Bending nonlinearity for manifold learning


As the manufacturing technology has been advancing and as the competition for machinery in the market mounts, the need for effective and efficient machine maintenance practices has been on the rise. Over the past few decades, efforts have been concentrated on monitoring the operational health of the machine to ensure that the performance of the machines remains at an optimal level. Machine health monitoring as a process entails observation of the condition of the machine using sensors either offline or on a continuous base. A major challenge in machine health monitoring is to eliminate redundant information and integrate multiple features to improve the efficiency and effectiveness of the process.

Recently, researchers at Xi’an Jiaotong University: Dr. Chuang Sun, Professor Ruqiang Yan, and Professor Xuefeng Chen together with Case Western Reserve University scientists Dr. Peng Wang and Professor Robert X. Gao illustrated how the performance of the manifold can be improved by eliminating the nonlinearity of the manifold. In this regard, they introduced Kernel Sparse Representation (KSR) into the manifold in a bid to better the machine. To solve the number of neighbors and connecting weights into Locally Linear Embedding (LLE), the authors used the KSR to leverage enhanced manifold learning. The research work is now published in journal, Mechanical Systems and Signal Processing. The authors identified that there is a problem with some of the current methods of manifold learning. One of the problems is that all the current methods of manifold learning lack the desired adaptability which can handle non-linear systems when variations occur. They therefore sought to counter the problem of adaptability when variations occur by developing an enhanced manifold learning method that would utilize the KSR when determining the neighbors and the weights.

In their research method, KSR for optimization involved utilization of sparse representation. This mode of representation modelled the neighborhood of the data while at the same time adaptively connecting the weights. Kernel space embedding as a process entailed several steps among them being an introduction to Locally Linear Embedding and embedding of the kernel space linearly. To monitor the health of the machine, the authors used features extracted from the frequency and time domains that are indicative of changing patterns in the vibration signal measured, as the machine transitioned from one state to another.

The authors arrived at several exciting findings. First, they identified Kernel Sparse- Locally Linear Embedding to be one of the most effective tools that can be used to monitor the health of the gearbox. However, this is not the case for all the machines considering that the latter vary from one to another. Other than determining the effectiveness of the machine, the KSR method presents itself as one of the most effective methods relative to the other methods. Although the KSR method is used to measure the health index of the machine, some limitations exist. The commonly used dimension space for presenting the data is 2-dimensional, while in reality, a 3-dimensional space would be better and more effective.

In summary, the study managed to illustrate how the identification of neighbors can be important when monitoring the health of the machine through manifold learning. Further, they showed that kernel sparse locally learning embedding can characterize both the adaptability and the nonlinearity and therefore justifies why manifold learning should be included in developing the next generation of machine health monitoring technologies.

Bending nonlinearity for manifold learning - Advances in Engineering
Figure 1. Sample distributions and health index calculated by KS-LLE.

About the author

Dr. Chuang Sun received the Ph.D. degree in mechanical engineering from Xi’an Jiaotong University, Xi’an, China, in 2014. From Mar. 2015 to Mar. 2016, he was a postdoctoral research associate at Case Western Reserve University, OH, USA. He is now an assistant research fellow in School of Mechanical Engineering, Xi’an Jiaotong University.

His research is focused on manifold learning, deep learning, sparse representation, mechanical fault diagnosis and prognosis, remaining useful life prediction.

About the author

Dr. Peng Wang is a postdoctoral research associate in the Department of Mechanical and Aerospace Engineering at Case Western Reserve University (CWRU) in Cleveland, Ohio. He received his B.S. and M.S. degree in Information Science from Beijing University of Chemical Engineering in 2010 and 2013, and his Ph.D. degree in Mechanical Engineering from Case Western Reserve University in 2017, respectively.

