Dynamic Evolving Neural-fuzzy Inference System Research Articles

Establishment of Dynamic Evolving Neural-Fuzzy Inference System Model for Natural Air Temperature Prediction

Air temperature (AT) prediction can play a significant role in studies related to climate change, radiation and heat flux estimation, and weather forecasting. This study applied and compared the outcomes of three advanced fuzzy inference models, i.e., dynamic evolving neural-fuzzy inference system (DENFIS), hybrid neural-fuzzy inference system (HyFIS), and adaptive neurofuzzy inference system (ANFIS) for AT prediction. Modelling was done for three stations in North Dakota (ND), USA, i.e., Robinson, Ada, and Hillsboro. The results reveal that FIS type models are well suited when handling highly variable data, such as AT, which shows a high positive correlation with average daily dew point (DP), total solar radiation (TSR), and negative correlation with average wind speed (WS). At the Robinson station, DENFIS performed the best with a coefficient of determination (R2) of 0.96 and a modified index of agreement (md) of 0.92, followed by ANFIS with R2 of 0.94 and md of 0.89, and HyFIS with R2 of 0.90 and md of 0.84. A similar result was observed for the other two stations, i.e., Ada and Hillsboro stations where DENFIS performed the best with R2: 0.953/0.960, md: 0.903/0.912, then ANFIS with R2: 0.943/0.942, md: 0.888/0.890, and HyFIS with R2: 0.908/0.905, md: 0.845/0.821, respectively. It can be concluded that all three models are capable of predicting AT with high efficiency by only using DP, TSR, and WS as input variables. This makes the application of these models more reliable for a meteorological variable with the need for the least number of input variables. The study can be valuable for the areas where the climatological and seasonal variations are studied and will allow providing excellent prediction results with the least error margin and without a huge expenditure.

Dynamic Neuro-Fuzzy Systems for Forecasting El Niño Southern Oscillation (ENSO) Using Oceanic and Continental Climate Parameters as Inputs

El Niño Southern Oscillation is one of the significant phenomena that drives global climate variability, showing a relationship with extreme events. Reliable forecasting of ENSO phases can minimize the risks in many critical areas, including water supply, food security, health, and public safety on a global scale. This study develops an ENSO forecasting model using the dynamic evolving neural fuzzy inference system (DENFIS), an artificial intelligence-based data-driven algorithm. To forecast ENSO phases for 1, 2, and 3 months ahead, 42 years (1979–2021) of monthly data of 25 oceanic and continental climatic variables and ENSO-characterizing indices are used. The dataset includes 12 El Niño and 14 La Niña events, of which the latest 2 El Niño and 4 La Niña events are reserved for testing while the remaining data are used for training the model. The potential input variables to the model are short-listed using a cross-correlation analysis. Then a systematic input selection procedure is conducted to identify the best input combinations for the model. The results of this study show that the best performing combination of such climate variables could achieve up to 78.57% accuracy in predicting short-term ENSO phases (up to 3 months ahead). Heat content at 0 to 300 m of central equatorial Pacific shows promising performance in forecasting ENSO phases. Moreover, DENFIS was found to be a reliable tool for forecasting ENSO events using multiple oceanic and continental climate variables.

Model variational consumer preferences based on online reviews using sentiment analysis and PSO-based DENFIS approaches

Previous studies developed consumer preference models mainly through customer surveys, ignoring the variability of consumer preferences over time. In addition, it is difficult to obtain time series data based on the customer surveys. In recent years, some previous studies tried to analyse consumer preferences based on online reviews. However, they have not solved the problems of modelling variational consumer preference based on time series data with the consideration of the ambiguity of emotions expressed by customers in online reviews. To solve the above problems, this article proposes the particle swarm optimization (PSO) based dynamic evolving neural-fuzzy inference system (DENFIS) method to model variational consumer preferences based on online customer reviews. Using the time series data mined by the sentiment analysis method and the product attribute settings of the review products, the PSO-based DENFIS method is offered to dynamically model consumer preferences, in which PSO is used to adjust DENFIS parameters adaptively.

