Adaptive fuzzy modeling versus artificial neural networks

doi:10.1016/j.envsoft.2007.06.004

Environmental Modelling & Software

Volume 23, Issue 2, February 2008, Pages 215-224

https://doi.org/10.1016/j.envsoft.2007.06.004 Get rights and content

Abstract

In this paper two areas of soft computing (fuzzy modeling and artificial neural networks) are discussed. Based on the fundamental mathematical similarity of fuzzy techniques and radial basis function networks a new training algorithm for fuzzy models is introduced. A feed forward neural network (NN), a radial basis function network (RBF) and a trained fuzzy algorithm are compared for regional yield estimation of agricultural crops (winter rye, winter barley). As training pattern a data set from a training region (Maerkisch-Oderland district, Germany) and as test pattern a data set from a three times larger region were used. Specific advantages and disadvantages of these methods for the estimation of yield were discussed.

Introduction

The modeling of natural process has to cope with uncertainty in the parameters and the modeling methods. The crux of ecological modeling lies in our understanding: “depending upon the nature of the study, complexity can confound the analysis of an ecosystem model; the more interacting components a model has, the less straightforward it is to extract and separate causes and consequences; this is compounded when uncertainty about components obscures the accuracy of a simulation” (Ecological Model, 2006). This leads to the wish of the modelers to use expert's knowledge as model basis or to extract models from the data in a straightforward way (Ghielmi and Eccel, 2006). The focus of this paper is on these soft computing methods and their application to a simplified but realistic problem.

In this paper models will be discussed as function approximators. On the one hand there are some inputs (for example soil quality, nitrogen fertilizer, and cropping year) and on the other hand a single output (crop yield). There are a lot of possible methods for developing models from data sets, such as multiple regression, artificial neural networks, fuzzy methods, etc. Because of the lack in understanding ecological modeling the introduction of expert's knowledge in form of fuzzy modeling or artificial neural networks as universal function approximators can be one step towards creating models without an explicit mathematical equation. It can be shown that fuzzy modeling and neural networks are similar from a mathematical point of view. This offers the opportunity to introduce a training algorithm in fuzzy models and to compare these with artificial neural networks.

The complete investigation was based on the software “Spatial Analysis and Modeling Tool” (SAMT). This tool is available as free open source software (SAMT, 2007). Additionally were used free open source libraries like the gnu scientific library (GSL, 2007), the hierarchical data format (HDF, 2007) and for the graphical user interface the QT-library (QT, 2007).

To be useful for practical simulations, models should satisfy the following requirements.

•
Accuracy: the error resulting between the simulated and measured values should be minimal.
•
Generalization: the model should reduce the complexity of the real world using an approximation of the data based on fundamental knowledge.
•
Portability: the model should be usable in different sites with slightly changed inputs (compared to the training data).

These requirements are contradictory (for example, a high accuracy can lead to low generalization) to some degree so a practical compromise between them must be found.

Section snippets

Description of the data sets

The handling of different artificial neural networks and fuzzy methods to develop simple models, their specifics (advantages and disadvantages) and their suitability for application in the field of ecology is shown using data sets for spatial grain yield (yield) estimation for winter rye and winter barley under practical field cropping conditions. An example from the literature using artificial neural networks in a similar application is given in Grzesiak et al. (2006); an introduction to the

Feed forward networks

An artificial neural network as function approximator is useful because it can approximate a desired behavior without the need to specify a particular function. This is a big advantage of artificial neural networks compared to multivariate statistics. The price for this is the difficult nonlinear optimization technique, that can lead to local optima or to the so called over training. Feed forward networks are the most established type of artificial neural networks. A good introduction is given

Radial basis function network (RBF)

A feed forward network used as a function approximator is a black box fed with inputs, which produces meaningful outputs. However, there are no methods for checking if the inputs are in the region where the network was trained. A further type of artificial neural network is the so called radial basis function network (Bishop, 1995), which uses a cluster algorithm in the first step (unsupervised training) and calculates the approximation in the second step (supervised training).

