Quick detection of product quality based on clustering hypersphere model☆
Graphical abstract
Introduction
In the manufacturing industry, the production of products involves multiple continuous and coupled processes [1], [2]. To ensure the final quality of the products, the setting values and the quality indicators of each process must be controlled within the predefined ranges. Only in this way, the setting process parameters can be considered to meet the product quality requirements, otherwise the quality is judged to be abnormal. At present, the main method of product quality detection is based on the “after the event” sampling method, which not only requires a lot of manpower, but easily causes the scrap of a batch of products [1].
In addition, individual requirements for product quality are becoming more stringent and prominent. The centralized manufacturing models and existing quality control methods are difficult to adapt to the changing market demands and stability requirements of the product quality. To continuously improve the product quality, it is necessary to study the production process and conduct the batch detection, which can help to detect abnormal products in time, as well as guarantee a faster detection speed and a lower false-detection rate. Furthermore, due to the characteristics of large batch size and short production cycle, the actual manufacturing processes are more complex and uncertain. To address the above issues, a considerable amount of research work has been devoted to the product quality detection. Generally, the methods for the product quality detection can be classified into three categories: statistical analysis, manifold learning, and Support Vector Data Description (SVDD).
Traditional statistical methods are mainly to adjust the various factors, which cause changes in product quality following the statistical laws between process parameters and quality indicators, to avoid abnormal product quality. Principal Component Analysis (PCA) and Partial Least Squares (PLS) are most popular Multivariate Statistical Process Monitoring (MSPM) models [2], [3], [4]. Choi et al. [5] proposed a nonlinear PCA-based method that uses kernel functions. Du et al. [6] proposed a Gaussian distribution transformation method for process monitoring. Rosipal et al. [7] proposed a non-linear regression model to theoretically describe the kernel PLS algorithm. Ji et al. [8] used a MSPM model with the smoothing technology to detect early faults in the industry. However, the MSPM models assume that the process variables are independent and normally distributed. This assumption is only valid in the case of the long sampling intervals.
To solve the above problem, the manifold learning methods are gradually applied to the production process control. Liu et al. [9] proposed an extended maximum variance unfolding flow-based learning method, which is suitable for nonlinear monitoring, to make up the shortcomings of PCA that lacks of consideration of the underlying data structure in modeling. Tong et al. [10] built the Multi-Manifold Projections (MMPs) and used orthogonal MMPs to model and monitor the changes in the subspace. To further extract features, Yu [11] designed a local and nonlocal preserving projection manifold learning algorithm, which can be used to extract the useful low-dimensional information from high-dimensional information. Xiao et al. [12] proposed a sparse representation preserving embedding algorithm, which solves the robust sparse representation problem through convex optimization to construct an adjacency graph, and captures the subtle dynamic relationship between each sample pair. However, the manifold learning methods depend heavily on the adjacency graph, and the construction of the graph is based on the Euclidean distance of the sample pairs, which is easily affected by noise and outliers in the process data.
SVDD is a single classification method proposed by Tax based on support vector machine [13], [14], [15], [16]. Its principle is to build the smallest hypersphere by using as many data points as possible. Recently, SVDD has been widely used for quality detection. Kumar et al. [17] proposed a robust K-chart based on a kernel distance support vector algorithm. Kim et al. [18] improved the original SVDD by introducing decision variables, and proposed a data description method with flexible decision boundaries. Gornitz et al [19] combined the advantages both of the SVDD method and k-means clustering to improve system flexibility. However, SVDD-based methods usually use a kernel function to represent the inner product among data points. In the detection process, the inner product of the detection points and each support vector need to be calculated, which greatly affects the detection speed in the actual manufacturing industry. To solve the problem, Liu et al. [20] proposed a fast anomaly detection method, which can improve the final detection function based on SVDD. However, the algorithm is only applicable to the case where the abnormal data are clearly separated from the normal data. When the abnormal data are close to the normal points, the hypersphere model will have a large false detection rate.
