Гібридна узагальнена адитивна нейро-фаззі система в задачах прогнозування часових рядів за умов невизначеності

Abstract

Запропоновано гібридну узагальнену адитивна нейро-фаззі систему, що об’єднує переваги нейро-фаззі системи Ванга–Менделя і узагальнених адитивних моделей Хасті– Тібшірані. Ця система характеризується простотою обчислювальної реалізації, високими апроксимувальними властивостями, швидкодією процесу навчання і призначена для розв’язання широкого класу задач динамічного інтелектуального аналізу даних, що пов’язані з прогнозуванням нестаціонарних стохастичних і хаотичних сигналів, що забруднені завадами та надходять до системи послідовно в режимі реального часу. Nowadays the computational intelligence methods and systems are widespread for solving of different Data Mining tasks, intelligent control, prediction, identification, pattern recognition ets [1–4] under conditions of uncertainty, nonlinearity, stochasticity, chaotic states, different kinds of disturbances and noises due to their universal approximation properties and learning possibility based on data that describe the operation of investigated signal, process or plant. Now the most known and popular approaches are connected with the artificial neural networks such as multilayer perceptrons that are learned using backpropagation learning algorithm. Nevertheless, the training set must be defined a priori, and the training process is implemented using many epochs of the synaptic weights training. In this case, we cannot use such systems for solving tasks in on-line mode, when the data are fed to the inputs in a sequential order in real time. Implementing of on-line learning process is possible for neural networks, whose output signal depends linearly from tuned synaptic weights, for example, Radial Basis Function Networks (RBFN) [1, 4] and Normalized Radial Basis Function Networks (NRBFN) [5, 6], however their using is often complicated by, so called, the curse of dimensionality. In addition, problem here is not connected with computational complexity, but the problem is obtaining of data sets from the real plant that can be too small for estimating of large synaptic weights number. Neuro-fuzzy systems that combine the learning ability of neural networks and transparency and interpretability of the soft computing results, have a range of advantages ahead of the conventional neural network. Here, first of all, it should be noticed TSK-system [7–9] and ANFIS [10, 11], whose output signal also depends linearly from the synaptic weights and has less number of synaptic weights than RBFN or NRBFN. The more complex hybrid systems of computational intelligence are well-known and have increasing approximation properties, for example, the hybrid fuzzy wavelet neural networks [12, 13], whose learning algorithms complexity limits their using in on-line mode. The hybrid generalized additive neuro-fuzzy system that connects advantages of the neuro-fuzzy system by Wang-Mendel and the generalized additive models by Hastie-Tibshirani, is proposed. Such system is characterized by the simplicity of computational implementation, improving approximation properties, high-speed of learning process and is intended to solve wide range tasks of dynamic data mining, which are connected with the prediction of nonstationary noised stochastic and chaotic processes in on-line mode (i.e. the observations are fed to the system sequentially in real time).