly used to optimize a model. Following the principle of natural biological evolution, it encodes the model that needs to be optimized to first obtain the initial population, then designs the fitness function and the genetic operation, and finally decodes a new population.³⁶

The traditional optimization algorithm searches a global optimal solution in a single individual search process in the model solving process. Conversely, the GA performs a large-scale search in a multi-body search mode to obtain the global optimal solution. This unique search method not only enlarges the model search area, but it also makes the model less likely to fall into the local optimal solution, and it reduces the time spent by the model in finding the model's optimal solution more efficiently.³⁷ The search method of the GA has been used widely in many fields. Many models combine their own characteristics with a GA to get a better result.

GA-BP neural network prediction model

In order to solve the problem that the BP neural network had a low accuracy in the prediction of the clothing pressure of girdles, the GA was used to genetically to find a set of optimal initial weights and thresholds for the BP neural network using a global search method. The implementation of the GA-BP neural network prediction model comprised six steps as explained below and for which the operational algorithm flow is presented in Figure 7.

Figure 7.

GA-BP neural network algorithm flow.

Create BP neural network

The three optimal parameters of the BP neural network were used to create a BP neural network model, and the network was trained to obtain its initial weights and thresholds.

Code for initial population

The initial weights and thresholds obtained by the BP neural network were encoded by the genetic algorithm.

The network had seven input samples and six output samples, and there were 27 neurons in the hidden layer. As a result, the weights from input layer to hidden layer were 189 (7 × 27) and the thresholds were 27. The weights from the hidden layer to output layer were 162 (27 × 6) and the thresholds were 6. Therefore the GA needed to optimize a total of 384 (189 + 27+162 + 6) parameters. Then the parameters were encoded in 10-bit binary numbers to produce 3840-bit encoding. After successful coding, a new GA-BP neural network was established.

Design fitness function

The new GA-BP neural network needed a fitness function to make it possible to adapt its coding to the final fitness function. The ultimate objective of this study was to make the GA-BP neural network model better predict the clothing pressures of the girdles. Therefore, the error matrix between the predicted output values and the real pressure of the network was taken as the fitness function for the genetic algorithm (obj,) as shown in equation (7). Finally, the fitness function was sorted by using the ranking function within MATLAB.

obj = ‖ T_{1} - t_{1} ‖ = (\sum_{1}^{80} \sum_{1}^{6} | T 1_{ij} - t 1_{ij} | 2)^{1 / 122}

(7)

where t₁ was the real pressure and T₁ was the predicted pressure.

Genetic manipulation

When the new GA-BP neural network model had obtained a fitness function, individuals with good fitness were directly inherited or cross-paired to the next generation and the individuals with poor fitness were eliminated. This operation was a genetic manipulation.

Genetic operations include selection operator operation, crossover operator operation and mutation operator operation. In this model, the selection operator was traversed randomly. The crossover operator firstly used the position intersection and then used the linear difference intersection. The mutation operator used the linear difference intersection.

Train GA-BP neural network

After the genetic manipulation process was finished, the new GA-BP neural network model was trained. Before training, six parameters (population size, mutation probability, mating probability, evolutionary algebra, generation gap and maximum genetic algebra in GA) needed to be designed rationally.

The design of these six parameters cannot be too large or too small. By continuously debugging the model, the selected population size was finally set to 60, the mutation probability value was 0.01, the mating probability was 0.7, the evolutionary algebra was 100, the generation gap was 0.95 and the maximum genetic algebra was 50.

Figure 8 shows that, when the numbers of training steps/epochs reached 200, the mean square error for the samples had dropped to the lowest value of 0.41652. As the performance target value for the network was 0.5, this met the forecast requirement.

Figure 8.

Mean square error of the GA-BP neural network training process.

Train is the mean square error. Epoch is the training step. Goal is the desired performance value.

