Optimization of garment sewing operation standard minute value prediction using an IPSO-BP neural network

Haina Shen; Xiaofen Ji

doi:10.1515/aut-2023-0034

Article Open Access

Optimization of garment sewing operation standard minute value prediction using an IPSO-BP neural network

Haina Shen and Xiaofen Ji

Published/Copyright: June 12, 2024

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From the journal AUTEX Research Journal Volume 24 Issue 1

Abstract

Standard minute value serves as a pivotal metric guiding the arrangement and balancing of production cycles in clothing production lines, and plays a crucial role in cost pricing and production order arrangement for clothing products. Given the complexity of the garment sewing process, ten influencing factors including fabric weight, fabric thickness, fabric density, stitching length, stitching shapes, cut pieces numbers, notch numbers, sewing technologies, sewing machine, and auxiliary accessories were identified. Upon this foundation, a standard sewing time prediction model, Improved particle swarm optimization - Back-propagation neural network (IPSO-BP), was proposed, focusing on non-quantitative factors. The IPSO-BP model was trained using actual sewing data from a women’s clothing production company. Compared to the unoptimized BP neural network, the IPSO-BP model demonstrated significant advantages in terms of convergence speed and prediction accuracy. Therefore, the IPSO-BP model proposed in this study holds promise for predicting standard sewing hours effectively.

Keywords: Standard minute value; improved particle swarm optimization; back-propagation neural network; complexity analysis

1 Introduction

With the increase in diversified and personalized demand for products from different levels of consumer groups, the “multi-variety, small-batch” production paradigm has become the norm in the apparel industry. This approach involves manufacturing a wide range of products in small quantities within a given timeframe, marked by brief production cycles and swift transitions between orders [1,2]. The heightened variability in product types, manufacturing processes, and batch sizes leads to imprecise production planning, scheduling, and dispatching, as well as discrepancies between actual and planned production timelines, thereby diminishing the manufacturer’s capacity for rapid response [3]. The fundamental issue stems from existing work hour determination strategies, which fail to timely and accurately capture the true work hour requirements for products in a multi-variety, small-batch production setting. Consequently, researching methods to efficiently and precisely predict the standard minute value for new products within such a manufacturing context is of paramount importance.

In conventional methods for establishing standard minute value, data are collected through measurement techniques to create standard minute value database for production purposes [4]. The measurement approach typically employs the stopwatch method and the predetermined motion time system. The stopwatch method involves directly observing operating times through repeated measurements using a stopwatch [5]. Conversely, the predetermined motion time system relies on predetermined values for various fundamental movements. It establishes a standard based on predetermined values for various fundamental movements, which are then used to calculate the theoretical standard minute value for a process by breaking it down into basic actions [6]. However, in the actual production process, these theoretical standard minute values can be influenced by real-world manufacturing factors such as employee skills, working environment, and production batch sizes, and more. Consequently, various methodologies have been developed to formulate standard minute value from different perspectives. He et al. introduced the use of MODAPTS analysis, which incorporates considerations of employee physiology, fatigue, and management float rate to construct theoretical working hours [7]. This approach supplements the traditional stopwatch method with a nuanced understanding of human factors. Similarly, Liu expanded upon this by integrating additional factors such as the working level coefficient, which encompasses proficiency, effort, working conditions, and consistency [8]. Moreover, considerations like workshop working margins are factored in to determine the final standard minute value. In summary, these methodologies represent sophisticated approaches for standardizing minute value, harmonizing theoretical principles with practical considerations to achieve a more precise calculation of standard minute value.

In response to the garment manufacturing industry’s shift towards smaller batch sizes and increased individualized orders, there is a growing emphasis on pre-production operation analysis. Scholars suggest grouping working processes based on standard minute value to expedite and streamline the calculation process. For instance, Wu and Mu employs group technology and similarity principles to encode processes, creating a typical process library. Benchmark working times are then determined using the principle of maximum proximity in actual production settings [9]. Similarly, Zheng et al. argues that clothing parts with similar shapes typically share similar processes. Hence, forming a parts component time library based on components like collars, sleeves, and fronts facilitates rapid determination of standard minute value for garments [10]. While these methods alleviate the complexity of process analysis and enhance formulation efficiency, the rapid evolution of clothing types, technology, and equipment conditions poses challenges. The standard minute value database may deviate significantly over time, necessitating regular revisions to typical process or component databases – a labor-intensive task.