Fuzzy modeling

Fuzzy modeling is designed to use knowledge of an experienced expert directly as basis of modeling. This means that:

•
fuzzy sets for the inputs of the model have to be created,
•
the outputs have to be created, and
•
a set of rules that combines the inputs with the outputs has to be created.

The rules are easy to understand and provide a basis for understanding of a fuzzy model and the discussion with other experts. We have learned that it is important to find the real expert and not a group of people

Comparison of feed forward network, radial basis function network, and a fuzzy system using an independent data set

The data sets B1 (winter barley) and B2 (winter rye) from the independent region are the basis for the comparison of different methods. The results shown here were produced with the trained neural network (NN) and the trained fuzzy system (FS) without any changes, and any retraining. The comparison shows how the models can cope with both these data sets.

Table 5 shows that the accuracy of the fuzzy model without training is very poor. At a first glance this is rather surprising, but it reflects

Conclusions and perspectives

It has been shown that the fuzzy system and neural networks have similar mathematical fundamentals, so that a training method used with neural networks could be applied to fuzzy models, and RBFs could be used as fuzzy models. An interesting approach to interpret Kohonen maps as linguistic variables is given in Predrycz and Card (1992). The combination of a fuzzy model with a training of the outputs has the advantage that the model can be understood by the expert and adapt to the measured

Acknowledgment

This contribution was supported by the German Federal Ministry of Consumer Protection, Food and Agriculture, and the Ministry of Agriculture, Environmental Protection and Regional Planning of the Federal State of Brandenburg (Germany). Thank you to Dr. W. Haberstock (Institute of Land Use Systems and Landscape Ecology) and to Dr. sc. G. Lutze (Institute of Landscape Systems Analysis) of the Leibniz-Center for Agricultural Landscape Research in Muencheberg (Germany) for the friendly

References (34)

L. Ghielmi et al.
Descriptive models and artificial neural networks for spring frost prediction in an agricultural mountain area
Computers and Electronics in Agriculture
(2006)
R. Hecht-Nielsen
Application of counterpropagation networks
Neural Networks
(1988)
A. Schultz et al.
The use of neural networks in agroecological modelling
Computers and Electronics in Agriculture
(1997)
R. Wieland et al.
Spatial Analysis and Modeling Tool (SAMT), structure and possibilities
Ecological Informatics
(2006)
L.A. Zadeh
Fuzzy algorithms
Information and Control
(1968)
Yu Bing et al.
Training radial basis function networks with differential evolution
(2006)
Ch.M. Bishop
Neural Networks for Pattern Recognition
(1995)
Ecological Model, 2006. Wikipedia homepage. Available from:...
J.A. Freemann
Simulating Neural Networks with Mathematica
(1992)
N. Gershenfeld
The Nature of Mathematical Modeling
(2002)

D.E. Goldberg

Genetic Algorithms in Search, Optimization, and Machine Learning

(1989)

W. Grzesiak et al.

Methods of prediction milk yield in dairy cows – predictive capabilities of Wood's lactation curve and artificial neural networks

Computers and Electronics in Agriculture

(2006)

GSL, 2007. Gsl homepage. Available from:...

HDF, 2007. Hdf homepage. Available from:...

R. Kindler

Ertragsschtzung in den neuen Bundeslaendern

(1992)

T. Kohonen

Self-organizing Maps

(2001)

Kohonen, T., 2006. Kohonen homepage. Available from:...