Machine learning algorithms for soil moisture estimation using Sentinel-1: Model development and implementation

The present study provided the first-time comprehensive evaluation of 12 advanced statistical and machine learning (ML) algorithms for the Soil Moisture (SM) estimation from dual polarimetric Sentinel-1 radar backscatter. The ML algorithms namely support vector machine (SVM) with linear, polynomial, radial and sigmoid kernel, random forest (RF), multi-layer perceptron (MLP), radial basis function (RBF), Wang and Mendel’s (WM), subtractive clustering (SBC), adaptive neuro fuzzy inference system (ANFIS), hybrid fuzzy interference system (HyFIS), and dynamic evolving neural fuzzy inference system (DENFIS) were used. Extensive field samplings were performed for collection of in-situ SM data and other parameters from the selected sites for seven different dates and at two different locations (Varanasi and Guntur District, India), concurrent to Sentinel-1 overpasses. The backscattering coefficients were considered as input variables and SM as output variable for the training, validation and testing of the ML algorithms. The site at Varanasi was used for the training, validation and testing of the models. On the other hand, the Guntur site was used as an independent site for checking the model performance, before finalizing the algorithms. The performances of different trained algorithms were evaluated in terms of correlation coefficient ( r ), root mean square error (RMSE) (in m 3 /m 3 ) and bias (in m 3 /m 3 ). The study identified the RF, SBC and ANFIS as the top three best performing models with comparable and promising SM estimation. In order to test the robustness of these best models (RF, SBC and ANFIS), further performance analysis was performed to the independent datasets of the Varanasi and Guntur test sites, which indicates that the performance of these three models were consistent and SBC can be recommended as the best among all for SM estimation.

Characterization and Predictive Analysis of Volatile Financial Markets Using Detrended Fluctuation Analysis, Wavelet Decomposition, and Machine Learning

This paper proposes a granular framework for examining the dynamics of stock indexes that exhibit nonparametric and highly volatile behavior, and subsequently carries out the predictive analytics task by integrating detrended fluctuation analysis (DFA), maximal overlap discrete wavelet transformation (MODWT), and machine learning algorithms. DFA test ascertains the key temporal characteristics of the daily closing prices. MODWT decomposes the time series into granular components. Four pattern recognition algorithms—adaptive neuro fuzzy inference system (ANFIS), dynamic evolving neural-fuzzy inference system (DENFIS), bagging and deep belief network (DBN)—are then used on the decomposed components to obtain granular level forecasts. The entire exercise is performed on daily closing prices of Dow Jones Industrial Average (DJIA), National Stock Exchange of India (NIFTY), Karachi Stock Exchange (KSE), Taiwan Stock Exchange (TWSE), Financial Times Stock Exchange (FTSE), and German Stock Exchange (DAX). MODWT-Bagging and MODWT-DBN appear as superior forecasting models.

Exploring the application of soft computing techniques for spatial evaluation of groundwater quality variables

The precise estimation of spatial variation of groundwater quality variables is necessary for making appropriate decisions regarding aquifer resources management and environmental systems. The aim of this research is to evaluate five different data-intelligent methods so as to get the best one in spatial estimation of electrical conductivity (EC) and total hardness (TH) of groundwater resources. The study uses water quality data including Na, Cl, Mg, Ca, SO4, HCO3, TH, and EC, observed at 367 wells, in the Chhattisgarh state, central India. Four different scenarios are decided by implementing Gamma and linear regression methods. Data-intelligent methods applied to selected scenarios to estimate EC and TH are dynamic evolving neural-fuzzy inference system (DENFIS), group method of data handling (GMDH), multivariate adaptive regression spline (MARS), M5 Tree model (M5 Tree), and gene expression programming (GEP). Evaluation of the methods with respect to correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe efficiency (NSE), Legates and McCabe index (LMI), and Willmott index of agreement (WI) indicates that the GEP for the input combination including TH, Na, Cl, HCO3 variables and the DENFIS by employing Ca, Mg, EC variables provide the best accuracy in estimating EC and TH, respectively. The statistical metrics of the GEP (DENFIS) for the best scenario are R = 0.970 (0.958), NSE = 0.941 (0.917), RMSE = 105.317 μs/cm (34.692 mg/L), MAE = 57.075 μs/cm (12.603 mg/L), WI = 0.984 (0.979) and LMI = 0.824 (0.868). The spatial distribution maps indicate that the EC and TH values of groundwater resources in the studied area are in their permissible limits for drinking consumption and the interpolated maps of the data-intelligent techniques have suitable precision in comparison with the observed maps.