Therefore, scholars have devised various schemes to predict the rated working hours of new products. Ye and Yan employs the standard data method and learning curve to formulate the rated working hours. This approach organizes working units based on processing hours data from previous orders, bypassing the time and energy-intensive nature of direct measurement. By deriving the learning coefficient from the learning curve of similar operations, Ye adjusts the standard minute value for new processes [11]. Similarly, Wang et al. takes a comprehensive approach, considering factors such as component characteristics, production configuration, operating standards, employee proficiency, working environment, and order batch size [12]. By establishing a process similarity coefficient through expert scoring, unknown processes are compared with benchmark processes. This enables the rapid formulation of work hour quotas based on the process similarity coefficient.

In the realm of predicting garment standard minute value, scholars have explored various approaches, including direct time research, action analysis, statistical analysis, mathematical modeling, and others. Direct time studies and action analyses boast high accuracy but entail heavy workloads and limited adaptability, making them best suited for large-scale centralized production of stable products. Statistical analysis, based on historical processing data, offers simplicity, convenience, and swift quota generation, but often suffers from lower prediction accuracy. Mathematical modeling methods establish regression models between working hour quotas and influencing factors, yielding high prediction accuracy and user convenience. However, the expert scoring method used to determine the weight distribution of influencing factors tends to be overly subjective. Consequently, scholars have proposed the use of neural network algorithms to mitigate the impact of subjective factors. For instance, Yang et al. identifies factors influencing working hours based on product structure complexity, trains samples using BP neural networks, and derives product working hours [13]. Wang et al. introduces a method for determining working hour quotas based on error influence coefficients, utilizing neural network methods to obtain error correction coefficients for accurate working hour calculations [14]. Yang et al. integrates genetic algorithms and case-based reasoning technology to address fixed hours in injection mold processing [15]. Therefore, these studies present a promising avenue for introducing neural network algorithms into garment standard minute value prediction. Drawing inspiration from other industries, this study analyzes the primary characteristics of components, processes, and operational procedures to identify the influencing factors of rated working hours. It endeavors to establish a neural network-based working hour calculation model to swiftly predict product working hours.

2 Research methodology

2.1 Back-propagation (BP) neural network

The BP neural network, consisting of input, hidden, and output layers, stands as one of the most extensively employed neural network models [16]. Its fundamental operation revolves around minimizing error functions. By moving in the negative gradient direction, the network adjusts weights and thresholds using the fastest descent method of nonlinear programming, propelled by external input samples [17]. This correction process continually diminishes error, thereby driving the network output closer to the anticipated output.

Kolmogorov’s theoretical proof establishes that a three-layer network, equipped with an adequate number of hidden nodes, can attain arbitrary mapping capabilities along with self-learning, self-organization, and adaptability [18]. This theorem underscores the three-layer network’s ability to precisely approximate any nonlinear mapping relationship. Consequently, a single hidden layer BP network emerges as capable of addressing the majority of practical problems encountered in our domain. Hence, the network proposed in this study also adheres to a single hidden layer model, comprising one input layer, one intermediary hidden layer, and one output layer, as illustrated in Figure 1.

Figure 1

The flowchart of single hidden layer BP neural network.