Get final weight and thresholds

After the prediction capability of the new GA-BP neural network model reached the desired level, the weights (w₁) and the thresholds (b₁) of the network from the input to the hidden layer and the weights (w₂) and the thresholds (b₂) from the hidden to the output layer were derived for defining the prediction relationship. These are shown in Table 5.

Table 5.

Final weights and thresholds for the GA-BP neural networks

	From the input to the hidden layer								From the hidden to the output layer
	Weight matrix w₁							Threshold matrix b₁	Weight matrix w₂						Threshold matrix b₂
Rank number	1	2	3	4	5	6	7	1	1	2	3	4	5	6	1
1	−1.67	−0.17	−0.13	0.06	0.56	0.44	2.17	−46.57	0.40	0.46	0.78	1.59	1.93	1.62	−0.31
2	0.81	−0.22	−0.17	0.03	−0.33	1.20	1.69	−28.16	0.26	0.35	0.34	−1.18	−1.86	−1.08	−0.75
3	−1.73	−0.39	−0.09	−1.59	1.04	1.41	−1.17	−39.04	−0.13	−0.16	−0.09	1.35	1.73	1.37	−0.66
4	−0.09	0.30	0.36	−0.12	−0.27	0.23	0.24	−60.84	0.80	0.89	1.35	0.20	1.56	−0.04	1.21
5	1.96	0.03	−0.17	0.08	−0.07	0.21	−1.37	−21.34	−0.26	−0.18	−0.35	−3.35	−3.61	−3.32	1.62
6	1.61	−0.52	−0.36	0.05	0.63	0.40	1.34	−10.52	0.29	0.16	0.04	0.85	−3.52	0.50	−0.12
7	−0.02	−0.53	0.20	−1.31	1.62	−0.27	0.90	18.12	0.49	0.49	1.00	1.65	2.96	1.59
8	0.29	0.47	−0.58	−0.15	0.16	−0.34	−0.06	−11.04	−0.20	−0.46	−0.57	−1.82	−1.69	−1.84
9	0.32	0.11	0.05	0.02	0.07	0.20	2.26	−51.32	0.43	0.23	0.29	1.81	1.70	1.76
10	−2.21	−0.65	0.33	−1.26	−0.51	1.71	1.43	65.37	0.16	0.10	0.00	−1.25	−1.25	−1.25
11	−0.36	0.00	0.22	−0.41	1.59	−0.78	−1.50	−74.52	−0.22	−0.19	−0.33	−1.48	−1.16	−1.57
12	−0.22	0.26	0.07	0.05	−0.36	−0.10	2.05	−11.54	1.06	0.95	0.80	1.46	1.62	1.57
13	0.08	0.38	−0.39	0.10	−0.24	0.07	0.64	−24.88	−0.34	0.09	−0.67	−0.51	−2.11	−0.62
14	−0.14	−0.31	−0.09	−2.09	1.96	0.46	−0.39	−45.34	−0.30	−0.18	−0.81	−0.77	−2.24	−0.73
15	2.93	0.26	0.13	0.11	−0.50	0.34	−2.76	−47.60	−0.16	−0.16	0.05	1.22	1.64	1.24
16	0.36	0.27	−1.12	−0.44	−0.06	−0.04	−0.03	65.15	0.12	−0.06	0.61	0.68	2.14	0.69
17	−9.41	−0.23	1.52	−0.70	0.60	−0.13	0.67	−10.15	−0.14	−0.09	−0.31	−4.39	−4.64	−4.41
18	1.01	−0.54	−0.31	0.57	0.19	1.68	−0.95	−79.67	−0.03	−0.14	0.03	1.15	1.95	1.08
19	−1.66	0.28	−1.26	−0.07	1.08	−0.91	0.18	31.95	−0.01	0.02	0.28	1.52	1.49	1.50
20	−0.06	−0.01	0.40	−0.18	−0.48	0.22	−1.34	9.87	−0.74	−0.67	−0.96	1.62	0.39	1.43
21	−1.69	−0.31	−0.11	0.25	0.50	0.24	−0.51	−10.90	−0.34	−0.39	−0.53	−0.99	−1.27	−1.05
22	0.02	0.00	0.15	−0.24	0.58	−0.24	2.01	−39.62	1.61	1.50	1.57	−0.47	−0.89	−0.24
23	0.43	−0.09	0.04	0.08	0.00	0.08	0.25	11.15	−0.38	0.53	0.16	0.21	0.72	1.09
24	0.97	0.50	−0.60	0.37	−0.25	0.17	0.74	−48.36	0.13	0.03	0.23	1.14	1.18	1.05
25	0.16	−0.21	−0.27	0.12	0.03	−0.07	0.80	46.68	0.94	1.29	0.63	−0.32	−1.32	−0.69
26	0.33	−0.03	−0.60	−0.08	0.24	−0.07	0.08	29.13	0.51	−0.07	0.33	−0.94	0.75	−1.00
27	0.51	0.05	0.03	0.19	−0.14	0.15	−0.57	40.66	0.85	0.42	0.56	0.31	0.97	0.32

