توسعه رگرسیون بردار پشتیبانی از مدل شناسایی برای پیش بینی رفتار ساختاری سد

The paper presents the application of support vector regression (SVR) to accurate forecasting of the tangential displacement of a concrete dam. The SVR nonlinear autoregressive model with exogenous inputs (NARX) was developed and tested using experimental data collected during fourteen years. A total of 573 data were used for training of the SVR model whereas the remaining 156 data were used to test the created model. Performance of a SVR model depends on a proper setting of parameters. The SVR parameters, the kernel function, the regularization parameter and the tube size of ε-insensitive loss function are specified carefully by the trail-and-error method. Efficiency of the SVR model is measured using the Pearson correlation coefficient (r), the mean absolute error (MAE) and the mean square error (MSE). Comparison of the values predicted by the SVR-based NARX model with the experimental data indicates that SVR identification model provides accurate results.

Dam parameters monitoring through installed instrumentation is the most important part of a dam safety program [1]. These parameters include seepage flows, seepage water clarity, pore pressure, deformations or movements, water levels, pressures, loading conditions, temperature variations, etc. Physical interpretation of significant indicators of the structural behaviour is the key factor to control and management of the dam system. Structural health monitoring of dams is based on acquisition of displacement measurements [2]. Deformation monitoring can reflect the structural behaviour of the dam [3]. Timely and accurate analysis and prediction of the dam displacement is an essential part of the dam safety control. The structural response of the dam is affected by many factors including reversible (hydrostatic pressure and temperature) and irreversible factors (due to residual deformations associated with creep, alkali-aggregate reaction and other nonlinear effects that may jeopardize the structural integrity [4]). There are different approaches to developing models for prediction of the nonlinear structural behaviour of the dam, and they include deterministic, statistical and hybrid models, which combine the first two. Deterministic modelling requires solving nonlinear partial differential equations for which closed form solutions may be difficult or impossible to obtain [5]. As a result, numerical methods, such as the finite element method, the finite-difference method and the finite volume method are employed. Advantages of the statistical methods include simplicity of formulation, speed of execution, availability of any kind of correlation between independent and dependent variables [6] and [7]. Performance of the existing statistical regression models is not satisfactory when multicollinearity and influential outliers exist between the variables [8]. Artificial intelligence techniques such as artificial neural networks, fuzzy logic systems, neuro-fuzzy systems and genetic algorithms have been used as effective alternative tools for modelling of complex civil engineering systems and they have been widely used for prediction and forecasting. Furthermore, in dam engineering, these techniques have been successfully used to obtain the optimal shape of dams [9] and [10] as well as for modelling of the dam behaviour [11], [12], [13] and [14]. System identification of dams is a significant field of structural engineering [15]. Displacement of the dam is a nonlinear time-varying function of hydrostatic pressure, temperature and other unexpected unknown causes. Nonlinear black-box system identification can be applied to develop complex nonlinear models. NARX input–output model can be used to describe nonlinear structural behaviour of the dam [14]. The output of the NARX model depends on the previous values of itself and inputs. Determination of the model order and the model structure of a general NARX model is a difficult task even for a single-input and single-output system [16]. Selection of a near-optimal set of time lags is an important and difficult computational task [17]. The main problem in model identification is to approximate the unknown function within a given accuracy from some sampled data sequences. This function is approximated by some general function approximators such as neural networks [18] or neuro-fuzzy systems [19] and [20]. SVR has recently been used in the framework of the nonlinear black-box system identification [21], [22], [23] and [24]. In the present work, SVR is used for structural identification of the dam. The support vector machine (SVM) is a new technique that has been intensively used to solve pattern classification and function–approximation problems in many areas. Hammer and Gersmann [25] showed the universal approximation capability of SVMs with various kernels, including Gaussian, several dot products, or polynomial kernels. The SVM implements the structural risk minimization principle, which has been shown to be superior to the traditional empirical risk minimization principle implemented by most of the conventional neural networks. Training of the SVM is equivalent to solving a linearly constrained quadratic programming problem so that the solution of the SVM is globally optimal and unique [26]. The support vector machine is based on the statistical learning theory [27]. The SVM was originally developed for binary classification problems. Support vector regression (SVR) presents an application of the SVM for function estimation [28] and [29]. The procedure based on neuro-fuzzy modelling was presented and discussed for the radial displacement of an arch dam by Rankovic et al. [30]. The objective of this study is to develop a support vector regression-based NARX model for the dam tangential displacement prediction and to demonstrate how it is applied to identify complex nonlinear relationships between the input and output variables.

Accurate forecasting of the future dam displacements is a challenging problem in dam engineering. The behaviuor of a dam is a nonlinear time-varying function of hydrostatic pressure, temperature and other unexpected irreversible factors. In recent years, feedforward, recurrent neural networks and neuro-fuzzy systems have been widely studied in nonlinear behaviour identification. This work concerns the use of nonlinear NARX black-box models for the prediction of the nonlinear structural behaviour. Support vector regression is applied in the context of black-box system identification. The prediction results show good agreement with the experimental data and they indicate that SVR identification is an effective tool for approximation of uncertain nonlinear structural behaviour of the dam. The performance of the SVR models was tested using correlation coefficients, the mean absolute error and the mean square error. Both SVR models for displacement prediction have excellent performance. However, the numbers of time lags of the inputs and the output influence both the autoregressive structures and the prediction performance. Therefore, an important direction for future investigations should be structural and systematic determination of the number of lags in the SVR models. In this paper, the SVR models are constructed based on the expert knowledge and the trial and error adjustment of parameters. Thus, there is no guarantee that the optimal solution will be found. The second important issue for future research involves a structured method of selecting an optimal value of parameters in SVR for the best forecasting performance.