A nonlinear method for monitoring industrial process

2020 ◽  
pp. 014233122095923
Author(s):  
Yuan Li ◽  
Chengcheng Feng
Keyword(s):  
Fault Detection ◽  
Objective Function ◽  
Dimensional Space ◽  
Detection Methods ◽  
High Dimensional ◽  
Locally Linear Embedding ◽  
Industrial Case Study ◽  
Laplacian Eigenmaps ◽  
Linear Embedding ◽  
Locally Linear

Aiming at fault detection in industrial processes with nonlinear or high dimensions, a novel method based on locally linear embedding preserve neighborhood for fault detection is proposed in this paper. Locally linear embedding preserve neighborhood is a feature-mapping method that combines Locally linear embedding and Laplacian eigenmaps algorithms. First, two weight matrices are obtained by the Locally linear embedding and Laplacian eigenmaps, respectively. Subsequently, the two weight matrices are combined by a balance factor to obtain the objective function. Locally linear embedding preserve neighborhood method can effectively maintain the characteristics of data in high-dimensional space. The purpose of dimension reduction is to map the high-dimensional data to low-dimensional space by optimizing the objective function. Process monitoring is performed by constructing T2 and Q statistics. To demonstrate its effectiveness and superiority, the proposed locally linear embedding preserve neighborhood for fault detection method is tested under the Swiss Roll dataset and an industrial case study. Compared with traditional fault detection methods, the proposed method in this paper effectively improves the detection rate and reduces the false alarm rate.

Supervised Locally Linear Embedding for Fault Diagnosis

2010 ◽  
Vol 139-141 ◽  
pp. 2599-2602
Author(s):  
Zheng Wei Li ◽  
Ru Nie ◽  
Yao Fei Han
Keyword(s):  
Fault Diagnosis ◽  
Recognition Performance ◽  
Feature Space ◽  
Difficult Problem ◽  
Fault Classification ◽  
High Dimensional ◽  
Locally Linear Embedding ◽  
Local Linear Embedding ◽  
Linear Embedding ◽  
Locally Linear

Fault diagnosis is a kind of pattern recognition problem and how to extract diagnosis features and improve recognition performance is a difficult problem. Local Linear Embedding (LLE) is an unsupervised non-linear technique that extracts useful features from the high-dimensional data sets with preserved local topology. But the original LLE method is not taking the known class label information of input data into account. A new characteristics similarity-based supervised locally linear embedding (CSSLLE) method for fault diagnosis is proposed in this paper. The CSSLLE method attempts to extract the intrinsic manifold features from high-dimensional fault data by computing Euclidean distance based on characteristics similarity and translate complex mode space into a low-dimensional feature space in which fault classification and diagnosis are carried out easily. The experiments on benchmark data and real fault dataset demonstrate that the proposed approach obtains better performance compared to SLLE, and it is an accurate technique for fault diagnosis.

Sorting 4DCT Images Using Locally Linear Embedding

2013 ◽  
Vol 462-463 ◽  
pp. 150-154
Author(s):  
Zhao Hui Luo ◽  
Zai Fang Xi
Keyword(s):  
Respiratory Motion ◽  
Dimensional Space ◽  
Image Data ◽  
Locally Linear Embedding ◽  
Time Resolved ◽  
One Dimensional ◽  
A Value ◽  
4D Computed Tomography ◽  
Linear Embedding ◽  
Locally Linear

Respiratory motion degrades anatomic position reproducibility, and result in significant errors in radiotherapy. 4D computed Tomography (4DCT) can characterize anatomy motion during breathing. Usually, the acquired 4DCT images sequences is out of order. How to rearrange the sequence, i.e. sort 4DCT images has been the focus of 4DCT. In this paper we propose a method based on locally linear embedding (LLE), to reconstruct time-resolved CT volumes. By mapping high dimensional image data with LLE into one dimensional space, each image is assigned a value, then 4DCT images is sorted according to the value to reconstruct a respiratory cycle. Experiments result shows that the method is feasible to sort 4 DCT images without using any external motion monitoring systems.