Modeling monthly streamflow in mountainous basin by MARS, GMDH-NN and DENFIS using hydroclimatic data

Accurate estimation of streamflow has a vital importance in water resources engineering, management and planning. In the present study, the abilities of group method of data handling-neural networks (GMDH-NN), dynamic evolving neural-fuzzy inference system (DENFIS) and multivariate adaptive regression spline (MARS) methods are investigated for monthly streamflow prediction. Precipitation, temperature and streamflows from Kalam and Chakdara stations at Swat River basin (mountainous basin), Pakistan, are used as inputs to the applied models in the form of different input scenarios, and models’ performances are evaluated on the basis of root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE) and combined accuracy (CA) indexes. Test results of the Kalam Station show that the DENFIS model provides more accurate prediction results in comparison of GMDH-NN and MARS models with the lowest RMSE (18.9 m3/s), MAE (13.1 m3/s), CA (10.6 m3/s) and the highest NSE (0.941). For the Chakdara Station, the MARS outperforms the GMDH-NN and DENFIS models with the lowest RMSE (47.5 m3/s), MAE (31.6 m3/s), CA (26.1 m3/s) and the highest NSE (0.905). Periodicity (month number of the year) effect on models’ accuracies in predicting monthly streamflow is also examined. Obtained results demonstrate that the periodicity improves the models’ accuracies in general but not necessarily in every case. In addition, the results also show that the monthly streamflow could be successfully predicted using only precipitation and temperature variables as inputs.

Reference Evapotranspiration Modeling Using New Heuristic Methods.

The study investigates the potential of two new machine learning methods, least-square support vector regression with a gravitational search algorithm (LSSVR-GSA) and the dynamic evolving neural-fuzzy inference system (DENFIS), for modeling reference evapotranspiration (ETo) using limited data. The results of the new methods are compared with the M5 model tree (M5RT) approach. Previous values of temperature data and extraterrestrial radiation information obtained from three stations, in China, are used as inputs to the models. The estimation exactness of the models is measured by three statistics: root mean square error, mean absolute error, and determination coefficient. According to the results, the temperature or extraterrestrial radiation-based LSSVR-GSA models perform superiorly to the DENFIS and M5RT models in terms of estimating monthly ETo. However, in some cases, a slight difference was found between the LSSVR-GSA and DENFIS methods. The results indicate that better prediction accuracy may be obtained using only extraterrestrial radiation information for all three methods. The prediction accuracy of the models is not generally improved by including periodicity information in the inputs. Using optimum air temperature and extraterrestrial radiation inputs together generally does not increase the accuracy of the applied methods in the estimation of monthly ETo.

Application of novel data mining algorithms in prediction of discharge and end depth in trapezoidal sections

