Sensitivity of Fractional-Order Recurrent Neural Network with Encoded Physics-Informed Battery Knowledge
In the field of state estimation for the lithium-ion battery (LIB), model-based methods (white box) have been developed to explain battery mechanism and data-driven methods (black box) have been designed to learn battery statistics. Both white box methods and black box methods have drawn much attent...
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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/11/640 |
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| author | Yanan Wang Xuebing Han Languang Lu Yangquan Chen Minggao Ouyang |
| author_facet | Yanan Wang Xuebing Han Languang Lu Yangquan Chen Minggao Ouyang |
| author_sort | Yanan Wang |
| collection | DOAJ |
| description | In the field of state estimation for the lithium-ion battery (LIB), model-based methods (white box) have been developed to explain battery mechanism and data-driven methods (black box) have been designed to learn battery statistics. Both white box methods and black box methods have drawn much attention recently. As the combination of white box and black box, physics-informed machine learning has been investigated by embedding physic laws. For LIB state estimation, this work proposes a fractional-order recurrent neural network (FORNN) encoded with physics-informed battery knowledge. Three aspects of FORNN can be improved by learning certain physics-informed knowledge. Firstly, the fractional-order state feedback is achieved by introducing a fractional-order derivative in a forward propagation process. Secondly, the fractional-order constraint is constructed by a voltage partial derivative equation (PDE) deduced from the battery fractional-order model (FOM). Thirdly, both the fractional-order gradient descent (FOGD) and fractional-order gradient descent with momentum (FOGDm) methods are proposed by introducing a fractional-order gradient in the backpropagation process. For the proposed FORNN, the sensitivity of the added fractional-order parameters are analyzed by experiments under the federal urban driving schedule (FUDS) operation conditions. The experiment results demonstrate that a certain range of every fractional-order parameter can achieve better convergence speed and higher estimation accuracy. On the basis of the sensitivity analysis, the fractional-order parameter tuning rules have been concluded and listed in the discussion part to provide useful references to the parameter tuning of the proposed algorithm. |
| first_indexed | 2024-03-09T19:03:36Z |
| format | Article |
| id | doaj.art-7e0ea6ddadfe44e7bd9ec4e05799ba47 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:03:36Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-7e0ea6ddadfe44e7bd9ec4e05799ba472023-11-24T04:45:16ZengMDPI AGFractal and Fractional2504-31102022-11-0161164010.3390/fractalfract6110640Sensitivity of Fractional-Order Recurrent Neural Network with Encoded Physics-Informed Battery KnowledgeYanan Wang0Xuebing Han1Languang Lu2Yangquan Chen3Minggao Ouyang4School of Vehicle and Mobility, Tsinghua University, Beijing 100084, ChinaSchool of Vehicle and Mobility, Tsinghua University, Beijing 100084, ChinaSchool of Vehicle and Mobility, Tsinghua University, Beijing 100084, ChinaDepartment of Engineering, University of California, Merced, CA 95343, USASchool of Vehicle and Mobility, Tsinghua University, Beijing 100084, ChinaIn the field of state estimation for the lithium-ion battery (LIB), model-based methods (white box) have been developed to explain battery mechanism and data-driven methods (black box) have been designed to learn battery statistics. Both white box methods and black box methods have drawn much attention recently. As the combination of white box and black box, physics-informed machine learning has been investigated by embedding physic laws. For LIB state estimation, this work proposes a fractional-order recurrent neural network (FORNN) encoded with physics-informed battery knowledge. Three aspects of FORNN can be improved by learning certain physics-informed knowledge. Firstly, the fractional-order state feedback is achieved by introducing a fractional-order derivative in a forward propagation process. Secondly, the fractional-order constraint is constructed by a voltage partial derivative equation (PDE) deduced from the battery fractional-order model (FOM). Thirdly, both the fractional-order gradient descent (FOGD) and fractional-order gradient descent with momentum (FOGDm) methods are proposed by introducing a fractional-order gradient in the backpropagation process. For the proposed FORNN, the sensitivity of the added fractional-order parameters are analyzed by experiments under the federal urban driving schedule (FUDS) operation conditions. The experiment results demonstrate that a certain range of every fractional-order parameter can achieve better convergence speed and higher estimation accuracy. On the basis of the sensitivity analysis, the fractional-order parameter tuning rules have been concluded and listed in the discussion part to provide useful references to the parameter tuning of the proposed algorithm.https://www.mdpi.com/2504-3110/6/11/640physics-informed neural networkfractional-order gradientfractional-order constraintpartial differential equationbattery mechanismbackpropagation process |
| spellingShingle | Yanan Wang Xuebing Han Languang Lu Yangquan Chen Minggao Ouyang Sensitivity of Fractional-Order Recurrent Neural Network with Encoded Physics-Informed Battery Knowledge Fractal and Fractional physics-informed neural network fractional-order gradient fractional-order constraint partial differential equation battery mechanism backpropagation process |
| title | Sensitivity of Fractional-Order Recurrent Neural Network with Encoded Physics-Informed Battery Knowledge |
| title_full | Sensitivity of Fractional-Order Recurrent Neural Network with Encoded Physics-Informed Battery Knowledge |
| title_fullStr | Sensitivity of Fractional-Order Recurrent Neural Network with Encoded Physics-Informed Battery Knowledge |
| title_full_unstemmed | Sensitivity of Fractional-Order Recurrent Neural Network with Encoded Physics-Informed Battery Knowledge |
| title_short | Sensitivity of Fractional-Order Recurrent Neural Network with Encoded Physics-Informed Battery Knowledge |
| title_sort | sensitivity of fractional order recurrent neural network with encoded physics informed battery knowledge |
| topic | physics-informed neural network fractional-order gradient fractional-order constraint partial differential equation battery mechanism backpropagation process |
| url | https://www.mdpi.com/2504-3110/6/11/640 |
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