Long Term Behavior Monitoring of an Arch DamLong Term Behavior Monitoring of an Arch DamUsing Adaptive Neuro-Fuzzy Model TechniqueUsing Adaptive Neuro-Fuzzy Model Technique

T-S (Takagi-Sugeno) type Fuzzy SystemT-S (Takagi-Sugeno) type Fuzzy System

The advantage of this fuzzy logic system (T-S) is that it provides a compact system and, therefore, parameter estimation methods such as neuro-fuzzy algorithms or neuro-adaptive learning techniques can be developed to estimate the parameters. These techniques provide a method for the fuzzy modeling procedure to learn information about a data set, in order to compute the membership function parameters that best allow the associated fuzzy inference system to track the given input/output data. In this study, the well known adaptive algorithm called ANFIS with the aid of Matlab Fuzzy Logic Toolbox is used.

UUğurğur ŞŞAHAHİİNN1 and Seyfullah DEMSeyfullah DEMİİRKAYARKAYA2

1İstanbul Technical University, Department of Mathematical Engineering, Istanbul, Turkey2Yildiz Technical University, School of Vocational Studies, Istanbul-Turkey

E-mail: demirkay@yildiz.edu.tr

Neuro-Fuzzy ModelingNeuro-Fuzzy Modeling

The neuro-fuzzy modeling refers to the way of applying various learning techniques developed in the neural network literature to fuzzy modeling or to a Fuzzy Inference System (FIS). The basic structure of a FIS consists of three conceptual components: a rule-base, which contains a selection of fuzzy rules; a data-base which defines the membership functions (MF) used in the fuzzy rules; and a reasoning mechanism, which performs the inference procedure upon the rules to derive an output. FIS implements a nonlinear mapping from its input space to the output space. This mapping is accomplished by a number of fuzzy if-then rules. The parameters of the if-then rules (antecedents or premises in fuzzy modeling) define a fuzzy region of the input space, and the output parameters (also consequents in fuzzy modeling) specify the corresponding output. Hence, the efficiency of the FIS depends on the estimated parameters.

In the presented study, the concept of the adaptive network, which is a generalization of the common back-propagation neural network, is employed to tackle the parameter identification problem in a FIS. This procedure of developing a FIS using the framework of adaptive neural networks is called an Adaptive Neuro Fuzzy Inference system (ANFIS).

Data Used In the AnalysisData Used In the AnalysisWe used the data from the Theme C of the 6th ICOLD Benchmark Workshop on Numerical Analysis of Dams (2001) was dedicated to the interpretation and a subsequent prediction of the crest displacements of Schlegeis arch dam. The observed radial crest displacements of dam are analyzed using the time histories of water level and concrete temperatures as input parameters. The data for this study are the water level, the air temperature and the concrete temperatures at 6 points-one value per day. The response value which has to be interpreted is the radial crest displacement of the central cross section. This crest displacement is measured by pendulums. All of these data are related to the period 1992 to 1998.

1

1

( )

Ml l

lM

l

l

w zZ x

w

Model ConstructionModel ConstructionIt is possible to estimate the displacements from a given water level and temperature values.

Gaussian-type MFs were used, so as to run T-S fuzzy inference system in this study. The 2555 data set (daily, 7 years) are divided into three independent subsets: the training, verification, and the testing subsets. The training subset includes 1095 data (3 years); the verification subset has 1095 data (3 years); while the testing subset has remaining 365 data (1 year).

One of the most important tasks in developing a forecasting model is the selection of the input variables which determines the model.

The input variables are consisted of: WL= Water level of the reservoir, UT, and DT are the values of the thermometer embedded in upstream and downstream face and MT is in the middle of the dam, respectively. AT is the air temperature near vicinity of the dam. The measured horizontal displacement values are showed with P. The MFs for input variables is shown in Fig:1.

All of the input MF’s has four subsets and named suitable as QL: Quite Low, L: Low, M: Medium and H: High.