Flow measurement in irrigation and drainage networks and water conveyance channels have particular importance. Direct methods of flow measurement are costly, time-consuming and are generally associated with losses of energy in flow. In this study, estimation of discharge and end depth of free overfall flows in trapezoidal channels section were investigated. For this purpose, data-driven techniques including dynamic evolving neural-fuzzy inference system (DENFIS), multivariate adaptive regression spline (MARS) and M5 model tree (M5Tree) were developed. 189 laboratory data experiments, six different scenarios based on geometric variables including side slope (m), bed width (B), bed slope (S0), and hydraulic variables including critical depth (Yc), critical slope (Sc) and end depth (YE) or discharge (Q) were applied. The model’s performance was evaluated thorough several statistical indicators and graphical presentations. The accuracy of all three models were apparent in estimation of the discharge and the end depth for most of the scenarios. The results showed that the DENFIS model for the input combination of all variables (Yc, YE, B, S0, m, Sc) with the maximum values of R2 and Nash-Sutcliffe efficiency coefficient (NSE) that were equal to 0.976 and 0.975, respectively, and the minimum values of RMSE, MAE, PBIAS and RSR, that were equal to 0.0015, 0.0989, −1.5906, and 0.1574, respectively, showed the highest estimation accuracy. Regarding the end depth estimation, DENFIS model for the input combination including the variables Yc, Q, Sc, m, B with the highest values of R2 and NSE equal to 0.993 and 0.992 respectively, and the lowest values of RMSE, MAE, PBIAS and RSR equal to 0.0028, 0.1628, 0.7383 and 0.0883, respectively, had a better performance compared to other MARS and M5Tree. The results of this study suggest DENFIS as a suitable and powerful model for estimation of discharge in irrigation and drainage networks.

Prediction of Suspended Sediment Load Using Data-Driven Models

Estimation of suspended sediments carried by natural rivers is essential for projects related to water resource planning and management. This study proposes a dynamic evolving neural fuzzy inference system (DENFIS) as an alternative tool to estimate the suspended sediment load based on previous values of streamflow and sediment. Several input scenarios of daily streamflow and suspended sediment load measured at two locations of China—Guangyuan and Beibei—were tried to assess the ability of this new method and its results were compared with those of the other two common methods, adaptive neural fuzzy inference system with fuzzy c-means clustering (ANFIS-FCM) and multivariate adaptive regression splines (MARS) based on three commonly utilized statistical indices, root mean square error (RMSE), mean absolute error (MAE), and Nash–Sutcliffe efficiency (NSE). The data period covers 01/04/2007–12/31/2015 for the both stations. A comparison of the methods indicated that the DENFIS-based models improved the accuracy of the ANFIS-FCM and MARS-based models with respect to RMSE by 33% (32%) and 31% (36%) for the Guangyuan (Beibei) station, respectively. The NSE accuracy for ANFIS-FCM and MARS-based models were increased by 4% (36%) and 15% (19%) using DENFIS for the Guangyuan (Beibei) station, respectively. It was found that the suspended sediment load can be accurately estimated by DENFIS-based models using only previous streamflow data.

Dynamic modelling of customer preferences for product design using DENFIS and opinion mining

Previous studies mainly employed customer surveys to collect survey data for understanding customer preferences on products and developing customer preference models. In reality, customer preferences on products could change over time. Thus, the time series data of customer preferences under different time periods should be collected for the modelling of customer preferences. However, it is difficult to obtain the time series data based on customer surveys because of long survey time and substantial resources involved. In recent years, a large number of online customer reviews of products can be found on various websites, from which the time series data of customer preferences can be extracted easily. Some previous studies have attempted to analyse customer preferences on products based on online customer reviews. However, two issues were not addressed in previous studies which are the fuzziness of the sentiment expressed by customers existing in online reviews and the modelling of customer preferences based on the time series data obtained from online reviews. In this paper, a new methodology for dynamic modelling of customer preferences based on online customer reviews is proposed to address the two issues which mainly involves opinion mining and dynamic evolving neural-fuzzy inference system (DENFIS). Opinion mining is adopted to analyze online reviews and perform sentiment analysis on the reviews under different time periods. With the mined time series data and the product attribute settings of reviewed products, a DENFIS approach is introduced to perform the dynamic modelling of customer preferences. A case study is used to illustrate the proposed methodology. The results of validation tests indicate that the proposed DENFIS approach outperforms various adaptive neuro-fuzzy inference system (ANFIS) approaches in the dynamic modelling of customer preferences in terms of the mean relative error and variance of errors. In addition, the proposed DENFIS approach can provide both crisp and fuzzy outputs that cannot be realized by using existing ANFIS and conventional DENFIS approaches.

