NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes
This paper presents a new approach for modelling nonlinear dynamic processes (NDP). It is based on a nonlinear autoregressive with exogenous (NARX) inputs model structure and a deep convolutional fuzzy system (DCFS). The DCFS is a hierarchical fuzzy structure, which can overcome the deficiency of ge...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/2/304 |
| _version_ | 1797439105160708096 |
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| author | Marjan Golob |
| author_facet | Marjan Golob |
| author_sort | Marjan Golob |
| collection | DOAJ |
| description | This paper presents a new approach for modelling nonlinear dynamic processes (NDP). It is based on a nonlinear autoregressive with exogenous (NARX) inputs model structure and a deep convolutional fuzzy system (DCFS). The DCFS is a hierarchical fuzzy structure, which can overcome the deficiency of general fuzzy systems when facing high dimensional data. For relieving the curse of dimensionality, as well as improving approximation performance of fuzzy models, we propose combining the NARX with the DCFS to provide a good approximation of the complex nonlinear dynamic behavior and a fast-training algorithm with ensured convergence. There are three NARX DCFS structures proposed, and the appropriate training algorithm is adapted. Evaluations were performed on a popular benchmark—Box and Jenkin’s gas furnace data set and the four nonlinear dynamic test systems. The experiments show that the proposed NARX DCFS method can be successfully used to identify nonlinear dynamic systems based on external dynamics structures and nonlinear static approximators. |
| first_indexed | 2024-03-09T11:46:55Z |
| format | Article |
| id | doaj.art-d6787f4274d14450a98ffb04a98fb35f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:46:55Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d6787f4274d14450a98ffb04a98fb35f2023-11-30T23:20:20ZengMDPI AGMathematics2227-73902023-01-0111230410.3390/math11020304NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic ProcessesMarjan Golob0Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, SI-2000 Maribor, SloveniaThis paper presents a new approach for modelling nonlinear dynamic processes (NDP). It is based on a nonlinear autoregressive with exogenous (NARX) inputs model structure and a deep convolutional fuzzy system (DCFS). The DCFS is a hierarchical fuzzy structure, which can overcome the deficiency of general fuzzy systems when facing high dimensional data. For relieving the curse of dimensionality, as well as improving approximation performance of fuzzy models, we propose combining the NARX with the DCFS to provide a good approximation of the complex nonlinear dynamic behavior and a fast-training algorithm with ensured convergence. There are three NARX DCFS structures proposed, and the appropriate training algorithm is adapted. Evaluations were performed on a popular benchmark—Box and Jenkin’s gas furnace data set and the four nonlinear dynamic test systems. The experiments show that the proposed NARX DCFS method can be successfully used to identify nonlinear dynamic systems based on external dynamics structures and nonlinear static approximators.https://www.mdpi.com/2227-7390/11/2/304process identificationinput-output modellingNARX modeldecomposed fuzzy systemhierarchical fuzzy systemdeep convolutional fuzzy system |
| spellingShingle | Marjan Golob NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes Mathematics process identification input-output modelling NARX model decomposed fuzzy system hierarchical fuzzy system deep convolutional fuzzy system |
| title | NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes |
| title_full | NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes |
| title_fullStr | NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes |
| title_full_unstemmed | NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes |
| title_short | NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes |
| title_sort | narx deep convolutional fuzzy system for modelling nonlinear dynamic processes |
| topic | process identification input-output modelling NARX model decomposed fuzzy system hierarchical fuzzy system deep convolutional fuzzy system |
| url | https://www.mdpi.com/2227-7390/11/2/304 |
| work_keys_str_mv | AT marjangolob narxdeepconvolutionalfuzzysystemformodellingnonlineardynamicprocesses |