FSLLE: A Fast K Selection Algorithm for Locally Linear Embedding

2018 ◽  
Vol 17 (01) ◽  
pp. 1850003
Author(s):  
Jin-Hang Liu ◽  
Tao Peng ◽  
Xiaogang Zhao ◽  
Kunfang Song ◽  
Minghua Jiang ◽  
...  
Keyword(s):  
Face Recognition ◽  
Spatial Correlation ◽  
Manifold Learning ◽  
High Dimensional ◽  
Locally Linear Embedding ◽  
Dimensional Manifold ◽  
Correlation Index ◽  
Recognition Algorithms ◽  
Linear Embedding ◽  
Locally Linear

Data in a high-dimensional data space may reside in a low-dimensional manifold embedded within the high-dimensional space. Manifold learning discovers intrinsic manifold data structures to facilitate dimensionality reductions. We propose a novel manifold learning technique called fast [Formula: see text] selection for locally linear embedding or FSLLE, which judiciously chooses an appropriate number (i.e., parameter [Formula: see text]) of neighboring points where the local geometric properties are maintained by the locally linear embedding (LLE) criterion. To measure the spatial distribution of a group of neighboring points, FSLLE relies on relative variance and mean difference to form a spatial correlation index characterizing the neighbors’ data distribution. The goal of FSLLE is to quickly identify the optimal value of parameter [Formula: see text], which aims at minimizing the spatial correlation index. FSLLE optimizes parameter [Formula: see text] by making use of the spatial correlation index to discover intrinsic structures of a data point’s neighbors. After implementing FSLLE, we conduct extensive experiments to validate the correctness and evaluate the performance of FSLLE. Our experimental results show that FSLLE outperforms the existing solutions (i.e., LLE and ISOMAP) in manifold learning and dimension reduction. We apply FSLLE to face recognition in which FSLLE achieves higher accuracy than the state-of-the-art face recognition algorithms. FSLLE is superior to the face recognition algorithms, because FSLLE makes a good tradeoff between classification precision and performance.

Nonlinear fault detection based on locally linear embedding

2013 ◽  
Vol 11 (4) ◽  
pp. 615-622 ◽  
Author(s):  
Aimin Miao ◽  
Zhihuan Song ◽  
Zhiqiang Ge ◽  
Le Zhou ◽  
Qiaojun Wen
Keyword(s):  
Fault Detection ◽  
Locally Linear Embedding ◽  
Linear Embedding ◽  
Locally Linear

CLASSIFICATION-ORIENTED LOCALLY LINEAR EMBEDDING

2010 ◽  
Vol 24 (05) ◽  
pp. 737-762 ◽  
Author(s):  
PI-FUEI HSIEH ◽  
MING-HUA YANG ◽  
YI-JAY GU ◽  
YU-CHENG LIANG
Keyword(s):  
Dimensional Space ◽  
Linear Method ◽  
Real Data ◽  
Data Representation ◽  
Classification Performance ◽  
Locally Linear Embedding ◽  
Real World Data ◽  
Label Information ◽  
Linear Embedding ◽  
Locally Linear

The locally linear embedding (LLE) algorithm is hypothetically able to find a lower dimensional space than a linear method for preserving a data manifold originally embedded in a high dimensional space. However, uneven sampling over the manifold in real-world data ultimately causes LLE to suffer from the disconnected-neighborhood problem. Consequently, the final dimensionality required for the data manifold is multiplied by the number of disjoint groups in the complete data representation. In addition, LLE as an unsupervised method is unable to suppress between-class connections. This means that samples from different classes are mixed during reconstruction. This study presents CLLE, a classification-oriented LLE method that uses class label information from training samples to guide unsupervised LLE. The criterion for neighbor selection is redesigned using class-conditional likelihood as well as Euclidean distance. This algorithm largely eliminates fractured classes and lowers the incidence of connections between classes. Also, a reconnection technique is proposed as a supporting method for ensuring a fully connected neighborhood graph, so that CLLE is able to extract the fewest features. Experiments with simulated and real data show that CLLE exceeds the performance of linear methods. Comparable classification performance can be achieved by CLLE using fewer features. In comparison with LLE, CLLE demonstrates a higher aptitude for and flexibility towards classification.

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