The input layer serves as the entry point for information, receiving input data x ₁, x ₂,···, x _n. The hidden layer processes this information, while the output layer yields the desired results y ₁, y ₂,···, y _m. The weights w _ij and w _jk denote the connection strengths from the input layer to the hidden layer and from the hidden layer to the output layer, respectively. The parameters a _j and b _k represent the thresholds for the hidden layer and output layer, respectively, serving as indicators of the neurons’ sensitivity to input signals. When the weighted sum of input signals exceeds these thresholds, the neuron is activated, leading to an output; otherwise, the neuron remains inactive, and the output remains zero [19]. In the Figure 1, the BP neural network symbolizes the function mapping relationship from n independent variables to m dependent variables, with q hidden nodes.

The process of the single hidden layer BP neural network is primarily divided into two stages. The first stage is forward propagation of signals, which involves allowing information to enter the network from the input layer and obtaining the final output layer result through sequential calculations across each layer.

The formula for computing the hidden layer is as follows:

(1) H j = ƒ ∑ i = 1 n w i j − a j , j = 1 , 2 , … . … . , q ,

where H represents the output of the hidden layer, j denotes the number of nodes in the hidden layer, w _ij is the connection weight between the input layer and the hidden layer, a _j signifies the threshold of the hidden layer, and f denotes the activation function of the hidden layer, which can take various forms. In this study, the Sigmoid function is chosen, which yields superior performance when employed in a classifier [20].

(2) ƒ ( x ) = 1 1 + e − x .

The formula for computing the output layer is as follows:

(3) Y ^ k = ∑ j = 1 q H j w j k − b k , k = 1 , 2 , … . , m ,

where Y ^ represents the output of the output layer, b _k denotes the threshold of the output layer, and w _jk signifies the connection weight between the hidden layer and the output layer.

Due to the initial weights (w _ij, w _jk) and thresholds (a _j, b _k) being random values, a significant error exists between the initially calculated result and the actual result. Therefore, parameter adjustment is necessary based on the error, aiming to achieve a better fit of the parameters until the error reaches its minimum value. Subsequently, the model proceeds to the second stage – BP.

In the second stage of the neural network, network parameters are adjusted by computing the error between the output layer and the expected value, aiming to minimize the error. The error is calculated as follows:

(4) E = 1 m ∑ k = 1 m ( Y ^ k − y k ) 2 , k = 1 , 2 , … . , m ,

where E represents the loss value, y _kdenotes the expected value, and, Y k ^ signifies the output value. When E fails to meet the convergence accuracy requirement E ＞ ε, the BP neural network performs reverse updates on the weights and thresholds:

(5) w i j = w i j + ϕ H j ( 1 − H j ) x ( i ) ∑ k = 1 m w j k e k , i = 1 , 2 , … . , n ; j = 1 , 2 , . , q ,

(6) w j k = w j k + ϕ H j e k , j = 1 , 2 , . , q ; k = 1 , 2 , . , m ,

(7) a j = a j + ϕ H j ( 1 − H j ) x ( i ) ∑ k = 1 m w j k e k , i = 1 , 2 , … . , n ; j = 1 , 2 , . , q ,

(8) b k = b k + e k , k = 1 , 2 , . , m ,

where φ denotes the learning rate. After updating the weights (w _ij, w _jk) and thresholds (a _j , b _k), the process returns to the first stage, and forward calculation is performed again until the network output error satisfies the accuracy requirements.

Nevertheless, the conventional BP neural network suffers from drawbacks such as low learning efficiency, slow convergence speed, and susceptibility to local minima [21,22]. This study introduces the particle swarm optimization algorithm (PSO) to expedite the optimization process of weights and thresholds, thereby facilitating the completion of network training tasks.

2.2 Improved particle swarm optimization (IPSO)

The PSO was initially proposed by American social psychologists and electrical engineers, drawing inspiration from the foraging behavior of birds [23]. PSO is an optimization algorithm rooted in the theory of swarm intelligence, which entails optimizing a group through collective cooperation among birds. The PSO algorithm has been successfully applied to optimization problems across various domains due to its straightforward concept, robustness, and global search capability.