Comparison of prediction effects of different models

Figure 9 (a) shows a comparison between the pressures (z-axis) predicted by the BP neural network and the actual pressure, and (b) shows a comparison between the pressure predicted by the GA-BP neural networks and the actual pressures in the six common postures (x-axis). The y-axis represents the 80 test samples. It can be seen that the pressure predicted by the GA-BP neural network is more accurate than that predicted by the BP neural network.

Figure 9.

Comparison of predicted pressure with actual pressure. (a) Pressures predicted by the BP neural network vs. the actual pressure and (b) Pressure predicted by the GA-BP neural networks vs. the actual pressures.

Grey BP neural network prediction model

The grey BP neural network model is a common prediction model. In order to compare its prediction capability with that of the GA-BP neural network model, it was used to predict the pressure of the girdles. Firstly, the samples data from the experiments were calculated cumulatively, and then differential equations were built with independent discrete samples. In order to find its intrinsic laws and development trends in discrete small samples, it was formed into a continuous distribution function. When there is a time series ${x^{θ} (i)}, i = 1, 2, \dots, n$ , grey differential values and residual sequences can be obtained using the differential equation of the grey model in formula (8), where a is the development coefficient and b is the grey interaction amount

\frac{d x^{(1)}}{dt} = a x^{(1)} + b

(8)

The BP neural network model was then employed to correct the residual sequence of the simulated values. When the weights thresholds of the BP neural network stopped updating and the minimum residual sequence values was obtained, the prediction level of the model was deemed to have reached the optimal state. Figure 10 shows the mean squared error of the grey BP neural network model. After the numbers of training steps reached 200, the mean square error of the samples reached a minimum value of 0.65813. However, as this was greater than the forecast requirement of 0.5 its predictive performance failed to meet the forecast requirement.

Figure 10.

Mean square error of grey BP neural network model in training process. BP: Back Propagation.

Train is the mean square error. Epoch is the training step. Goal is the desired performance value.

GRNN neural network prediction model

A GRNN neural network is a kind of neural network model modified on the basis of a radial basis network structure. It adopts the approximation principle of local response, which makes the training speed of the network faster. It also has the powerful function of nonlinear mapping, and can approximate any nonlinear function mapping relation.³⁸ Compared with the BP neural network, it needs to adjust fewer parameters, just the setting of the value for the spread of a network extension speed. It can avoid the errors caused by some factors, and make the network less easily trapped into the local optimal value.³⁹

Therefore, a GRNN neural network model was also used to predict the pressure of the girdles. Figure 11 shows the mean squared error of the GRNN neural network model during training. The mean square error of the network reached a minimum value of only 0.60023 when the number of training steps reached 200, which exceeded the forecast requirement of 0.5. Therefore, this model also failed to meet the required prediction performance.