Cited by (45)

A new artificial intelligence strategy for predicting the groundwater level over the Rafsanjan aquifer in Iran
2020, Journal of Hydrology
This study presents a new strategy to predict the monthly groundwater level with short- and long-lead times over the Rafsanjan aquifer in Iran using an ensemble machine learning method called Gradient Boosting Regression (GBR). In this way, the satellite-based products, including the Tropical Rainfall Measuring Mission (TRMM) and the Gravity Recovery and Climate Experiment (GRACE) datasets, as well as the pumping rate, are used as the predictive variables in different lag times. To obtain the optimal input combinations, the Gamma Test (GT) is employed as a non-linear feature selection technique. The spatial analysis of the performance prediction is performed using several error metrics (e.g., $R^{2}$ , and NRMSE). Results indicate that the GBR provides a high prediction performance to predict the GWL, whereas the GRACE product is an accurate predictive variable. The correlation analysis between the predicted and observed GWL shows that the coefficient of determination values vary in the range of 0.66 to 0.94 over the different lead times. The spatial pattern of the prediction accuracy indicates that the regions with higher water depth and pumping rate offer higher performance. Moreover, the increasing trends in performance accuracy are observed from the north to south and the west to east of the Rafsanjan aquifer. In general, the proposed approach provides a reliable insight for water resources planner to make a decision based on the accurate modeling results.
Seasonal crop yield forecast: Methods, applications, and accuracies
2019, Advances in Agronomy
The perfect knowledge of yield before harvest has been a wish puzzling human being since the beginning of agriculture because seasonal forecast of crop yield plays a critical role in decision making for different stakeholders—from farmers to policy makers to governments for food security, to commodities traders. Different methods have been used to forecast yield with different levels of granularity, accuracy and timing.
This chapter presents a critical review of the current seasonal crop yield forecasting methods found in the scientific literature. Extensive research has been conducted on crop yield forecast, particularly for wheat, maize, rice, barley, and soybean.
Yield forecast are mainly based on field surveys, statistical regressions between historical yield and in-season variables (agrometeorological, or remotely sensed data), crop simulation models, or on integration between statistical modeling with dynamic process-based crop simulation models. A low number of studies rely on field surveys as a means to forecast yield, but they remain the main methods of yield forecast and estimation in several countries (i.e., USA). This chapter aims to report results found in peer-review journals for different crops, methods, geographies, and accuracies, and to end with a critical perspective on the advantage and disadvantage of the different methods currently employed by researchers and stakeholders.
Modelling the potential distribution of an invasive mosquito species: comparative evaluation of four machine learning methods and their combinations
2018, Ecological Modelling
Citation Excerpt :
When simulating the spread of this species, rivers, roads and railways as pathways to distant locations, which may be climatically suitable, but not accessible by active migration of the mosquito, should also be analysed (Tannich, 2015; Holloway and Miller 2017). To solve the problem of adaptability of the species to the new environment, which produces uncertainties in specific variables, it is proposed to use a fuzzy modelling approach (Wieland and Mirschel, 2008; Costa et al., 2015). By using eight weather variables and a dataset of different mosquito species, all four models calculate accurate predictions of the potential occurrence of Ae.
We tested four machine learning methods for their performance in the classification of mosquito species occurrence related to weather variables: support vector machine, random forest, logistic regression and decision tree. The objective was to find a method which showed the most accurate model for the prediction of the potential geographical distribution of Aedes japonicus japonicus, an invasive mosquito species in Germany.
The evaluation of the model trainings was conducted using derivations of a confusion matrix. Furthermore, we introduced two quality indices, ‘selectivity’ and ‘exactness’, for the evaluation of the spatial simulation, visualised through the Hasse diagram technique.
From the evaluation results we can conclude that a specific combination of two to three models performs better in predicting the potential distribution of the mosquito species than a single model or the random combination of models.
Combining expert knowledge with machine learning on the basis of fuzzy training
2017, Ecological Informatics
Citation Excerpt :