When employing the standard particle swarm optimization algorithm to solve optimization problems, it organizes a particle swarm consisting of N particles within a D-dimensional space [24]. The continuous iterative process can be described as the pursuit of two extreme values by particles: one aims to find the optimal value specific to the particle itself, known as the local best value pbest; the other strives to discover the optimal value across the current particle population, referred to as the global best value gbest. By iteratively tracking these two “extreme values,” the particle consistently updates its velocity v and displacement x to best approximate the expected value (Figure 2).

Figure 2

Flowchart of PSO algorithm.

Upon finding these two optimal solutions, the particle updates its velocity and new position according to the following formula:

(9) v i = v i + c 1 ⋅ r 1 ⋅ ( p best i − x i ) + c 2 ⋅ r 2 ⋅ ( g best i − x i ) , i = 1 , 2 , . , m ,

(10) x i = x i + v i , i = 1 , 2 , . , m ,

where c ₁ and c ₂ are the acceleration coefficients, where c ₁ expresses how much confidence a particle has in itself, while c ₂ expresses how much confidence a particle has in its neighbors [25]. And r ₁ and r ₂ are random numbers between [0,1].

To enhance the performance of the PSO algorithm, Shi and Eberhart introduced the inertia weight w as a mechanism to control the group’s search and exploration abilities [26], as depicted in formula (11). Dynamic w can achieve better exploration than a fixed value. Currently, Shi’s linearly decreasing inertia weight (LDW) is the most commonly used approach formula (12).

(11) v i = w ⋅ v i + c 1 ⋅ r 1 ⋅ ( p best i − x i ) + c 2 ⋅ r 2 ⋅ ( g best i − x i ) , i = 1 , 2 , . , m ,

(12) w = w max − t ⋅ ( w max − w min ) t max ,

where w _max and w _min represent the maximum and minimum values of w, respectively. t represents the number of current iteration steps, and t _max represents the maximum number of iteration steps [27].

However, in Shi’s LDW strategy, the algorithm is anticipated to swiftly converge towards the optimal advantage if identified early in operation. While, the linear decline of w may hinder the algorithm’s convergence speed [28]. Furthermore, as w decreases during the later stages of execution, the algorithm’s global search capability diminishes, leading to a reduction in diversity and an elevated risk of local optima convergence. Therefore, this study proposes the use of a nonlinear weighting method (IPSO) to address the shortcomings of the standard algorithm. This method can be described as:

(13) w = w max − ( w max − w min ) ⋅ tan t t max ⋅ π 4 .

In the early stages, when t is small, w approximates to W _max to uphold the algorithm’s global search proficiency. As t increases, nonlinear reduction ensures the algorithm’s local search capability, allowing for adaptive adjustment between global and local search prowess.

3 Framework for standard sewing time prediction based on IPSO-BP method

3.1 Analysis of factors affecting standard sewing hours

Standard minute value serves as a fundamental metric within the garment industry, reflecting labor efficiency and facilitating processing cost analysis [29]. These hours represent the duration required to fulfill quality standards using standardized methods, ensuring reasonable labor intensity and speed under typical operational conditions. However, numerous factors in the actual production process contribute to variations in work duration for identical processes. These factors encompass fabric properties, working environments, equipment capabilities, product quality, and staff expertise, among others. Quantifying the precise impact of these factors on operations presents challenges in practical settings [30]. Garment manufacturing constitutes a complex process involving interactions among personnel, machinery, materials, methods, and the environment [31]. From the standpoint of implementing garment processing, the sewing process can be summarized as follows: operators in the garment sewing process primarily receive task-related information (such as cut piece details, equipment specifications, and process requirements) during their work. They subsequently utilize this information, in conjunction with their own knowledge and experience, to carry out specific sewing operations, as shown in Figure 3.

Figure 3

The process of assembling cut piece.

This analytical approach, rooted in the realm of garment processing, encompasses three crucial aspects: cut piece characteristics, operational elements, and operator cognitive factors during the cutting and stitching process. It fundamentally captures the influencing factors of processing time for this operation.