Based on the analysis of the existing methods, in this paper, a fast product quality detection method using a clustering hypersphere model is proposed. The contributions are:1) A k-means clustering method is used to segment the original data for the purpose of dividing and conquering, hence the detection boundary can be optimized, and the false-detection rate can be reduced. 2) A mirror sphere is used as the reference point for product quality detection, which can reduce the time complexity of quality detection and speeds up the detection process. 3) The k-means clustering is combined with the hypersphere to form a joint quality detection boundary for multiple hyperspheres, which can adapt to various shape distributions of the process data.
The rest of this paper is organized as follows. In Section 2, related work is introduced. In Section 3, the implementation of the algorithm for this research is described in detail. Results are presented in Section 4. Section 5 summarizes this study.
Section snippets
k-means clustering
The k-means clustering has only one parameter of cluster number k, which is easy to be adjusted [21], [22], [23]. Given a large number of samples S=(x1,x2,…, xm), where xi are data vectors of p-dimension in the actual production, the above samples are divided into k disjoint subsets based on the k-means algorithm, which are defined as T={T1,T2,…, Tk}, where Ti (i = 1, 2, ..., k) is the ith subsets. Therefore, the cumulative minimized squared error of T can be expressed as:
Design of quick quality detection
The proposed method for product quality detection is mainly to build a boundary for quick detection. In this paper, the k-means clustering method is firstly used for dividing sample data into k subsets. Then, a hypersphere modeling is performed on every subset to form the final joint detection. By controlling the parameter k, the purpose of controlling the number of hyperspheres is achieved, which makes the boundary more flexible, and enhances the accuracy of product quality detection
Simulation verification
To show the detection boundaries of clustering hyperspheres more intuitively, simulation is performed based on the 2D data. The data containing 200 normal samples and 200 abnormal samples is shown in Fig. 2. It is noted that 150 normal samples are used as the training set, and the remaining 250 samples are used as the test set. The grid search method is used to find the suitable effect parameters including penalty coefficients and kernel function parameters. For better comparison, SVDD [13] and
Conclusions
To enhance the production efficiency, effective and feasible quality detection of the products is essential. In this paper, we proposed a clustering hypersphere model, blending the ideas of the k-means clustering and the conventional SVDD into a single scheme. We carefully analyzed their properties and theoretical derived that the scheme performs better in the detection accuracy. Meanwhile, to reduce the time complexity of the scheme, we designed a simplified detection function based on solving
Statement
We declare that the work “Quick detection of product quality based on clustering hypersphere model” is entirely ours and no parts of it are taken from other researchers.
Declaration of competing interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript titled “Quick detection of product quality based on clustering hypersphere model”.
Acknowledgment
The work is supported by the National Natural Science Foundation of China (Grant NO. 51975430, 51975433), the Program for Guangdong Introducing Innovative and Enterpreneurial Teams (Grant NO. 2017ZT07G493), National defence Pre-research Foundation and Graduate Innovative and Enterpreneurial Foundation of WUST (Grant NO. GF201903, JCX201963).
Weipeng Huang is now pursuing his M.S. degree at School of information Science and Engineering, Wuhan University of Science and Technology. His main research interests include cyber-physical system and clustering modeling.
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Weipeng Huang is now pursuing his M.S. degree at School of information Science and Engineering, Wuhan University of Science and Technology. His main research interests include cyber-physical system and clustering modeling.
Shaowu Lu received Ph.D. degree from Huazhong University of Science and Technology in 2013. He is currently an associate professor in School of information Science and Engineering, Wuhan University of Science and Technology. His research interests include quality detection and intelligent control.
Bao Song received Ph.D. degree from Huazhong University of Science and Technology in 2005. She is currently a professor at Huazhong University of Science and Technology. Her research interests include intelligent control and industrial robot technology.
Yajie Ma received Ph.D. degree from Huazhong University of Science and Technology in 2005. She is currently a professor at Wuhan University of Science and Technology. Her research interests include communication and information engineering.
Fengxing Zhou received B.Eng. degree from Wuhan University of Science and Technology in 1981. He is currently a professor in School of information Science and Engineering, Wuhan University of Science and Technology. His-research interests include signal analysis and adaptive control.
Xiaoqi Tang received Ph.D. degree from Huazhong University of Science and Technology in 1998. He is currently a chief scientist in Dongguan Samsun Optical Technology Co., Ltd. His research interests include robot engineering and distributed control system.
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