Echo state kernel recursive least squares algorithm for machine condition prediction
•A combination of reservoir computing and kernel adaptive filter.•The fixed reservoir facilitates the capability of performing long-term prediction.•The novel online learning method still maintains the simplicity of the training process.•A online prognostic method based on KAF and a Bayesian techniq...
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| Vydáno v: | Mechanical systems and signal processing Ročník 111; s. 68 - 86 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Berlin
Elsevier Ltd
01.10.2018
Elsevier BV |
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| ISSN: | 0888-3270, 1096-1216 |
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| Abstract | •A combination of reservoir computing and kernel adaptive filter.•The fixed reservoir facilitates the capability of performing long-term prediction.•The novel online learning method still maintains the simplicity of the training process.•A online prognostic method based on KAF and a Bayesian technique is developed.
Kernel adaptive filter (KAF) has been widely utilized for time series prediction due to its online adaptation scheme, universal approximation capability and convexity. Nevertheless, KAF’s ability to handle temporal tasks is limited, because it is essentially a feed-forward neural network that lacks dynamic characteristics. Traditionally, a sliding widow that contains consecutive data points is constructed to deal with the temporal dependency between data points at neighboring time steps, but the restricted widow length may be incapable of capturing temporal patterns on a larger time scale. To manage this issue, a novel sequential learning approach called echo state KRLS (ES-KRLS) algorithm is proposed by incorporating a dynamic reservoir into kernel recursive least squares (KRLS) algorithm. The reservoir, consisting of a large number of sparsely interconnected hidden units, is treated as a temporal function that transforms the history of the time series into a high-dimensional reservoir state space. Subsequently, the spatial relationship between the reservoir state and the target output is effectively approximated by KRLS algorithm. With the utilization of the fixed reservoir, our novel method not only maintains the simplicity of the learning process but also leads to a significant improvement in the capability of modeling dynamic systems. Numerical results on benchmark tasks demonstrate the excellent performance of the novel method with respect to long-term prediction. Finally, an online prognostic method that combines ES-KRLS and a Bayesian technique is developed for tracking the health status of a degraded system and predicting remaining useful life (RUL). This prognostic method is applied to a turbofan engine degradation dataset to demonstrate its effectiveness. |
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| AbstractList | Kernel adaptive filter (KAF) has been widely utilized for time series prediction due to its online adaptation scheme, universal approximation capability and convexity. Nevertheless, KAF’s ability to handle temporal tasks is limited, because it is essentially a feed-forward neural network that lacks dynamic characteristics. Traditionally, a sliding widow that contains consecutive data points is constructed to deal with the temporal dependency between data points at neighboring time steps, but the restricted widow length may be incapable of capturing temporal patterns on a larger time scale. To manage this issue, a novel sequential learning approach called echo state KRLS (ES-KRLS) algorithm is proposed by incorporating a dynamic reservoir into kernel recursive least squares (KRLS) algorithm. The reservoir, consisting of a large number of sparsely interconnected hidden units, is treated as a temporal function that transforms the history of the time series into a high-dimensional reservoir state space. Subsequently, the spatial relationship between the reservoir state and the target output is effectively approximated by KRLS algorithm. With the utilization of the fixed reservoir, our novel method not only maintains the simplicity of the learning process but also leads to a significant improvement in the capability of modeling dynamic systems. Numerical results on benchmark tasks demonstrate the excellent performance of the novel method with respect to long-term prediction. Finally, an online prognostic method that combines ES-KRLS and a Bayesian technique is developed for tracking the health status of a degraded system and predicting remaining useful life (RUL). This prognostic method is applied to a turbofan engine degradation dataset to demonstrate its effectiveness. •A combination of reservoir computing and kernel adaptive filter.•The fixed reservoir facilitates the capability of performing long-term prediction.•The novel online learning method still maintains the simplicity of the training process.•A online prognostic method based on KAF and a Bayesian technique is developed. Kernel adaptive filter (KAF) has been widely utilized for time series prediction due to its online adaptation scheme, universal approximation capability and convexity. Nevertheless, KAF’s ability to handle temporal tasks is limited, because it is essentially a feed-forward neural network that lacks dynamic characteristics. Traditionally, a sliding widow that contains consecutive data points is constructed to deal with the temporal dependency between data points at neighboring time steps, but the restricted widow length may be incapable of capturing temporal patterns on a larger time scale. To manage this issue, a novel sequential learning approach called echo state KRLS (ES-KRLS) algorithm is proposed by incorporating a dynamic reservoir into kernel recursive least squares (KRLS) algorithm. The reservoir, consisting of a large number of sparsely interconnected hidden units, is treated as a temporal function that transforms the history of the time series into a high-dimensional reservoir state space. Subsequently, the spatial relationship between the reservoir state and the target output is effectively approximated by KRLS algorithm. With the utilization of the fixed reservoir, our novel method not only maintains the simplicity of the learning process but also leads to a significant improvement in the capability of modeling dynamic systems. Numerical results on benchmark tasks demonstrate the excellent performance of the novel method with respect to long-term prediction. Finally, an online prognostic method that combines ES-KRLS and a Bayesian technique is developed for tracking the health status of a degraded system and predicting remaining useful life (RUL). This prognostic method is applied to a turbofan engine degradation dataset to demonstrate its effectiveness. |
| Author | Kirubarajan, Thia Zhou, Haowen Huang, Jinquan Lu, Feng Thiyagalingam, Jeyarajan |
| Author_xml | – sequence: 1 givenname: Haowen surname: Zhou fullname: Zhou, Haowen email: zhouhaowen@nuaa.edu.cn organization: Jiangsu Province Key Laboratory of Aerospace Power Systems, College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China – sequence: 2 givenname: Jinquan surname: Huang fullname: Huang, Jinquan organization: Jiangsu Province Key Laboratory of Aerospace Power Systems, College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China – sequence: 3 givenname: Feng surname: Lu fullname: Lu, Feng organization: Jiangsu Province Key Laboratory of Aerospace Power Systems, College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China – sequence: 4 givenname: Jeyarajan surname: Thiyagalingam fullname: Thiyagalingam, Jeyarajan organization: Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool, United Kingdom – sequence: 5 givenname: Thia surname: Kirubarajan fullname: Kirubarajan, Thia organization: Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, Canada |
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| Keywords | Kernel adaptive filter Remaining useful lifeprediction Reservoir computing Prognostics Long-term prediction |
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| Snippet | •A combination of reservoir computing and kernel adaptive filter.•The fixed reservoir facilitates the capability of performing long-term prediction.•The novel... Kernel adaptive filter (KAF) has been widely utilized for time series prediction due to its online adaptation scheme, universal approximation capability and... |
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| SubjectTerms | Adaptive algorithms Adaptive filters Algorithms Bayesian analysis Convexity Data points Dependence Dynamic characteristics Kernel adaptive filter Least squares Life prediction Long-term prediction Machine learning Mathematical models Neural networks Numerical analysis Principal components analysis Prognostics Remaining useful lifeprediction Reservoir computing Signal processing Time series Turbofan engines |
| Title | Echo state kernel recursive least squares algorithm for machine condition prediction |
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