PSI - Issue 17

Ahmed Belmokre et al. / Procedia Structural Integrity 17 (2019) 698–703 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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predicted at least a few times. The random forest regression approach has the ability to appraise the importance of the input variables (Grömping 2009). The importance of a given variable, x i , is measured through the mean increase in a tree error when the observed values x i are randomly exchanged in the sample OOB . We denote by errOOB t the error of a single tree t on the OOB t sample. Now, randomly permute the values of x i in OOB t to get a perturbed sample, denoted by ̂ , and compute ̂ , the error of predictor on the perturbed sample. Variable importance, VI , of x i is then equal to (Genuer et al. 2010): · ( ) 1 1 ( ) tree J N J t i t l tree VI x errOOB errOOB N = = −  (2) Support Vector Regression (SVR) is the most common application form of support vector machine (Basak et al. 2007). It was developed by Vladimir Vapnik (1995) for binary classification problems. The regression function is expressed as: ( ) ( ) ( ) * * 1 , , , N i i i i f x K x x b     = = − +  (3) Where ( ) ( ) ( ) , , i i K x x x x   = is the kernel function; * ,   are Lagrangian multipliers, and N is the number of observations. The choice of kernel functions influences the accuracy of prediction. Using trial and error method, we choose Gaussian or Radial Basis Function (RBF) as kernels. 2.3. Support vector regression method

3. Results and discussion

3.1. Case study

Beni Haroun is a 90 m high roller compacted concrete gravity dam located in north of Algeria. Operated since 2002, the dam is equipped with flowmeters at different points: rock gallery, concrete gallery and concrete rock abutment. Data recorded at flowmeters FL-175 and FR-175, situated at elevation 175 m in the left and right abutment respectively, are available for this study. Moreover, the daily evolution of water level and temperature are also available (Figs. 1 and 2). Daily water temperature, water level and time are the inputs to our models. The 70% of data are used for training the models and the remaining data for assessing their performance.

Fig. 1. Evolution of water level