His research interests are in the areas of stochastic modeling, machine learning, and data fusion for machine performance prediction under uncertainty, manufacturing process modeling, and product quality assessment. Dr. Wang has published 16 papers in journals such as ASME Journal of Manufacturing Science and Engineering, CIRP Annals- Manufacturing Technology, IEEE Transactions of Automation Science and Engineering, SME Journal of Manufacturing Systems, etc. He is the recipient of the Best Student Paper Award from the IEEE Conference on Automation Science and Engineering (CASE) in 2015, and the Outstanding Technical Paper Award from the North American Manufacturing Research Conference in 2017. He also received the First Prize in the Digital Manufacturing Commons (DMC) Hackathon, organized by DMDII in 2016. He is currently serving as a Guest Editor for two journals: Computers in Industry and IEEE Sensors Journal, on special issues related to smart sensing and artificial intelligence-enabled data analytics for system health monitoring.

About the author

Professor Ruqiang Yan received the M.S. degree in precision instrument and machinery from the University of Science and Technology of China, Hefei, China, in 2002, and the Ph.D. degree in mechanical engineering from the University of Massachusetts Amherst, Amherst, MA, USA, in 2007.

He is now a Professor with Xi’an Jiaotong University. His research interests include data analytics, machine learning, multi-domain signal processing, and energy-efficient sensing and sensor networks for the condition monitoring and health diagnosis of large-scale, complex, dynamical systems.

Dr. Yan is an Associate Editor-in-Chief of the IEEE Transactions on Instrumentation and Measurement, and Associate Editor of IEEE Systems Journal and IEEE Access. He received the New Century Excellent Talents in University Award from the Ministry of Education in China, in 2009.

About the author

Professor Robert X. Gao is the Cady Staley Professor of Engineering and Chair of the Department of Mechanical and Aerospace Engineering at the Case Western Reserve University. Since receiving his Ph.D. degree from the Technical University of Berlin, Germany in 1991, he has been working in the areas of physics-based sensing and mechatronic systems design and characterization, multi-resolution data analytics, stochastic modeling, and machine learning techniques for improving the observability of cyber physical systems such as manufacturing machines and processes, ultimately enhancing process and product quality control.

Professor Gao is currently a Guest Editor for the Focused Section on AI-Based Monitoring in Smart Manufacturing (AISM) of the IEEE/ASME Transactions on Mechatronics, and was the lead Guest Editor for the Special Issue on Data Science-Enhanced Manufacturing of the ASME Journal of Manufacturing Science and Engineering. He is a recipient of multiple honors and awards, including the IEEE Instrumentation and Measurement Society Best Application Award (2019) and Technical Award (2013), SME Eli Whitney Productivity Award (2019), ASME Blackall Machine Tool and Gage Award (2018), ISFA (International Symposium for Flexible Automation) Hideo Hanafusa Outstanding Investigator Award (2018), multiple Best Paper Awards, CAREER award (1996), etc. He is a Fellow of the ASME, IEEE, SME, and CIRP (International Academy for Production Engineering).

About the author

Professor Xuefeng Chen (M’12) received the Ph.D. degree from Xi’an Jiaotong University, Xi’an, China, in 2004. He is currently a Professor and Dean of the School of Mechanical Engineering at Xi’an Jiaotong University.

His current research interests include finite-element method, mechanical system and signal processing, diagnosis and prognosis for complicated industrial systems, smart structures, aero-engine fault diagnosis, and wind turbine system monitoring.

Dr. Chen was a recipient of the National Excellent Doctoral Dissertation of China in 2007, the National Science Fund for Distinguished Young Scholars in 2012, and a Chief Scientist of the National Key Basic Research Program of China (973 Program) in 2015, and the Second Award of Technology Invention of China in 2009 and 2018, respectively. He is the Chapter Chairman of the IEEE Xi’an and Chengdu Joint Section Instrumentation and Measurement Society.


Chuang Sun, Peng Wang, Ruqiang Yan, Robert X. Gao, and Xuefeng Chen. Machine Health Monitoring Based on Locally Linear Embedding with Kernel Sparse Representation for Neighborhood Optimization. Mechanical Systems and Signal Processing. 114 (2019) 25–34

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