سیستم تطبیقی ​​برای مدل سازی رفتار سد بر اساس رگرسیون خطی و الگوریتم ژنتیک

Most of the existing methods for dam behavior modeling require a persistent set of input parameters. In real-world applications, failures of the measuring equipment can lead to a situation in which a selected model becomes unusable because of the volatility of the independent variables set. This paper presents an adaptive system for dam behavior modeling that is based on a multiple linear regression (MLR) model and is optimized for given conditions using genetic algorithms (GA). Throughout an evolutionary process, the system performs real-time adjustment of regressors in the MLR model according to currently active sensors. The performance of the proposed system has been evaluated in a case study of modeling the Bocac dam (at the Vrbas River located in the Republic of Srpska), whereby an MLR model of the dam displacements has been optimized for periods when the sensors were malfunctioning. Results of the analysis have shown that, under real-world circumstances, the proposed methodology outperforms traditional regression approaches.

Dams have strong interactions with environmental, hydraulic and geomechanical factors, such as air and water temperature, water level, pore pressure, and rock deformability, each of which influences the structural behavior of the dam [1]. To describe and predict the structural behavior of dams, over the past decades, a number of deterministic, statistical and hybrid mathematical models have been developed. For a long time, statistical models have been applied to dam safety monitoring to find out the contribution of external loads to dam displacements [2]. A number of statistical models based on multiple linear regression (MLR) and their advanced forms such as hierarchical regression, stepwise multiple regression, robust regression, ridge regression, and partial least squares regression have been shown to be more or less successful in dam modeling [3]. The advantages of the statistical models are the simplicity of formulation, the speed of execution and the availability of any type of correlation between independent and responses variables. In contrast, deterministic models require solving differential equations, for which closed form solutions could be difficult or impossible to obtain [4]. Therefore, many models that are based on numerical methods, such as the finite element method, have been developed as well [5]. Recently, numerical and statistical methods have been enriched with various heuristics from the artificial intelligence (AI) domain, creating hybrid models that combine their advantages. Some of these artificial intelligence techniques and heuristic algorithms are artificial neural networks (ANN) [6], genetic algorithms (GA) [7], support vector machines (SVM) [8], adaptive neuro-fuzzy inference systems (ANFIS) [9] and [10], Monte Carlo simulations [11], the modified complex method [12] and the artificial immune algorithm (AIA) [13]. Recently, Rankovic et al. [9] presented a study in which the objective was to develop an adaptive neuro-fuzzy inference system (ANFIS) to predict the radial displacements of Bocac arch dam. ANFIS models have been proposed as an alternative approach for an evaporation estimation of the Yuvacik Dam [10]. In his paper, Mata [6] presented a comparison between MLR and ANN models for the characterization of dam behavior under environmental loads for the Alto Rabagao arch dam. In their study, Wang et al. [14] investigated several Artificial Intelligence techniques for modeling monthly river flow discharge time series, which included an ANN approach, an ANFIS technique, GP models and support vector machines (SVM), and compared their performance with traditional time series modeling techniques, such as autoregressive moving-average (ARMA) models. To improve prediction, support vector regression (SVR) upgraded with GAs is often combined with existing ANN and ARMA techniques [8]. Hybrid algorithms and their applications in prediction and optimization are also presented in a number of papers. Gholizadeh and Seyedpoor [15] used a hybrid methodology with a combination of metaheuristics (GA and Particle Swarm Optimization-PSO) and neural networks to propose an efficient soft computing approach to achieve optimal shape design of arch dams that were subjected to natural frequency constraints. There are several recent studies that describe applications of AIA techniques, which imitate the function of the natural immune system. For example, Xi et al. [16] proposed an immune statistical model to resolve the data analysis problems of dam horizontal crest upstream–downstream displacements. The above-mentioned methods play a crucial role in modeling structural dam behavior. However, all of the methods require a persistent set of input parameters, i.e., all of the measurements must be available during the entire examined period. In real-world applications, failures of the measuring equipment can lead to a situation in which the selected model becomes unusable because of volatility of the independent variables. In this paper, the concept of an adaptive system for dam behavior modeling (ASDBM) that is resistant to the variations in the set of measured variables is presented. This system is based on a multiple linear regression model of a dam, the form of which is optimized for the given conditions using genetic algorithms.

In this paper, the concept of an adaptive system for dam behavior modeling (ASDBM) that is resistant to the variations in the set of measured variables is presented. Using genetic algorithms, the system optimizes the multiple linear regression model of a dam according to currently active sensors. The MLR model is optimized based on two criteria: the accuracy and the complexity. For measuring the model accuracy, the adjusted coefficient of multiple determination is used, while the total number of regressors is used as a measure of the model complexity. According to the proposed approach, several software modules have been developed. The performance of the ASDBM system was tested using the Bocac dam case study, in which the radial displacements of a point inside the dam structure as a function of the headwater, precipitation, temperature and time have been modeled. Every time that any sensor became active or inactive, the ASDBM system adjusted the MLR model according to the currently available set of input data. In the time periods in which one or more sensors were inactive, the proposed system showed a significantly better prediction than the original MLR model (which assumes that all of the sensors are always active). In addition, the system has shown the capability of rejecting variables that have no influence on the modeled dam. This capability makes the proposed system useful for monitoring activities and makes it a robust and powerful predictive management tool. The robustness with respect to instrumental error in the monitored data can be improved if the “least square method” component (Fig. 2, label 7) is simply replaced by more robust linear regression method such as robust regression or resistant regression, that are less sensitive to outliers and heteroscedasticity [21]. The main limitation of this approach lies in the fact that it does not directly consider the mechanical properties and any possible damage. Additional analysis in the form of non-destructive tests (static and dynamical), computational mechanical modeling and inverse analysis will also be required. Further research should be directed toward the improvement of the complexity criterion using the statistical significance of individual regressors. Another direction for further investigation should be the development of a novel evolutionary heuristic that would force the genetic modification of individuals according to the statistical significance of their regressors.