To efficiently assess the working hour quota for various products and establish a robust foundation for enterprise production planning in the context of multi-variety and small-batch manufacturing, it is imperative for enterprises to devise effective and versatile evaluation metrics to gauge and appraise the three aforementioned characteristics in garment processing. Complexity analysis, a method prevalent in task feature research within the industrial technology domain, has emerged as a pivotal tool [32]. Liu’s synthesis of recent research on task complexity underscores complexity as the summation of all factors influencing a task, and promotes a thorough evaluation across various dimensions [33]. Ham et al. advocated for a multi-level analysis of task characteristics, spanning functional, behavioral, and structural aspects [34]. Additionally, Kong and Ye examination of job execution and cognitive psychological processes through complexity indices offers insights into evaluating job elements and process characteristics [35]. In essence, complexity serves as a holistic evaluation metric that considers all facets of characteristic factors in task processes. For garment processing tasks, this metric fulfills the systematic requirements of evaluating rated working hour.

The complexity of garment sewing is influenced by various factors that collectively impact the time required to complete the task. First, different fabric characteristics, such as thickness, elasticity, and smoothness, play a significant role in determining sewing difficulty. For example, silk and knitted fabrics present greater challenges compared to cotton. Additionally, the garment’s structural design, including features like multiple cutting lines, princess lines, underarm darts, and armhole darts, require higher operating skills and contribute to increased sewing complexity. Moreover, lengthy stitching lines necessitate frequent pauses for cutting piece adjustments, leading to extended rated working hours. Special parts such as armholes and necklines often require additional notches for alignment, further lengthening pause times. Different sewing techniques, such as French seams, are more challenging than flat seams. Integration of advanced sewing machines and tools, like the blind hem foot, can simplify complex sewing tasks to some extent. Furthermore, an experienced operator with rapid learning abilities and high technical proficiency can reduce rated sewing time [36].

In general, the skill level of employees is typically factored into the arrangement of the assembly line to ensure optimal efficiency. This study primarily focuses on predicting the standard minute value required for garment sewing tasks, emphasizing objective factors such as the characteristics of the cut pieces and operational elements. Through an analysis of the sewing processes for cut pieces, the study conducts a feature analysis spanning cut piece attributes, technological operations, and equipment considerations. This analysis culminates in the establishment of an evaluation index system that encompasses cut piece processing performance complexity, cut piece structural relationship complexity, and job complexity, as depicted in Figure 4. Notably, cut piece performance complexity reflects the impact of fabric types and properties on sewing, while cut piece structural relationship complexity pertains to factors such as stitching line shapes and the arrangement of cut pieces. Job complexity accounts for the influence of sewing technologies and equipment types on the sewing process.

Figure 4

The factors of standard sewing hours.

3.2 Construction of IPSO-BP prediction model

In BP neural networks, weight updating is critical and plays a central role in the network’s learning process. Through refined adjustments of these weights using an IPSO method, the training accuracy and predictive capabilities of neural networks can be significantly enhanced. Consequently, in this study, the error function of the BP neural network is adopted as the fitness function for the IPSO algorithm to determine the optimal weights. The complete optimization process is delineated in the flowchart illustrated in Figure 5.

Determining neural network topology: A single hidden layer was adopted in the BP neural network topology for this study. The input variables consisted of factors influencing working hours, including fabric properties, stitching length, stitching shapes, number of cut pieces, number of notches, sewing technologies, and equipment type. The output variable was the standard minute value.
Initialization of IPSO parameters: Parameters for the IPSO were initialized, encompassing the particle dimension (D), swarm size (N), acceleration coefficients (c ₁, c ₂), maximum and minimum inertia weights (w _max, w _min), maximum velocity constraint (v _max), maximum number of iterations (t _max), and the initial weights for the neural network connections.
Fitness calculation and extreme search: The fitness value for each particle in the swarm was computed to identify both individual and global extremes.
Particle update mechanism: Formulas (10) and (11) were utilized to update the positions and velocities of the particles. The IPSO algorithm concluded upon reaching the optimal solution or reaching the maximum number of iterations.
Network training with optimized parameters: The BP neural network was trained using the optimized parameters obtained from the IPSO algorithm. The training process concluded once the network error fell below a specified threshold or the maximum iteration limit was met, at which point the trained network model was exported.