In this study, our aim is to demonstrate that the ANFIS has the ability to deal with expert knowledge and enhance the model performance. In the beginning, we developed two ANFIS models named of Model_1 and Model_2 based on the number of MF for displacement forecasting. They have 4 and 6 MF. Lastly, the Model_3 is being obtained from divided the data set to year based models and has 4 MF. The training, verification and testing data sets had been selected randomly. The rules related to the proposed model of the displacement forecasting can be given as follows in the Rule Base:

1.17*WL-3.044* -2.281* -1.412* -0.02781* -1967

0.2844*WL+0.256* +1.25* -1.439* +0.01542* -455

T T T T

T T T T

T T T T

T T T T

IF WLis H and U is M and M is H and D is M and A is M THEN

P U M D A

IF WLis QL and U is L and M isQL and D is L and A is L THEN

P U M D A

IF WL

0.548*WL+ 1.154* -2.359* -1.058* +0.0007784* -893.4

0.4676*WL +1.145* +3.737* -1.829* -0.1407* -795

T T T T

T T T T

T T T T

T T T T

is M and U is QL and M is M and D is QL and A isQL THEN

P U M D A

IF WLis L and U is H and M is L and D is H and A is H THEN

P U M D A

.9

Rule Base Rule Base

ConclusionConclusion•The ANFIS models have been provided accurate and reliable displacement forecasting, where the correlation coefficients (CC) are very close unity.

•Constructed ANFIS models, through the subtractive fuzzy clustering, can efficiently deal with vast and complex input–output patterns, and has a great ability to learn and build up a neuro-fuzzy inference system for prediction, and the forecasting results provide a useful guidance for deformation analysis studies.

•Investigations should be carried out using the ANFIS in combination with results from structural and/or statistical analysis.

Schlegeis Dam

(Austria)

Figure 1: The Membership Functions for the Input Variables.

Figure 4: Crest Displacements versus water level for training data.

Figure 5: Crest Displacements versus water levels for testing data.

Evaluation of the Model PerformanceEvaluation of the Model PerformanceBecause of there are no fixed rules to develop an ANFIS, we followed a way based on trials and found that the data set 1992, 1996 and 1997 are used for training whilst that 1993, 1994 and 1995 are used for verification. Lastly, 1998 data set is used for testing.

This ANFIS models are compared based on their performance in training and testing sets. The results are summarized in Table 1.

It appears that the ANFIS models are accurate and consistent in different subsets, where all the values of the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are smaller and all Correlation Coefficients (CC) are also very close to unity.

Table 1: Evaluation the Performance of the models with training and testing data.

It also shows that the forecasting Model_3 results in a much lower value of the RMSE, MAE and higher value of the CC than Model_1 and 2.

These results might also suggests that the ANFIS has a great ability to learn from input-output patterns, which represent the water level and temperatures are lumped effects on displacements of dam’s crest.

Overall, the performance of three ANFIS models is very good. The results demonstrate that the ANFIS can be successfully applied to establish the forecasting models that could provide accurate and reliable daily horizontal displacement prediction of the Schlegeis Arch Dam’s crest.

Fig. 2 and Fig. 3 nicely show that models’ performances are accurate and Model_3 is consistently superior to the others in training (training+verification) and testing phases.

To get a brief picture of the general performance of the constructed model, we also provide the pendulum records of the crest displacements versus water levels for training and testing data, in Fig.

4 and Fig. 5, respectively.

AcknowledgementsAcknowledgementsWe would like to thank to Prof. Dr. E. BAUER, Prof. Dr. G. GENZ and Mr. F. PERNER and also their valuable working friends for providing data. In addition, the authors are indebted to the reviewers and auditions of the LTBD_09 conference for their valuable comments and suggestions.

2nd International Conference on Long Term 2nd International Conference on Long Term BehaviourBehaviour of Dams of Dams

12th-13th October 2009-Graz, Austria 12th-13th October 2009-Graz, Austria

Input Data

Input Data

Output D

ataO

utput Data

Data Base Rule Base

Fuzzification Defuzzi-fication

Fuzzy Inference System

Figure 3: Forecasts of Crest Displacements for Testing Data.

Figure 2: Forecasts of Crest Displacements for Training Data.

Selected ReferencesSelected References• http://nw-ialad.uibk.ac.at/Wp3/Tg4/Se2/Files/6_BW_C.pdf • Demirkaya, S., Sahin, U. (2008). ANFIS approach for modeling horizontal displacements of an arch dam, In: Topcu, I. B. et al (eds), Proc. of The Symposium for Modern Methods in Science, Eskisehir, Turkey, 2008, pp. 345-356 (in Turkish). • Jang, J.S.R.(1993). “ANFIS: Adaptive-Network-based Fuzzy Inference Systems”, IEEE Transaction Systems, Man, and Cybernetics, vol. 23, pp. 665-685, May 1993.