Regularization was proven to be useful in this experiment. This is particularly noticeable if a trained model is applied for training again (Wieland and Mirschel, 2008). Without regularization, the outputs are close to each other; however, regularization ensures the distance between the outputs and avoids over training.
The paper introduces a fuzzy training approach based on nonlinear regularization in an effort to avoid over training. The main idea is to restrict training so that the basic expert knowledge used to build the model is still visible. This is implemented by a new nonlinear regularization approach which can be applied to any kind of training data set. The approach is demonstrated using a large crop yield data set (>4500 field records) for sugar beet collected in agricultural farms over a 14-year period (1976–1989) in East Germany. The software is implemented in SAMT2, free and open source software, using the Python programming language.
Application of least square support vector machine and multivariate adaptive regression spline models in long term prediction of river water pollution
2016, Journal of Hydrology
Citation Excerpt :
But the shortcomings of the statistical approach include handling nonlinear characteristics of data because the statistical models are usually based on the linear correlations of the data can be expressed with a correlation coefficient. To overcome the shortcomings of the statistical methods, least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS), M5 model tree, models are developed to address the nonlinearity of data (Nayak et al., 2004; Partal and Kisi, 2007; Wieland and Mirschel, 2008; Hanbay et al., 2009; Kisi, 2009, 2013; Alves et al., 2011; Maheshwaran and Khosa, 2012, 2013; Kisi and Tombul, 2013; Soni et al., 2014; Cheng and Cao, 2014; Bhardwaj and Parmar, 2013, 2015). LSSVM model is based on kernel methods, which have proved capable of estimating more accurate than different techniques, for example, linear models ARIMA, neural networks, ANFIS, neuro-fuzzy systems, in terms of various different assessment measures during both the validation and test stages (Hong and Pai, 2006; Xu et al., 2006; Liu et al., 2007; Wang et al., 2009).
This study investigates the accuracy of least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5Tree) in modeling river water pollution. Various combinations of water quality parameters, Free Ammonia (AMM), Total Kjeldahl Nitrogen (TKN), Water Temperature (WT), Total Coliform (TC), Fecal Coliform (FC) and Potential of Hydrogen (pH) monitored at Nizamuddin, Delhi Yamuna River in India were used as inputs to the applied models. Results indicated that the LSSVM and MARS models had almost same accuracy and they performed better than the M5Tree model in modeling monthly chemical oxygen demand (COD). The average root mean square error (RMSE) of the LSSVM and M5Tree models was decreased by 1.47% and 19.1% using MARS model, respectively. Adding TC input to the models did not increase their accuracy in modeling COD while adding FC and pH inputs to the models generally decreased the accuracy. The overall results indicated that the MARS and LSSVM models could be successfully used in estimating monthly river water pollution level by using AMM, TKN and WT parameters as inputs.
Dynamic fuzzy models in agroecosystem modeling
2013, Environmental Modelling and Software
A new concept of dynamic fuzzy models used to estimate yield of agricultural crops (demonstrated for winter wheat) under the terms of climate change is introduced. Results of this fuzzy approach were compared to simulation results of MONICA, a traditional deterministic agro-ecosystem model, and YIELDSTAT, a statistics-based yield estimation model, for the federal state of Thuringia, Germany. The pros and cons of the fuzzy approach are discussed in terms of modeling effort, accuracy, calculation speed and maintenance. Some enhancements, including ensemble simulation using different experts models, are discussed. The main aim of this paper is to prove the concept of the dynamic fuzzy approach.

View all citing articles on Scopus

View full text

Adaptive fuzzy modeling versus artificial neural networks

Abstract

Introduction

Section snippets

Description of the data sets

Feed forward networks

Radial basis function network (RBF)

Fuzzy modeling

Comparison of feed forward network, radial basis function network, and a fuzzy system using an independent data set

Conclusions and perspectives

Acknowledgment

Computers and Electronics in Agriculture

Neural Networks

Computers and Electronics in Agriculture

Ecological Informatics

Information and Control

Training radial basis function networks with differential evolution

Neural Networks for Pattern Recognition

Simulating Neural Networks with Mathematica

The Nature of Mathematical Modeling

Genetic Algorithms in Search, Optimization, and Machine Learning

Methods of prediction milk yield in dairy cows – predictive capabilities of Wood's lactation curve and artificial neural networks

Computers and Electronics in Agriculture

Ertragsschtzung in den neuen Bundeslaendern

Self-organizing Maps