Hydrodynamics of river-channel confluence: toward modeling separation zone using GEP, MARS, M5 Tree and DENFIS techniques

Hydrodynamics of confluence as a natural component in river-channel networks is complicated. Having sufficient knowledge about erosion and sedimentation in the river-channel confluences requires determination of the separation zone dimensions. In this paper, we estimated dimension of separation zone (i.e. length and width) by utilizing data driven techniques: gene expression programming (GEP), M5 Tree model, multivariate adaptive regression spline (MARS), and dynamic evolving neural-fuzzy inference system (DENFIS) trained with hydraulics input variables including discharge ratio (Qr), downstream Froude number (Fr3), and side slope angle of main channel ( $$\sin \,\theta$$ ). Different splitting scenarios, 50–50%, 60–40% and 75–25%, for train-test parts after randomizing, were considered achieving more robust evaluation of the models. The estimated dimensionless length and width (i.e. $$\frac{L}{{B_{3} }}$$ and $$\frac{H}{{B_{3} }}$$ ) were compared with experimental results. In order to measure the accuracy of various models, different statistical criteria including root mean square error (RMSE), Nash–Sutcliffe model efficiency coefficient (NS), correlation coefficient (R), mean absolute error, Legates and McCabe index and Willmott Index of Agreement have been used. For 50–50% train-test scenario, there is a slight difference among the DENFIS, MARS and M5 Tree models while the GEP has the worst accuracy in estimating length of separation zone. The results indicated that by increasing the percentage of training data (i.e. from 50 to 75%), the accuracy of models in term of RMSE was improved as 22, 12, 14, and 15% for the DENFIS, GEP, M5 Tree and MARS models, respectively. Regarding estimation of separation zone width, adding $$\sin \,\theta$$ variable as input considerably increases the models’ performances. The results revealed that M5 Tree is more sensitive to data number in training phase.

The applicability of Generic Self-Evolving Takagi-Sugeno-Kang neuro-fuzzy model in modeling rainfall–runoff and river routing

Abstract Recent advancements in neuro-fuzzy models (NFMs) have made possible the implementation of dynamic rule base systems. This is in comparison with static applications commonly seen in global NFMs such as the Adaptive-Network-Based Fuzzy Inference System (ANFIS) model widely used in hydrological modeling. This study underlines key differences between local and global NFMs with an emphasis on rule base dynamics, in the context of two common flow forecast applications. A global NFM, ANFIS, and two local NFMs, Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) and Generic Self-Evolving Takagi-Sugeno-Kang (GSETSK), were tested. Results from all NFMs compared favorably when benchmarked against physically based models. Rainfall–runoff modeling is a complex process which benefits from the advanced rule generation and pruning mechanisms in GSETSK, resulting in a more compact rule base. Although ANFIS resulted in the same number of rules, this came about at the expense of having the need for a large training dataset. All NFMs generated a similar number of rules for the river routing application, although local NFMs yielded better results for forecasts at longer lead times. This is attributed to the fact that the routing procedure is less complex and can be adequately modeled by static NFMs.

Dynamic evolving neural fuzzy inference system equalization scheme in mode division multiplexer for optical fiber transmission

The performance of optical mode division multiplexer (MDM) is affected by inter-symbol interference (ISI), which arises from higher-order mode coupling and modal dispersion in multimode fiber (MMF). Existing equalization algorithms in MDM can mitigate linear channel impairments, but cannot tackle nonlinear channel impairments accurately. Therefore, mitigating the noise in the received signal of MDM in the presence of ISI to recover the transmitted signal is important issue. This paper aims at controlling the broadening of the signal from MDM and minimizing the undesirable noise among channels. A dynamic evolving neural fuzzy inference system (DENFIS) equalization scheme has been used to achieve this objective. Results illustrate that nonlinear DENFIS equalization scheme can improve the received distorted signal from an MDM with better accuracy than previous linear equalization schemes such as recursive‐least‐square (RLS) algorithm. Desirably, this effect allows faster data transmission rate in MDM. Additionally, the successful offline implementation of DENFIS equalization in MDM encourages future online implementation of DENFIS equalization in embedded optical systems.