Figure 5

The framework of IPSO-BP prediction model.

4 Case studies

4.1 Data description and preparation

The raw data used in this study were sourced from ZS Company, a privately held family-owned women’s clothing company located in China. Founded in 1989, the company operates four fashion brands and has its own production workshop. Over the years, it has amassed a significant amount of sewing standard time data through its manufacturing operations. This study collected a portion of dress orders from 2023 and extracted sewing process, order information, material specifications, pattern information, process specification, and other relevant information from the process analysis table.

Among the primary factors influencing fabric sewing performance, composition, structure, density, weight, thickness, formability, extensibility, bending rigidity, and shear rigidity are crucial. This study focuses on commonly used fabric testing indicators in clothing enterprises: fabric thickness, weight, and density (the warp and weft density per inch). Fabric density is calculated by summing the number of warp and weft threads per inch of yarn. The evaluation index for stitching shapes is determined by the ratio of the curved part’s length to the total length of the pattern. Sewing technologies refer to the seam types specified in the ISO standard [37]. Equipment types are categorized into two segments: the first involves the types of sewing machines utilized, predominantly featuring computerized and conventional sewing machines in the ZS Company workshop. The second segment pertains to the utilization of auxiliary accessories, which serve to mitigate sewing difficulty.

Following data cleaning procedures to remove incomplete records, the finalized dataset consists of 231 sewing processes, each accompanied by the standard minute value and corresponding influencing factors, as outlined in Table 1.

Table 1

Raw dataset of influencing factors and standard minute value of the sewing process

No.	Fabric weight (g/m²)	Fabric thickness (mm)	Fabric density (T)	Stitching length (mm)	Stitching shapes (%)	Cut pieces numbers	Notch numbers	Sewing technologies	Sewing machine	Auxiliary accessories	Standard minute value (s)
1	228	0.32	150	75	25	3	4	5.04	Computerized	No	89.4
2	228	0.32	150	70	23	3	4	5.04	Computerized	Yes	67.2
3	84	0.22	56	80	50	2	2	1.01	Conventional	No	95.4
4	185	0.34	142	20	13	2	4	6.03	Computerized	Yes	127.2
5	160	0.25	128	24	30	2	4	1.01	Computerized	No	34.2
6	52	0.32	48	75	0	1	2	1.01	Computerized	No	55.2
7	30	0.14	44	44	15	2	2	1.01	Computerized	No	69.0
8	35	0.22	56	76	25	1	4	3.05	Conventional	Yes	105.6
9	245	0.24	160	70	0	4	6	1.01	Computerized	No	115.2
10	185	0.34	142	81	10	1	2	5.01	Computerized	No	98.4
···	···	···	···	···	···	···	···	···	···	···	···
231	84	0.23	56	95	0	2	2	1.01	Computerized	No	109.8

To facilitate data processing, prevent neural output saturation resulting from excessive net input absolute values, and expedite the convergence of the training network, it is imperative to normalize all data. Different preprocessing methods are employed based on the nature of the data.

For quantitative data, the min-max method is applied for normalization, utilizing formula (14). This method is used for variables such as fabric thickness, fabric density, fabric weight, stitching length, cut number, and notch numbers.
(14) x = x − x min x max − x min .
For binary categorical data, such as the utilization of auxiliary accessories and the type of sewing equipment, a binary assignment is applied. Here “1” and “0” are employed to denote the presence or absence of a particular feature. Specifically, the use of auxiliary accessories is represented by “1,” while their non-use is indicated by “0.” Similarly, the utilization of a computerized sewing machine is coded as “1,” whereas the use of a conventional sewing machine is coded as “0.” This binary coding system effectively transforms these categorical variables into a numerical format suitable for analysis by data processing and machine learning algorithms.
For multidimensional categorical variables, such as sewing technologies, frequency coding is employed for encoding. This method entails substituting the original category label with the frequency of occurrence of each category within the dataset. By doing so, each category is represented by a single numerical value, effectively circumventing the introduction of high dimensions or additional relationships.

