A novel industrial process monitoring method based on improved local tangent space alignment algorithm

Abstract

With the rapid development of manufacturing industries and the complexity increment of processes, a large number of streaming data with high-dimensionality and nonlinearity are obtained in actual industrial processes. As a result, it is essential for process monitoring to make dimension reduction. In this paper, a novel process monitoring method combining improved local tangent space alignment (ILTSA) and support victor data description (SVDD) is put forward. Considering the local geometric structures and the correlations among global variables of the original dataset, ILTSA algorithm is proposed to obtain the projection matrix from original space to feature one. Firstly, since the similarities in both spatial and temporal scales of streaming data cannot be neglected, time weighted distance is defined as the measurement of neighborhoods determination in ILTSA. Secondly, the objective function of ILTSA is reconstructed by introducing mutual information (MI) matrix of global variables. Finally, SVDD algorithm is adopted to establish the monitoring model. The corresponding monitoring statistic and control limit are calculated as well. A real hot strip mill process (HMSP) is employed to validate the proposed method and the result demonstrates its efficiency.

Introduction

Manufacturing industries develops towards large-scale, high-complexity, information-integration, distributed-platform and hierarchical-plant [1], [2], [3], which may result in frequent fault occurrences. Process monitoring provides a way to make industrial processes efficient and safe. With the development of control engineering, various sensors and controllers have been designed to adept certain complex characteristics of systems [4], [5], meanwhile, the filtering and network techniques have been advanced [6], which promotes modern industries extensively equipped with data sampling devices. A large number of streaming data can be collected from real production process, which accelerates data-driven process monitoring becoming a mainstream [7]. Data-driven methods involving multiple statistics and machine learning [8], [9], [10], [11], [12], [13] aim to mine the intrinsic relationships among variables. Due to those inherent characteristics in process data, such as large-amount, high-dimension, nonlinearity and complex correlations among variables, dimension reduction become an essential step before developing monitoring models.

Plenty of studies about dimension reduction [14], [15], [16], [17], [18] have been done in order to achieve preferable monitoring performances. Principle component analysis (PCA) is one of the most fundamental dimension reduction strategies and has been commonly adopted in real process monitoring due to its concise derivation and effectiveness in extracting major variations of variables [19]. On the one hand, PCA focuses on the global structure of the original dataset while certain local features are neglected, which causes an unsatisfactory monitoring result especially for dynamic processes [20]. To solve this problem, Zhang [21] and Yu [22] improved PCA and proposed global local structure analysis (GLSA) and local and global principal component analysis (LGPCA), respectively. On the other hand, as a linear dimension reduction algorithm, PCA performs poorly in complex industrial processes with nonlinearities. To solve this problem, kernel principal component analysis (KPCA) was introduced in process monitoring [23], [24]. The monitoring performance of KPCA can be dramatically affected by the option of kernel functions and parameters which lacks of theoretical directions. Therefore, it is a challenge to popularize KPCA in practical industrial processes.

As a nonlinear dimension reduction method based on data geometry, manifold learning algorithms are raised in pattern recognition and now are widely applied in process monitoring, such as local linear embedding (LLE) [25], neighborhood preserving embedding (NPE) [26], local preserving projection (LPP) [27] and local tangent space alignment (LTSA) [28]. Considering that preserving local geometric features is an inherent nature of manifold learning algorithms, a variety of improvements have been achieved to make them more suitable for process monitoring. On the basis of global plus local projection to latent structures (GPLPLS) [29], a statistical model named locally linear embedding projection to latent structure (LLEPLS) [30] was proposed, which incorporated PLS with LLE. This method extends the properties of PLS and can preserve the local structure with the introduction of LLE. To solve the regularization problem of weighted matrix in LLE, modified LLE (MLLE) and Hessian LLE (HLLE) [31] algorithms were proposed successively. Ma [32] proposed local and nonlocal embedding (LNLE), a nonlinear dimension reduction method for preserving both local and global information of original dataset by introducing a non-local objective function into NPE. Tong [33] and Song [34] proposed multi-manifold projection (MMP) and temporal-spatial global locality projections (TSGLP) based on LPP algorithm, respectively, to solve the problem of data structure changing after certain abnormal states and multimode process monitoring. Wang [35] developed local linear exponential discriminant analysis (LLEDA) and neighbourhood preserving embedding discriminant analysis (NPEDA) fault detection schemes, which can retain the intrinsic characteristics of original dataset by the integration of global discriminant analysis and local feature preservation.

LTSA algorithm was first proposed by Zhang [28]. It is a manifold learning algorithm based on tangent space for nonlinear dimension reduction. LTSA has strong robustness and high embedding accuracy in handling with high-dimensional manifolds. Particularly, LTSA can well exploit the underlying geometrical manifold of the original dataset without the singularity problem of weighted matrix. Zhang [36] adopted LTSA to extract the low-dimensional manifold from process data and then built SVDD monitoring model for chemistry processes. Noticing the complex distributions of process data, Wang [37] conducted dimension reduction by LTSA, and constructed a joint monitoring index by combining those of modified independent component analysis (MICA) and PCA. In the above studies, the projection matrices were obtained by linear approximation. Tian [38] proposed a fault diagnosis and visualization scheme, using LTSA to reduce dimensions and self-organizing maps (SOM) to distinguish diverse states on the output map. At present, there are only a few monitoring methods involving LTSA. These methods have been demonstrated to be generally available, but they just employed LTSA as a feature extraction technique without considering time-sequential and dynamic features of process data. Furthermore, low-dimensional manifold extracted by LTSA is proved to be over-dependent on local geometries while the correlation among global variables is neglected, which results in a damage on actual manifold structure.

Large-capacity and high-dimensionality are the inherent characteristics of process data. In conventional LTSA, the local neighborhood is determined by Euclidean distance, which causes inaccuracies in the high-dimensional space. Compared with Euclidean distance, geodesic distance can better characterize the geometry of samples. From another perspective, as a high-dimensional time sequence, there usually exists strong dynamicity in process data [39]. Therefore, in the determination of local neighborhood, the similarities of samples in temporal scale should also be considered. Based on the above two observations, time weighted distance is proposed in this paper. The neighborhoods determined by time weighted distance can reflect the similarities of samples in both spatial and temporal scales. Considering the inherent nature of manifold learning algorithm focusing on local geometries, the objective function of improved local tangent space alignment (ILTSA) is reconstructed by introducing mutual information (MI) matrix of variables to represent global data structure. The objective function of ILTSA is consisted of two sub-objective functions. The local one stresses local geometries of original manifold, while the global one tries to preserve the correlation of global variables. Accordingly, the projection matrix from original space to feature one can be obtained by solving the optimal problem with dual-objectives. Considering that multiple distributions may exist in streaming data, SVDD is utilized to establish the monitoring model in feature space. The corresponding monitoring statistic and control limit are calculated as well. In this paper, the simulation and experiment are conducted on a hot strip rolling process to verify the effectiveness of the proposed ILTSA-SVDD scheme.

The rest of this paper is organized as follows. In Section 2, the feature extracting method based on ILTSA is illustrated, including a briefly review of traditional LTSA, the definition of time weighted distance and reconstruction of the objective function of ILTSA. In Section 3, the process monitoring model based on ILTSA and SVDD is developed. In Section 4, a real hot strip mill process (HSMP) is employed for experimental validation. Finally, certain conclusions are demonstrated in Section 5.