The Impact of Training Data Sequence on the Performance of Neuro-Fuzzy Rainfall-Runoff Models with Online Learning

The learning algorithms in many of conventional Neuro-Fuzzy Systems (NFS) are based on batch or global learning where all parameters of the fuzzy system are optimized off-line. Although these models have frequently been used, they suffer from a reduced flexibility in their architecture as the number of rules need to be predefined by the user. This study uses a Dynamic Evolving Neural Fuzzy Inference System (DENFIS) in which an evolving, online clustering algorithm, the Evolving Clustering Method (ECM), is implemented. This study focused on evaluating the performance of this model in capturing the rainfall-runoff process and rainfall-water level relationship. The two selected study catchments are located in an urban tropical and in a semi-urbanized area, respectively. The first catchment, Sungai Kayu Ara (23.22 km2), is located in Malaysia, with 10-min rainfall-runoff time-series from which 30 major events are used. The second catchment, Dandenong (272 km2), is located in Victoria, Australia, with daily rainfall and river stage (water level) data from which 11 years of data is used. DENFIS results were then compared with two groups of benchmark models: a regression-based data-driven model known as the Autoregressive Model with Exogenous Inputs (ARX) for both study sites, and physical models Hydrologic Engineering Center–Hydrologic Modelling System (HEC–HMS) and Storm Water Management Model (SWMM) for Sungai Kayu Ara and Dandenong catchments, respectively. DENFIS significantly outperformed the ARX model in both study sites. Moreover, DENFIS was found comparable if not superior to HEC–HMS and SWMM in Sungai Kayu Ara and Dandenong catchments, respectively. A sensitivity analysis was then conducted on DENFIS to assess the impact of training data sequence on its performance. Results showed that starting the training with datasets that include high peaks can improve the model performance. Moreover, datasets with more contrasting values that cover wide range of low to high values can also improve the DENFIS model performance.

Comparison of multi-gene genetic programming and dynamic evolving neural-fuzzy inference system in modeling pan evaporation

AbstractAccurately modeling pan evaporation is important in water resources planning and management and also in environmental engineering. This study compares the accuracy of two new data-driven methods, multi-gene genetic programming (MGGP) approach and dynamic evolving neural-fuzzy inference system (DENFIS), in modeling monthly pan evaporation. The climatic data, namely, minimum temperature, maximum temperature, solar radiation, relative humidity, wind speed, and pan evaporation, obtained from Antakya and Antalya stations, Mediterranean Region of Turkey were utilized in the study. The MGGP and DENFIS methods were also compared with genetic programming (GP) and calibrated version of Hargreaves Samani (CHS) empirical method. For Antakya station, GP had slightly better accuracy than the MGGP and DENFIS models and all the data-driven models performed were superior to the CHS while the DENFIS provided better performance than the other models in modeling pan evaporation at Antalya station. The effect of periodicity input to the models' accuracy was also investigated and it was found that adding periodicity significantly increased the accuracy of MGGP and DENFIS models.

A New Method for Evaporation Modeling: Dynamic Evolving Neural-Fuzzy Inference System

Evaporation estimation is very essential for planning and development of water resources. The study investigates the ability of new method, dynamic evolving neural-fuzzy inference system (DENFIS), in modeling monthly pan evaporation. Monthly maximum and minimum temperatures, solar radiation, wind speed, and relative humidity data obtained from two stations located in Turkey are used as inputs to the models. The results of DENFIS method were compared with the classical adaptive neural-fuzzy inference system (ANFIS) by using root mean square error (RMSE), mean absolute relative error (MARE), and Nash-Sutcliffe Coefficient (NS) statistics. Cross validation was applied for better comparison of the models. The results indicated that DENFIS models increased the accuracy of ANFIS models to some extent. RMSE, MARE, and NS of the ANFIS model were increased by 11.13, 11.45, and 6.83% for the Antalya station and 20.11, 12.94%, and 8.29% for the Antakya station using DENFIS.

