A kernel least mean square algorithm for fuzzy differential equations and its application in earth’s energy balance model and climate
| Autor: | H. Sadoghi Yazdi, Morteza Pakdaman, Ali Ahmadian, Soheil Salahshour, Yashar Falamarzi, Massimiliano Ferrara |
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| Rok vydání: | 2020 |
| Předmět: |
BFGS optimization algorithm
Differential equation Computer science 020209 energy Numerical analysis Least mean square General Engineering 02 engineering and technology Interval (mathematics) Function (mathematics) Engineering (General). Civil engineering (General) 01 natural sciences Fuzzy logic 010305 fluids & plasmas Adaptive filter Nonlinear system Kernel method 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Fuzzy dynamical differential equation TA1-2040 Kernel space Energy balance model Algorithm |
| Zdroj: | Alexandria Engineering Journal, Vol 59, Iss 4, Pp 2803-2810 (2020) |
| ISSN: | 1110-0168 |
| DOI: | 10.1016/j.aej.2020.06.016 |
| Popis: | This paper concentrates on solving fuzzy dynamical differential equations (FDDEs) by use of unsupervised kernel least mean square (UKLMS). UKLMS is a nonlinear adaptive filter which works by applying kernel trick to LMS adaptive filter. UKLMS estimates multivariate function which is embedded to estimate the solution of FDDE. Adaptation mechanism of UKLMS helps for finding solution of FDDE in a recursive scenario. Without any desired response, UKLMS finds nonlinear functions. For this purpose, an approximate solution of FDDE is constructed based on adaptable parameters of UKLMS. An optimization algorithm, optimizes the values of adaptable parameters of UKLMS. The proposed algorithm is applied for solving Earth energy balance model (EBM) which is considered as a fuzzy differential equation for the first time. The method in comparison with the other existing approaches (such as numerical methods) has some advantages such as more accurate solution and also that the obtained solution has a functional form, thus the solution can be obtained at each time in training interval. Low error and applicability of developed algorithm are examined by applying it for solving several problems. After comparing the numerical results, with relative previous works, the superiority of the proposed method will be illustrated. |
| Databáze: | OpenAIRE |
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