4.2 Initialization of IPSO-BP model parameters

In the BP neural network section, the input layer consists of 10 neurons (n = 10), and the output layer consists of 1 neuron (m = 1). The number of hidden layers m is determined using a formula q = m + n + a , where a is a tuning constant ranging from 1 to 10. Here a is set to 9, thus the number of hidden layers q is 12. The transfer functions between layers are implemented using the Levenberg–Marquardt algorithm.

In the IPSO section, the particle swarm size N is set to 20, and the particle swarm dimension D is calculated as (n + 1) × q + (q + 1) × m = 145. The acceleration coefficients c ₁and c ₂are set to 2.05, while the maximum and minimum inertia weights w _max and w _min are set to 0.9 and 0.4, respectively. The maximum velocity constraint v _max is 1, and the maximum number of iterations t _max is established at 3,000 [38].

The dataset of 231 samples is randomly split into a training set of 174 samples and a testing set of 57 samples, maintaining a ratio of approximately 3:1. The expected error (ε) is set to be less than 1 × 10⁻³. To further compare the results and confirm the efficacy of the IPSO-BP model, a BP network training is also conducted using MATLAB’s built-in toolbox. In this training setup, 75% of the data are allocated to the training set.

4.3 Result and discussion

Performance analysis

The IPSO-BP network was trained automatically until reaching the predefined accuracy threshold of 10⁻³, with training halted at the 3,000th iteration. During the simulation, the optimal mean square error validation result of 23.2653 was observed at the 1,064th iteration, as illustrated in Figure 6. Here the x-axis represents the number of training iterations, while the y-axis depicts the mean square error value.

Figure 6

The mean square error curve of IPSO-BP.

Subsequently, the trained IPSO-BP neural network’s regression analysis is presented in Figure 7. In this representation, the x-axis denotes the target output, and the y-axis illustrates the fitting function between the predicted output and the target output. The regression coefficient, R, signifies the degree of correlation between the predicted and target outputs. For this IPSO-BP network, R stands at 0.9818. A higher R value closer to 1 indicates a stronger relationship between the predicted and output data, while an R value closer to 0 suggests greater randomness between the predicted and output data.

Figure 7

Linear regression curve of IPSO-BP standard minute value prediction model.

Figure 8 displays the comparison between the actual and predicted values within the training set. The x-axis represents the sample size of the training set, while the y-axis denotes the standard time of the sewing process. Following this, regression predictions were conducted for the test data, consisting of randomly selected test samples. Figure 9 visualizes the comparison between the actual and predicted values for this test dataset.

Figure 8

Comparison of actual values and predicted values of the IPSO-BP training set.

Figure 9

Comparison of actual values and predicted values of the IPSO-BP test set.

The prediction model based on the IPSO-BP optimization algorithm consistently demonstrates superior prediction performance, whether applied to training data experiments or testing data evaluations. This highlights the model’s robustness and efficacy across different datasets. Consequently, the IPSO-BP prediction model exhibits exceptional generalization capabilities, providing scientifically reliable predictions for the standard time of the sewing process.

Comparative analysis of BP and IPSO-BP neural network models for prediction

The training outcomes of the unoptimized BP neural network in the MATLAB toolbox are portrayed in Figure 10, where the optimal mean square error of 67.4107 was achieved at the 1,493rd iteration. The regression analysis of the trained BP neural network is depicted in Figure 11, revealing a correlation coefficient (R) of 0.96528. Table 2 presents a comparative analysis of the training performance between the IPSO-BP and BP neural network models. It is evident that IPSO, as an optimization algorithm adept at conducting global searches in solution spaces, can expedite the convergence of network weights toward global optima. This not only accelerates the convergence rate but also mitigates the risk of conventional BP neural networks getting trapped in local minima. Consequently, the IPSO-BP method demonstrates efficacy in training models for predicting standard sewing time.