Water level forecasting using neuro-fuzzy models with local learning

The global learning method is widely used to train data-driven models for hydrological forecasting. The drawback of global models is that a long data record is required and the model is not easily adapted once it is trained. This study investigated the local learning approach applied in the dynamic evolving neural-fuzzy inference system (DENFIS) to provide 5-lead-day water level forecasts for the Mekong River. The local learning method focuses on the relationship between input and output variables at the most recent state. The results obtained from DENFIS were found to be better than results obtained from adaptive neuro-fuzzy inference system, which uses global learning approach, and the unified river basin simulator model. Local learning provides continuous model updating, and the results obtained in this study show that local learning is a promising tool for water level forecasting in real-time flood warning applications.

A fully-online Neuro-Fuzzy model for flow forecasting in basins with limited data

Current state-of-the-art online neuro fuzzy models (NFMs) such as DENFIS (Dynamic Evolving Neural-Fuzzy Inference System) have been used for runoff forecasting. Online NFMs adopt a local learning approach and are able to adapt to changes continuously. The DENFIS model however requires upper/lower bound for normalization and also the number of rules increases monotonically. This requirement makes the model unsuitable for use in basins with limited data, since a priori data is required. In order to address this and other drawbacks of current online models, the Generic Self-Evolving Takagi-Sugeno-Kang (GSETSK) is adopted in this study for forecast applications in basins with limited data. GSETSK is a fully-online NFM which updates its structure and parameters based on the most recent data. The model does not require the need for historical data and adopts clustering and rule pruning techniques to generate a compact and up-to-date rule-base. GSETSK was used in two forecast applications, rainfall-runoff (a catchment in Sweden) and river routing (Lower Mekong River) forecasts. Each of these two applications was studied under two scenarios: (i) there is no prior data, and (ii) only limited data is available (1year for the Swedish catchment and 1 season for the Mekong River). For the Swedish Basin, GSETSK model results were compared to available results from a calibrated HBV (Hydrologiska Byråns Vattenbalansavdelning) model. For the Mekong River, GSETSK results were compared against the URBS (UnifiedRiverBasin Simulator) model. Both comparisons showed that results from GSETSK are comparable with the physically based models, which were calibrated with historical data. Thus, even though GSETSK was trained with a very limited dataset in comparison with HBV or URBS, similar results were achieved. Similarly, further comparisons between GSETSK with DENFIS and the RBF (Radial Basis Function) models highlighted further advantages of GSETSK as having a rule-base (compared to opaque RBF) which is more compact, up-to-date and more easily interpretable.

Rainfall-runoff Modeling Using Dynamic Evolving Neural Fuzzy Inference System with Online Learning

Neuro-Fuzzy Systems (NFS) are computational intelligence tools that have recently been employed in hydrological modeling. In many of the common NFS the learning algorithms used are based on batch learning where all the parameters of the fuzzy system are optimized off-line. Although these models have frequently been used, there is a criticism on such learning process as the number of rules are needed to be predefined by the user. This will reduce the flexibility of the NFS architecture while dealing with different data with different level of complexity. On the other hand, online or local learning evolves through local adjustments in the model as new data is introduced in sequence. In this study, dynamic evolving neural fuzzy inference system (DENFIS) is used in which an evolving, online clustering algorithm called the Evolving Clustering Method (ECM) is implemented. ECM is an online, maximum distance-based clustering method which is able to estimate the number of clusters in a data set and find their current centers in the input space through its fast, one-pass algorithm. The 10-minutes rainfall-runoff time series from a small (23.22 km2) tropical catchment named Sungai Kayu Ara in Selangor, Malaysia, was used in this study. Out of the 40 major events, 12 were used for training and 28 for testing. Results obtained by DENFIS were then compared with the ones obtained by physically-based rainfall-runoff model HEC-HMS and a regression model ARX. It was concluded that DENFIS results were comparable to HEC-HMS and superior to ARX model. This indicates a strong potential for DENFIS to be used in rainfall-runoff modeling.