Figure 11.

Mean square error of GRNN neural network model in training process. GRNN: General Regression Neural Network.

Train is the mean square error. Epoch is the training step. Goal is the desired performance value.

Determining the model function relation

After comparing the four different neural networks, only the GA-BP neural network model achieved the desired prediction accuracy by having a mean square error of less than the forecast requirement 0.5. However, the model could only predict the output through the input, such that the degree of influence of different body parameters on the girdle pressure and the relationship between them could not be derived. The model needed to be explored to define the specific relationship inside the network. In order to do this, the final weights and the thresholds of the GA-BP neural network in Table 3 were used to derive the network's internal functions.

The hidden layer of the network had 27 neurons, the input layer, p_1, was an 80 × 7 matrix, the input to the hidden layer weights, w₁,was a 7 × 27 matrix. An 80 × 7 matrix was calculated after w₁ matrix-computed with the input matrix p₁ based on the principle of BP neural network algorithm. Then, each row of the matrix was summed with the thresholds b₁ and an 80 × 27 output matrix was calculated. After the output matrix was mapped by the logsig function, the output f₁ in the hidden layer was calculated. The operation is shown in equation (9), where w₂ is the weights from the hidden to the output layer, which is a 27 × 6 matrix. f₁ continues to be the input in the output to the input layer and when matrix-computed with w₂, an 80 × 6 output matrix was calculated. Then, each row of the output matrix was added to the threshold b₂. The final result was T₁. The results of this operation are consistent with the results of the pressure predicted by the neural GA-BP neural network. Therefore, the derived network internal functions are considered to be correct.

p_{1} \frac{w_{1}}{b_{1}} = f_{1} log sig (w_{1} \times p_{1} + b_{1}) \frac{w_{2}}{b_{2}} T_{1} = w_{2} \times f_{2} + b_{2}

(9)

Equation (10) is the derived GA-BP neural network internal function. Therefore, based on the seven parameters, the pressure of the girdles can be derived

T_{1} = w_{2} \times [log sig (w_{1} \times p_{1} + b_{1})] + b_{2}

(10)

In this experiment, the limited number of samples and insufficient experimental conditions led to a few errors in the prediction. However, the prediction results show that the GA-BP neural network model could accurately predict the girdle pressure without the need for a complicated calculation process.

Conclusion

In this study, the clothing pressure exerted by a commercially available girdle on the bodies of 80 subjects together with 12 body parameters were measured. A stepwise regression analysis model identified six of the body parameters, which, together with the pressure location, made seven parameters in total that affected the clothing pressure exerted by the girdles. Then, the seven parameters were input into a BP neural network model to predict the clothing pressure of the girdles. By adjusting the network parameters, the three optimal parameters of the BP neural network were inferred to predict the pressures.

The initial weights and thresholds of the BP neural network could not be calculated when predicting the pressures, resulting in the final prediction of the model failing to meet the expected goals of the network. Therefore, a GA model was proposed to optimize the BP neural network, and the new GA-BP neural network model was combined to make the prediction. The results showed that the prediction level of the model reached the expected target for the network and achieved the desired level of accuracy. The prediction capability of this model was better than that of a grey BP neural network and a GRNN neural network. Finally, the internal function of the GA-BP neural network was derived based on its final weights and thresholds.

Compared with the traditional girdle pressure prediction model, the GA-BP neural network model does not require complex modeling processes or many predictive factors, and the clothing pressure of the girdles could be predicted accurately.

Due to the current limitations of experimental facilities and research methods, there are many deficiencies in the research. Based on the improvement of experimental facilities in the future, this study should use more advanced algorithms to optimize the model to improve the overall accuracy.

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 Shaanxi Science and Technology Department International Science Technology Cooperation Funding (Grant Number 2018KW-056). and Xi'an Polytechnic University Graduate Innovation Funding (Grant Number chx2019016).

ORCID iD

Ma Qiurui

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