Water Quality Prediction Model Based on Interval Type-2 Fuzzy Neural Network with Adaptive Membership Function
摘要
This paper presents an interval type-2 fuzzy neural network with an adaptive membership function (IT2FNN-AMF) designed as a model for predicting water quality. This approach seeks to address the time-varying nature, high nonlinearity, and complex prediction challenges associated with water quality environments, ultimately enhancing prediction accuracy. The study introduces an adaptive membership function that can generate a footprint of uncertainty based on diverse input data, thereby overcoming the limitation of the traditional membership function in the Interval Type-2 Fuzzy Neural Network (IT2FNN), which is restricted to producing a single Gaussian footprint of uncertainty. The membership function parameterizes the power of the original Gaussian distribution, enabling it to approximate different graphical regions and thereby enhancing the system’s ability to describe and address nonlinear problems. The structure learning of IT2FNN with Adaptive Membership Function (IT2FNN-AMF) employs fuzzy C-means clustering with a two-step splitting of cluster centers (FCM-CTS) to automatically determine the number of fuzzy rules and the initial values for the adaptive membership function’s uncertain center and variance. Furthermore, an Improved Sequential Batch Gradient Descent (ISBGD) algorithm is introduced to address the challenges posed by traditional gradient descent algorithms, which may experience gradient explosion or disappearance due to excessive iterations during neural network training. To update the gradient based on training sample batches, ISBGD randomly shuffles the training data and divides it into batches. This approach facilitates the identification of the most effective network model parameters and accelerates the convergence of the network training process. The performance of the IT2FNN-AMF model is notably superior when compared to other network models, as demonstrated by its application to second-order nonlinear time-varying system identification and water quality prediction.