Figure 10

The mean square error curve of IPSO-BP.

Figure 11

Linear regression curve of BP standard minute value prediction model.

Table 2

Comparison of the training performance by the IPSO-BP and BP neural network

Index	IPSO-BP	BP
MES	23.2653	67.4107
R	0.9818	0.96528

Figure 12 presents a comparative analysis between the actual and predicted values of the testing dataset for the BP neural network. In contrast to Figure 9, there is a greater fluctuation in the predicted data. Table 3 provides a comprehensive assessment of the testing dataset results for both neural network models, encompassing metrics such as maximum relative error, minimum relative error, average relative error, and sample variance. The sample variance serves as a critical indicator of data fluctuation, with diminished values indicative of heightened precision. From Table 3, it is discernible that the IPSO-BP model exhibits a substantially lower sample variance of 98.1663, in contrast to the BP neural network model’s variance of 2000.6402. This underscores the superior predictive accuracy of the IPSO-BP model in forecasting standard sewing time.

Figure 12

Comparisons of actual values and predicted values of the BP test set.

Table 3

Error analysis of prediction results of BP neural network and PSO-BP neural network models

Index	IPSO-BP	BP
Maximum relative error	0.4057	2.4088
Minimum relative error	0.0165	0.0006
Average relative error	0.0038	0.1484
Sample variance	98.1663	2000.6402

5 Conclusion

This study conducts an in-depth exploration of the sewing process, focusing on three critical domains: cut piece technology, technological operations, and machinery. It identifies 10 independent variables to assess their influence on standard sewing time by examining cut piece performance complexity, cut piece structural relationship, and job complexity. These variables encompass fabric weight, fabric thickness, fabric density, stitching length, stitching shapes, cut pieces numbers, notch numbers, sewing technologies, sewing machine, and auxiliary accessories.

The sewing standard hours prediction model is an enhanced BP neural network training model structured as 10-12-1. This study leverages the global optimization capability of the PSO algorithm to refine the BP neural network model, mitigating the issue of local minima. Furthermore, the study employs the nonlinear weighting method, known as IPSO, to address the challenge of declining global search energy associated with the linear decrease in w in the PSO standard algorithm.

The model training and prediction experiment results conducted on the sewing hours data from ZS Company, totaling 231 sewing hours, along with its influencing factors, reveal the effectiveness of the IPSO-BP sewing hours prediction model proposed in this study. This model establishes a potential relationship between unmeasurable factors and standard minute value, enabling accurate prediction of standard sewing hours. Furthermore, in comparison to the non-optimized BP neural network prediction model, the IPSO-BP model demonstrates superior convergence speed and accuracy. Moreover, when contrasted with traditional methods such as manual reasoning and table lookup, the IPSO-BP algorithm proves more adept at capturing the nonlinear relationship between working hours and influencing factors. This enhancement is particularly beneficial in forecasting working hours in advance, especially under the multi-variety and small-batch production mode. Consequently, it facilitates tasks such as product pricing and production order arrangement.

With the digital transformation underway in the garment industry, apparel enterprises can leverage the accumulation of big data. By integrating the unique characteristics of their products and refining the proposed prediction model, they can achieve more accurate estimates of the standard minute value required for the sewing process. Moreover, the IPSO-BP sewing time prediction model, functioning as a multi-input single-output neural network training model, is not only suitable for calculating standard sewing hours but also holds relevance for addressing similar multi-input single-output calculation problems in other domains.

Funding information: No funding involved.
Author contributions: H.S. conceived the original idea, collected and analyzed data, and drafted the manuscript and X.J. conducted the processing.
Conflict of interest: Authors state no conflict of interest.
Data availability statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2024-04-26

Accepted: 2024-05-15

Published Online: 2024-06-12

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/aut-2023-0034

Keywords for this article

Standard minute value; improved particle swarm optimization; back-propagation neural network; complexity analysis

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