Application of adaptive fuzzy rule-based models for reconstruction of missing precipitation events

Abstract

This paper describes a fuzzy rule-based approach applied for reconstruction of missing precipitation events. The working rules are formulated from a set of past observations using an adaptive algorithm. A case study is carried out using the data from three precipitation stations in northern Italy. The study evaluates the performance of this approach compared with an artificial neural network and a traditional statistical approach. The results indicate that, within the parameter sub-space where its rules are trained, the fuzzy rule-based model provided solutions with low mean square error between observations and predictions. The problems that have yet to be addressed are overfitting and applicability outside the range of training data.Application de modèles basés sur la logique floue adaptative pour la reconstitution d'événements de précipitation manquants Résumé Cet article décrit l'application d'une approche basée sur la logique floue à la reconstitution d'événements de précipitation manquants. Le calage des règles d'inference est effectué à partir des observations passées au moyen d'un algorithme adaptatif. Une étude de cas a été effectuée sur des données provenant de trois stations pluviométriques du Nord de l'Italie. L'étude compare les performances de cette approche à celles d'un réseau de neurones artificiels et à une approche statistique classique. Les résultats indiquent que, dans le sous-espace de paramètres où le modèle est calé, le résidu aux moindres carrés entre les observations et les prévisions du modèle basé sur la logique floue est très faible. Les problèmes qui restent à examiner sont le surparamétrage et l'applicabilité du modèle au-delà de l'intervalle de variation des données ayant servi au calage.

A Takagi-Sugeno Fuzzy System for the Prediction of River Stage Dynamic

“…Given properly defined input variables and membership functions, the Takagi-Sugeno fuzzy rules for a system considered herein are in the form of (1) where denotes the ith fuzzy rule, are the input (antecedent) variables, y i are the rule output variables, A i1 , …, A im are fuzzy sets defined in the antecedent space, and a i1 , …, a im , a i0 are the model consequent parameters that have to be identified in a given data set. For a given input crisp vector , the inferred global output of the Takagi-Sugeno model is computed by taking the weighted average of the individual rules' contributions (2) where is the degree of fulfillment of the ith fuzzy rule, defined by…”

“…There are two reasons for using the JARQ 40 (4) 2006 Takagi-Sugeno fuzzy system for hydrological studies: (1) the simplicity of the inference procedure, and (2) the possibility to incorporate a general condition on the physical structure of the system into the fuzzy system. Therefore, during recent decades, a number of simulation studies can be noticed 1,3,4,8,12,13 , which are dedicated to the Takagi-Sugeno fuzzy system. However, detailed studies that compare the Takagi-Sugeno fuzzy model with the traditional model for river stage estimation under limited data, especially in developing and under-developed countries, are less available.…”

Comparison of fuzzy inference systems for streamflow prediction

“…proposed a fuzzy unit hydrograph to account for the number of uncertainties raised from both model assumptions and data acquisition in representing the rainfall-runoff transformation. There are other FL modelling applications in: rainfall-runoff processes (Abebe et al, 2000;Hundecha et al, 2001;Jacquin & Shamseldin, 2006); river flow routing (See & Openshaw, 2000;Chang & Chang, 2001); groundwater modelling (Hong et al, 2002); water-level prediction in reservoirs ; and time series modelling (Nayak et al, 2004). Deka & Chandramouli (2005) proposed a new approach combining FL and ANNs, which is referred to as fuzzy neural networks (FNN), for river flow prediction.…”

Updating Real-Time Flood Forecasting Using a Fuzzy Rule-Based Model/Mise à Jour de Prévision de Crue en Temps Réel Grâce à un Modèle à Base de Règles Floues

“…The fuzzy rule-based models have been successfully and extensively applied to many fields associated with water resources engineering. Recently, fuzzy rule-based modelling has been applied to reconstruct missing precipitation data (Abebe et al, 2000); to predict regional droughts and to model the relationship between climatic forcing and droughts (Pongrácz et al, 1999(Pongrácz et al, , 2003; to derive the rating curve (Deka & Chandramouli, 2003); to facilitate single-purpose reservoir operation (Panigrahi & Mujumdar, 2000); real-time multipurpose reservoir operation (Dubrovin et al, 2002); and a combined sewer pumping station control (Yagi & Shiba, 1999). It has also been used in rainfall-runoff modelling (Hundecha et al, 2001); in estimating groundwater recharge (Coppola et al, 2002); and in groundwater vulnerability evaluation (Chen Shouyu & Fu Guangtao, 2003).…”