A kernel least mean square algorithm for fuzzy differential equations and its application in earth’s energy balance model and climate

• Published in: Alexandria engineering journal 2020-08, Vol.59 (4), p.2803-2810
• Main Authors: Pakdaman, M., Falamarzi, Y., Sadoghi Yazdi, H., Ahmadian, A., Salahshour, S., Ferrara, M.
• Format: Article
• Language: English
• Subjects: BFGS optimization algorithm; Energy balance model; Fuzzy dynamical differential equation; Kernel space; Least mean square
• ISSN: 1110-0168
• DOI: 10.1016/j.aej.2020.06.016

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.